rfc9881.original.xml   rfc9881.xml 
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<front> <front>
<title abbrev="ML-DSA in Certificates">Internet X.509 Public Key Infrastruct <title abbrev="ML-DSA in Certificates">Internet X.509 Public Key Infrastruct
ure - Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algor ure -- Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algo
ithm (ML-DSA)</title> rithm (ML-DSA)</title>
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-dilithium-certific <seriesInfo name="RFC" value="9881"/>
ates-13"/>
<author initials="J." surname="Massimo" fullname="Jake Massimo"> <author initials="J." surname="Massimo" fullname="Jake Massimo">
<organization>AWS</organization> <organization>AWS</organization>
<address> <address>
<postal> <postal>
<country>US</country> <country>United States of America</country>
</postal> </postal>
<email>jakemas@amazon.com</email> <email>jakemas@amazon.com</email>
</address> </address>
</author> </author>
<author initials="P." surname="Kampanakis" fullname="Panos Kampanakis"> <author initials="P." surname="Kampanakis" fullname="Panos Kampanakis">
<organization>AWS</organization> <organization>AWS</organization>
<address> <address>
<postal> <postal>
<country>US</country> <country>United States of America</country>
</postal> </postal>
<email>kpanos@amazon.com</email> <email>kpanos@amazon.com</email>
</address> </address>
</author> </author>
<author initials="S." surname="Turner" fullname="Sean Turner"> <author initials="S." surname="Turner" fullname="Sean Turner">
<organization>sn3rd</organization> <organization>sn3rd</organization>
<address> <address>
<email>sean@sn3rd.com</email> <email>sean@sn3rd.com</email>
</address> </address>
</author> </author>
<author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan"> <author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan">
<organization>Cloudflare</organization> <organization>Cloudflare</organization>
<address> <address>
<email>bas@cloudflare.com</email> <email>bas@cloudflare.com</email>
</address> </address>
</author> </author>
<date year="2025" month="September" day="30"/> <date year="2025" month="October"/>
<area>SEC</area> <area>SEC</area>
<workgroup>LAMPS WG</workgroup> <workgroup>lamps</workgroup>
<keyword>ML-DSA Certificate X.509 PKIX</keyword> <keyword>ML-DSA</keyword>
<abstract> <keyword>Certificate</keyword>
<?line 147?> <keyword>X.509</keyword>
<keyword>PKIX</keyword>
<t>Digital signatures are used within X.509 certificates, Certificate <abstract>
<t>Digital signatures are used within X.509 certificates and Certificate
Revocation Lists (CRLs), and to sign messages. This document specifies Revocation Lists (CRLs), and to sign messages. This document specifies
the conventions for using FIPS 204, the Module-Lattice-Based Digital the conventions for using FIPS 204, the Module-Lattice-Based Digital
Signature Algorithm (ML-DSA) in Internet X.509 certificates and Signature Algorithm (ML-DSA) in Internet X.509 certificates and
certificate revocation lists. The conventions for the associated CRLs. The conventions for the associated
signatures, subject public keys, and private key are also described.</t> signatures, subject public keys, and private key are also described.</t>
</abstract> </abstract>
<note removeInRFC="true">
<name>About This Document</name>
<t>
The latest revision of this draft can be found at <eref target="https://
lamps-wg.github.io/dilithium-certificates/#go.draft-ietf-lamps-dilithium-certifi
cates.html"/>.
Status information for this document may be found at <eref target="https
://datatracker.ietf.org/doc/draft-ietf-lamps-dilithium-certificates/"/>.
</t>
<t>
Discussion of this document takes place on the
Limited Additional Mechanisms for PKIX and SMIME (lamps) Working Group m
ailing list (<eref target="mailto:spasm@ietf.org"/>),
which is archived at <eref target="https://mailarchive.ietf.org/arch/bro
wse/spasm/"/>.
Subscribe at <eref target="https://www.ietf.org/mailman/listinfo/spasm/"
/>.
</t>
<t>Source for this draft and an issue tracker can be found at
<eref target="https://github.com/lamps-wg/dilithium-certificates"/>.</t>
</note>
</front> </front>
<middle> <middle>
<?line 156?>
<section anchor="introduction"> <section anchor="introduction">
<name>Introduction</name> <name>Introduction</name>
<t>The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a <t>The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a
quantum-resistant digital signature scheme standardized by the US quantum-resistant digital signature scheme standardized by the US
National Institute of Standards and Technology (NIST) PQC project National Institute of Standards and Technology (NIST) PQC project
<xref target="NIST-PQC"/> in <xref target="FIPS204"/>. This document <xref target="NIST-PQC"/> in <xref target="FIPS204"/>. This document
specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX) specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX)
certificates and Certificate Revocation Lists (CRLs) at three security certificates and Certificate Revocation Lists (CRLs) at three security
levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.</t> levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.</t>
<t><xref target="FIPS204"/> defines two variants of ML-DSA: a pure and a p re-hash variant. <t><xref target="FIPS204"/> defines two variants of ML-DSA: pure and pre-h ash.
Only the former is specified in this document. Only the former is specified in this document.
See <xref target="sec-disallow-hash"/> for the rationale. See <xref target="sec-disallow-hash"/> for the rationale.
The pure variant of ML-DSA supports the typical pre-hash flow. Refer to The pure variant of ML-DSA supports the typical pre-hash flow. Refer to
<xref target="externalmu"/> for more details.</t> <xref target="externalmu"/> for more details.</t>
<t>Prior to standardisation, ML-DSA was known as Dilithium. ML-DSA and <t>Prior to standardization, ML-DSA was known as Dilithium. ML-DSA and
Dilithium are not compatible.</t> Dilithium are not compatible.</t>
<section anchor="requirements-language"> <section anchor="requirements-language">
<name>Requirements Language</name> <name>Requirements Language</name>
<t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp <t>
14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECO "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>
MMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", ",
"<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be i "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
nterpreted as "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
only when, they be
appear in all capitals, as shown here.</t> interpreted as described in BCP&nbsp;14 <xref target="RFC2119"/> <xref
<?line -18?> target="RFC8174"/> when, and only when, they appear in all capitals, as
shown here.
</section> </t>
</section>
</section> </section>
<section anchor="oids"> <section anchor="oids">
<name>Identifiers</name> <name>Identifiers</name>
<t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t> <t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
SEQUENCE { SEQUENCE {
algorithm ALGORITHM-TYPE.id({AlgorithmSet}), algorithm ALGORITHM-TYPE.id({AlgorithmSet}),
parameters ALGORITHM-TYPE. parameters ALGORITHM-TYPE.
Params({AlgorithmSet}{@algorithm}) OPTIONAL &Params({AlgorithmSet}{@algorithm}) OPTIONAL
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with
the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for th e 1988 ASN.1 the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for th e 1988 ASN.1
syntax.</t> syntax.</t>
</aside> </aside>
<t>The fields in AlgorithmIdentifier have the following meanings:</t> <t>The fields in AlgorithmIdentifier have the following meanings:</t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> identifies the cryptographic algorithm with an o bject <t><tt>algorithm</tt> identifies the cryptographic algorithm with an o bject
identifier (OID).</t> identifier (OID).</t>
</li> </li>
<li> <li>
<t><tt>parameters</tt>, which are optional, are the associated paramet ers for the <t><tt>parameters</tt>, which are optional, are the associated paramet ers for the
algorithm identifier in the algorithm field.</t> algorithm identifier in the algorithm field.</t>
</li> </li>
</ul> </ul>
<t>The NIST registered OIDs <xref target="CSOR"/> are:</t> <t>The NIST-registered OIDs <xref target="CSOR"/> are:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) }
id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) }
id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) }]]></sourcecode>
]]></artwork>
<t>The contents of the <tt>parameters</tt> component for each <tt>algorith m</tt> <bcp14>MUST</bcp14> be <t>The contents of the <tt>parameters</tt> component for each <tt>algorith m</tt> <bcp14>MUST</bcp14> be
absent.</t> absent.</t>
</section> </section>
<section anchor="ml-dsa-signatures-in-pkix"> <section anchor="ml-dsa-signatures-in-pkix">
<name>ML-DSA Signatures in PKIX</name> <name>ML-DSA Signatures in PKIX</name>
<t>ML-DSA is a digital signature scheme built upon the <t>ML-DSA is a digital signature scheme built upon the
Fiat-Shamir-with-aborts framework <xref target="Fiat-Shamir"/>. The security is based Fiat-Shamir-with-aborts framework <xref target="Fiat-Shamir"/>. The security is based
upon the hardness of lattice problems over module lattices <xref target="Dilithi um"/>. upon the hardness of lattice problems over module lattices <xref target="Dilithi um"/>.
ML-DSA provides three parameter sets for the NIST PQC security categories ML-DSA provides three parameter sets for the NIST PQC security categories
2, 3 and 5.</t> 2, 3, and 5.</t>
<t>Signatures are used in a number of different ASN.1 structures. As shown <t>Signatures are used in a number of different ASN.1 structures. As shown
in the ASN.1 representation from <xref target="RFC5280"/> below, in an X.509 in the ASN.1 equivalent to that in <xref target="RFC5280"/> below, in an X.509
certificate, a signature is encoded with an algorithm identifier in the certificate, a signature is encoded with an algorithm identifier in the
<tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute th at contains <tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute th at contains
the actual signature.</t> the actual signature.</t>
<artwork><![CDATA[
<sourcecode type="asn.1"><![CDATA[
Certificate ::= SIGNED{ TBSCertificate } Certificate ::= SIGNED{ TBSCertificate }
SIGNED{ToBeSigned} ::= SEQUENCE { SIGNED{ToBeSigned} ::= SEQUENCE {
toBeSigned ToBeSigned, toBeSigned ToBeSigned,
algorithmIdentifier SEQUENCE { algorithmIdentifier SEQUENCE {
algorithm SIGNATURE-ALGORITHM. algorithm SIGNATURE-ALGORITHM.
&id({SignatureAlgorithms}), &id({SignatureAlgorithms}),
parameters SIGNATURE-ALGORITHM. parameters SIGNATURE-ALGORITHM.
&Params({SignatureAlgorithms} &Params({SignatureAlgorithms}
{@algorithmIdentifier.algorithm}) {@algorithmIdentifier.algorithm})
OPTIONAL OPTIONAL
}, },
signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value( signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value(
{SignatureAlgorithms} {SignatureAlgorithms}
{@algorithmIdentifier.algorithm})) {@algorithmIdentifier.algorithm}))
} }]]></sourcecode>
]]></artwork>
<t>Signatures are also used in the CRL list ASN.1 representation from <t>Signatures are also used in the CRL list ASN.1 representation from
<xref target="RFC5280"/> below. In a X.509 CRL, a signature is encoded with an <xref target="RFC5280"/> below. In an X.509 CRL, a signature is encoded with an
algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a
<tt>signatureValue</tt> attribute that contains the actual signature.</t> <tt>signatureValue</tt> attribute that contains the actual signature.</t>
<artwork><![CDATA[
CertificateList ::= SIGNED{ TBSCertList } <sourcecode type="asn.1"><![CDATA[
]]></artwork> CertificateList ::= SIGNED{ TBSCertList }]]></sourcecode>
<t>The following <tt>SIGNATURE-ALGORITHM</tt> ASN.1 classes are for ML-DSA -44, <t>The following <tt>SIGNATURE-ALGORITHM</tt> ASN.1 classes are for ML-DSA -44,
ML-DSA-65, and ML-DSA-87:</t> ML-DSA-65, and ML-DSA-87:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-44 IDENTIFIER id-ml-dsa-44
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-44 } PUBLIC-KEYS { pk-ml-dsa-44 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 }
} }
sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-65 IDENTIFIER id-ml-dsa-65
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-65 } PUBLIC-KEYS { pk-ml-dsa-65 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 }
} }
sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-87 IDENTIFIER id-ml-dsa-87
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-87 } PUBLIC-KEYS { pk-ml-dsa-87 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 }
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The identifiers defined in <xref target="oids"/> can be used as the <t>The identifiers defined in <xref target="oids"/> can be used as the
<tt>AlgorithmIdentifier</tt> in the <tt>signatureAlgorithm</tt> field in the seq uence <tt>AlgorithmIdentifier</tt> in the <tt>signatureAlgorithm</tt> field in the seq uence
<tt>Certificate</tt>/<tt>CertificateList</tt> and the <tt>signature</tt> field i n the sequence <tt>Certificate</tt>/<tt>CertificateList</tt> and in the <tt>signature</tt> fiel d in the sequence
<tt>TBSCertificate</tt>/<tt>TBSCertList</tt> in certificates and CRLs, respectiv ely, <tt>TBSCertificate</tt>/<tt>TBSCertList</tt> in certificates and CRLs, respectiv ely,
<xref target="RFC5280"/>. The <tt>parameters</tt> of these signature algorithms <bcp14>MUST</bcp14> be <xref target="RFC5280"/>. The <tt>parameters</tt> of these signature algorithms <bcp14>MUST</bcp14> be
absent, as explained in <xref target="oids"/>. That is, the <tt>AlgorithmIdentif ier</tt> absent, as explained in <xref target="oids"/>. That is, the <tt>AlgorithmIdentif ier</tt>
<bcp14>SHALL</bcp14> be a <tt>SEQUENCE</tt> of one component, the OID id -ml-dsa-*, where * <bcp14>SHALL</bcp14> be a <tt>SEQUENCE</tt> of one component, the OID id -ml-dsa-*, where *
is 44, 65, or 87 - see <xref target="oids"/>.</t> is 44, 65, or 87 -- see <xref target="oids"/>.</t>
<t>The <tt>signatureValue</tt> field contains the corresponding ML-DSA sig nature <t>The <tt>signatureValue</tt> field contains the corresponding ML-DSA sig nature
computed upon the ASN.1 DER encoded <tt>tbsCertificate</tt>/<tt>tbsCertList</tt> computed upon the ASN.1 DER-encoded <tt>tbsCertificate</tt>/<tt>tbsCertList</tt>
<xref target="RFC5280"/>. The optional context string (ctx) parameter <xref target="RFC5280"/>. The optional context string (ctx) parameter
as defined in Section 5.2 of <xref target="FIPS204"/> is left to its default val ue: as defined in Section 5.2 of <xref target="FIPS204"/> is left to its default val ue:
the empty string.</t> the empty string.</t>
<t>Conforming Certification Authority (CA) implementations <bcp14>MUST</bc p14> specify <t>Conforming Certification Authority (CA) implementations <bcp14>MUST</bc p14> specify
the algorithms explicitly by using the OIDs specified in <xref target="oids"/> w hen the algorithms explicitly by using the OIDs specified in <xref target="oids"/> w hen
encoding ML-DSA signatures in certificates and CRLs. Conforming client encoding ML-DSA signatures in certificates and CRLs. Conforming client
implementations that process certificates and CRLs using ML-DSA <bcp14>MUST</bcp 14> implementations that process certificates and CRLs using ML-DSA <bcp14>MUST</bcp 14>
recognize the corresponding OIDs. Encoding rules for ML-DSA signature recognize the corresponding OIDs. Encoding rules for ML-DSA signature
values are specified in <xref target="oids"/>.</t> values are specified in <xref target="oids"/>.</t>
</section> </section>
<section anchor="ML-DSA-PublicKey"> <section anchor="ML-DSA-PublicKey">
<name>ML-DSA Public Keys in PKIX</name> <name>ML-DSA Public Keys in PKIX</name>
<t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he <t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he
<tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t> <tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE { SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}}, algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
subjectPublicKey BIT STRING subjectPublicKey BIT STRING
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t> <t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> is the algorithm identifier and parameters for t he <t><tt>algorithm</tt> is the algorithm identifier and parameters for t he
public key (see above).</t> public key (see above).</t>
</li> </li>
skipping to change at line 266 skipping to change at line 256
</li> </li>
</ul> </ul>
<t>Algorithm 22 in Section 7.2 of <xref target="FIPS204"/> defines the raw byte string <t>Algorithm 22 in Section 7.2 of <xref target="FIPS204"/> defines the raw byte string
encoding of an ML-DSA public key. When used in a <tt>SubjectPublicKeyInfo</tt> t ype, encoding of an ML-DSA public key. When used in a <tt>SubjectPublicKeyInfo</tt> t ype,
the <tt>subjectPublicKey BIT STRING</tt> contains this raw byte string encoding of the the <tt>subjectPublicKey BIT STRING</tt> contains this raw byte string encoding of the
public key. When an ML-DSA public key appears outside of a <tt>SubjectPublicKeyI nfo</tt> type in an public key. When an ML-DSA public key appears outside of a <tt>SubjectPublicKeyI nfo</tt> type in an
environment that uses ASN.1 encoding, it could be encoded as an <tt>OCTET STRING </tt> by environment that uses ASN.1 encoding, it could be encoded as an <tt>OCTET STRING </tt> by
using the <tt>ML-DSA-44-PublicKey</tt>, <tt>ML-DSA-65-PublicKey</tt>, and <tt>ML -DSA-87-PublicKey</tt> types using the <tt>ML-DSA-44-PublicKey</tt>, <tt>ML-DSA-65-PublicKey</tt>, and <tt>ML -DSA-87-PublicKey</tt> types
corresponding to the correct key size defined below.</t> corresponding to the correct key size defined below.</t>
<t>The <tt>PUBLIC-KEY</tt> ASN.1 types for ML-DSA are defined here:</t> <t>The <tt>PUBLIC-KEY</tt> ASN.1 types for ML-DSA are defined here:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
pk-ml-dsa-44 PUBLIC-KEY ::= { pk-ml-dsa-44 PUBLIC-KEY ::= {
IDENTIFIER id-ml-dsa-44 IDENTIFIER id-ml-dsa-44
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
CERT-KEY-USAGE CERT-KEY-USAGE
{ digitalSignature, nonRepudiation, keyCertSign, cRLSign } { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
PRIVATE-KEY ML-DSA-44-PrivateKey } -- defined in Section 6 PRIVATE-KEY ML-DSA-44-PrivateKey } -- defined in Section 6
pk-ml-dsa-65 PUBLIC-KEY ::= { pk-ml-dsa-65 PUBLIC-KEY ::= {
IDENTIFIER id-ml-dsa-65 IDENTIFIER id-ml-dsa-65
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
skipping to change at line 292 skipping to change at line 282
IDENTIFIER id-ml-dsa-87 IDENTIFIER id-ml-dsa-87
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
CERT-KEY-USAGE CERT-KEY-USAGE
{ digitalSignature, nonRepudiation, keyCertSign, cRLSign } { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
PRIVATE-KEY ML-DSA-87-PrivateKey } -- defined in Section 6 PRIVATE-KEY ML-DSA-87-PrivateKey } -- defined in Section 6
ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312)) ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312))
ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952)) ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952))
ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2592)) ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2592))]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t><xref target="RFC5958"/> specifies the Asymmetric Key Package's <tt>One AsymmetricKey</tt> type for <t><xref target="RFC5958"/> specifies the Asymmetric Key Package's <tt>One AsymmetricKey</tt> type for
encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded a s encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded a s
a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-ke y"/>.</t> a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-ke y"/>.</t>
<t>When the ML-DSA private key appears outside of an Asymmetric Key Packag e in an <t>When the ML-DSA private key appears outside of an Asymmetric Key Packag e in an
environment that uses ASN.1 encoding, it can be encoded using one of the environment that uses ASN.1 encoding, it can be encoded using one of the
the <tt>ML-DSA-PrivateKey CHOICE</tt> formats defined in <xref target="priv-key" />. The <tt>seed</tt> format <tt>ML-DSA-PrivateKey CHOICE</tt> formats defined in <xref target="priv-key"/>. The <tt>seed</tt> format
is <bcp14>RECOMMENDED</bcp14> as it efficiently stores both the private and publ ic key.</t> is <bcp14>RECOMMENDED</bcp14> as it efficiently stores both the private and publ ic key.</t>
<t><xref target="examples"/> contains example ML-DSA public keys encoded u sing the <t><xref target="examples"/> contains example ML-DSA public keys encoded u sing the
textual encoding defined in <xref target="RFC7468"/>.</t> textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="key-usage-bits"> <section anchor="key-usage-bits">
<name>Key Usage Bits</name> <name>Key Usage Bits</name>
<t>The intended application for the key is indicated in the <tt>keyUsage</ tt> <t>The intended application for the key is indicated in the <tt>keyUsage</ tt>
certificate extension; see <xref section="4.2.1.3" sectionFormat="of" target="RF C5280"/>. If the certificate extension; see <xref section="4.2.1.3" sectionFormat="of" target="RF C5280"/>. If the
<tt>keyUsage</tt> extension is present in a certificate that includes <tt>id-ml- dsa-*</tt> <tt>keyUsage</tt> extension is present in a certificate that includes <tt>id-ml- dsa-*</tt>
(where * is 44, 65, or 87 - see <xref target="oids"/>) in the <tt>SubjectPublicK eyInfo</tt>, (where * is 44, 65, or 87 -- see <xref target="oids"/>) in the <tt>SubjectPublic KeyInfo</tt>,
then the subject public key can only be used then the subject public key can only be used
for verifying digital signatures on certificates or CRLs, or those used in an for verifying digital signatures on certificates or CRLs, or those used in an
entity authentication service, a data origin authentication service, an entity authentication service, a data origin authentication service, an
integrity service, and/or a non-repudiation service that protects against integrity service, and/or a non-repudiation service that protects against
the signing entity falsely denying some action. This means that the the signing entity falsely denying some action. This means that the
<tt>keyUsage</tt> extention <bcp14>MUST</bcp14> have at least one of the followi <tt>keyUsage</tt> extension <bcp14>MUST</bcp14> have at least one of the followi
ng bits set:</t> ng bits set:</t>
<artwork><![CDATA[
digitalSignature <ul spacing="normal">
nonRepudiation <li>digitalSignature</li>
keyCertSign <li>nonRepudiation</li>
cRLSign <li>keyCertSign</li>
]]></artwork> <li>cRLSign</li>
</ul>
<t>ML-DSA subject public keys cannot be used to establish keys or encrypt data, so the <t>ML-DSA subject public keys cannot be used to establish keys or encrypt data, so the
<tt>keyUsage</tt> extention <bcp14>MUST NOT</bcp14> have any of following bits s <tt>keyUsage</tt> extension <bcp14>MUST NOT</bcp14> have any of the following bi
et:</t> ts set:</t>
<artwork><![CDATA[
keyEncipherment, <ul spacing="normal">
dataEncipherment, <li>keyEncipherment</li>
keyAgreement, <li>dataEncipherment</li>
encipherOnly, and <li>keyAgreement</li>
decipherOnly. <li>encipherOnly</li>
]]></artwork> <li>decipherOnly</li>
</ul>
<t>Requirements about the <tt>keyUsage</tt> extension bits defined in <xre f target="RFC5280"/> <t>Requirements about the <tt>keyUsage</tt> extension bits defined in <xre f target="RFC5280"/>
still apply.</t> still apply.</t>
</section> </section>
<section anchor="priv-key"> <section anchor="priv-key">
<name>Private Key Format</name> <name>Private Key Format</name>
<t><xref target="FIPS204"/> specifies two formats for an ML-DSA private ke y: a 32-octet <t><xref target="FIPS204"/> specifies two formats for an ML-DSA private ke y: a 32-octet
seed (xi) and an (expanded) private key. The expanded private key (and public ke y) seed (xi) and an (expanded) private key. The expanded private key (and public ke y)
is computed from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt> (algorithm 6 ).</t> is computed from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt> (algorithm 6 ).</t>
<t>"Asymmetric Key Packages" <xref target="RFC5958"/> specifies how to enc ode a private <t>"Asymmetric Key Packages" <xref target="RFC5958"/> specifies how to enc ode a private
key in a structure that both identifies what algorithm the private key key in a structure that both identifies what algorithm the private key
is for and allows for the public key and additional attributes about the is for and allows for the public key and additional attributes about the
key to be included as well. For illustration, the ASN.1 structure key to be included as well. For illustration, the ASN.1 structure
<tt>OneAsymmetricKey</tt> is replicated below.</t> <tt>OneAsymmetricKey</tt> is replicated below.</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
OneAsymmetricKey ::= SEQUENCE { OneAsymmetricKey ::= SEQUENCE {
version Version, version Version,
privateKeyAlgorithm SEQUENCE { privateKeyAlgorithm SEQUENCE {
algorithm PUBLIC-KEY.&id({PublicKeySet}), algorithm PUBLIC-KEY.&id({PublicKeySet}),
parameters PUBLIC-KEY.&Params({PublicKeySet} parameters PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm}) {@privateKeyAlgorithm.algorithm})
OPTIONAL} OPTIONAL}
privateKey OCTET STRING (CONTAINING privateKey OCTET STRING (CONTAINING
PUBLIC-KEY.&PrivateKey({PublicKeySet} PUBLIC-KEY.&PrivateKey({PublicKeySet}
{@privateKeyAlgorithm.algorithm})), {@privateKeyAlgorithm.algorithm})),
attributes [0] Attributes OPTIONAL, attributes [0] Attributes OPTIONAL,
..., ...,
[[2: publicKey [1] BIT STRING (CONTAINING [[2: publicKey [1] BIT STRING (CONTAINING
PUBLIC-KEY.&Params({PublicKeySet} PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm}) {@privateKeyAlgorithm.algorithm})
OPTIONAL ]], OPTIONAL ]],
... ...
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5958"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5958"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>.</t> 2021 ASN.1 syntax <xref target="X680"/>.</t>
</aside> </aside>
<t>For ML-DSA private keys, the <tt>privateKey</tt> field in <tt>OneAsymme tricKey</tt> contains one of <t>For ML-DSA private keys, the <tt>privateKey</tt> field in <tt>OneAsymme tricKey</tt> contains one of
the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> format i s a the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> format i s a
fixed 32 byte <tt>OCTET STRING</tt> (34 bytes total with the <tt>0x8020</tt> tag and fixed 32-byte <tt>OCTET STRING</tt> (34 bytes total with the <tt>0x8020</tt> tag and
length) for all security levels, while the <tt>expandedKey</tt> and <tt>both</tt > formats length) for all security levels, while the <tt>expandedKey</tt> and <tt>both</tt > formats
vary in size by security level:</t> vary in size by security level:</t>
<artwork><![CDATA[
<sourcecode type="asn.1"><![CDATA[
ML-DSA-44-PrivateKey ::= CHOICE { ML-DSA-44-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (32)), seed [0] OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (2560)), expandedKey OCTET STRING (SIZE (2560)),
both SEQUENCE { both SEQUENCE {
seed OCTET STRING (SIZE (32)), seed OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (2560)) expandedKey OCTET STRING (SIZE (2560))
} }
} }
ML-DSA-65-PrivateKey ::= CHOICE { ML-DSA-65-PrivateKey ::= CHOICE {
skipping to change at line 404 skipping to change at line 395
} }
} }
ML-DSA-87-PrivateKey ::= CHOICE { ML-DSA-87-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (32)), seed [0] OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (4896)), expandedKey OCTET STRING (SIZE (4896)),
both SEQUENCE { both SEQUENCE {
seed OCTET STRING (SIZE (32)), seed OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (4896)) expandedKey OCTET STRING (SIZE (4896))
} }
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The <tt>CHOICE</tt> allows three representations of the private key:</t > <t>The <tt>CHOICE</tt> allows three representations of the private key:</t >
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1"><li>
<t>The <tt>seed</tt> format (tag <tt>[0]</tt>) contains just the 32-by te seed value (xi) <t>The <tt>seed</tt> format (tag <tt>[0]</tt>) contains just the 32-by te seed value (xi)
from which both the expanded private key and public key can be derived from which both the expanded private key and public key can be derived
using <tt>ML-DSA.KeyGen_internal(xi)</tt>.</t> using <tt>ML-DSA.KeyGen_internal(xi)</tt>.</t>
</li> </li>
<li> <li>
<t>The <tt>expandedKey</tt> format contains the expanded private key t hat was <t>The <tt>expandedKey</tt> format contains the expanded private key t hat was
derived from the seed.</t> derived from the seed.</t>
</li> </li>
<li> <li>
<t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing for <t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing for
for interoperability; some may want to use and retain the seed and interoperability; some may want to use and retain the seed and
others may only support expanded private keys.</t> others may only support expanded private keys.</t>
</li> </li>
</ol> </ol>
<t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> obje ct, any of <t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> obje ct, any of
these three formats may be used, though the seed format is <bcp14>RECOMMENDED</b cp14> these three formats may be used, though the seed format is <bcp14>RECOMMENDED</b cp14>
for storage efficiency.</t> for storage efficiency.</t>
<t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure with <t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure with
the appropriate OID as defined in <xref target="oids"/>. If present, the <tt>pub licKey</tt> the appropriate OID as defined in <xref target="oids"/>. If present, the <tt>pub licKey</tt>
field will hold the encoded public key as defined in <xref target="ML-DSA-Public Key"/>.</t> field will hold the encoded public key as defined in <xref target="ML-DSA-Public Key"/>.</t>
<aside>
<t>NOTE: While the private key can be stored in multiple formats, the seed -only <t>NOTE: While the private key can be stored in multiple formats, the seed -only
format is <bcp14>RECOMMENDED</bcp14> as it is the most compact representation. B oth the format is <bcp14>RECOMMENDED</bcp14> as it is the most compact representation. B oth the
expanded private key and the public key can be deterministically derived expanded private key and the public key can be deterministically derived
from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt>. Alternatively, the publ ic from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt>. Alternatively, the publ ic
key can be generated from the private key. While the <tt>publicKey</tt> field key can be generated from the private key. While the <tt>publicKey</tt> field
and <tt>expandedKey</tt> format are technically redundant when using the seed-on ly and <tt>expandedKey</tt> format are technically redundant when using the seed-on ly
format, they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during format, they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during
import operations.</t> import operations.</t>
</aside>
<t>When parsing the private key, the ASN.1 tag explicitly indicates which <t>When parsing the private key, the ASN.1 tag explicitly indicates which
variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt> variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt>
(raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and (raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and
<tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any <tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any
other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t> other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t>
<t><xref target="examples"/> contains example ML-DSA private keys encoded using the <t><xref target="examples"/> contains example ML-DSA private keys encoded using the
textual encoding defined in <xref target="RFC7468"/>.</t> textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="iana-considerations"> <section anchor="iana-considerations">
<name>IANA Considerations</name> <name>IANA Considerations</name>
<t>For the ASN.1 module in <xref target="asn1"/>, IANA is requested to ass <t>For the ASN.1 module in <xref target="asn1"/>, IANA has assigned the fo
ign an object llowing object identifier (OID) in the "SMI Security for PKIX Module Identifier"
identifier (OID) for the module identifier (TBD1) with a Description registry (1.3.6.1.5.5.7.0): </t>
of "id-mod-x509-ml-dsa-2025". The OID for the module should be
allocated in the "SMI Security for PKIX Module Identifier" registry <table anchor="oid">
(1.3.6.1.5.5.7.0).</t> <name></name>
<thead>
<tr>
<th>Decimal</th>
<th>Description</th>
<th>Reference</th>
</tr>
</thead>
<tbody>
<tr>
<td>119</td>
<td>id-mod-x509-ml-dsa-2025</td>
<td>RFC 9881</td>
</tr>
</tbody>
</table>
</section> </section>
<section anchor="operational-considerations"> <section anchor="operational-considerations">
<name>Operational Considerations</name> <name>Operational Considerations</name>
<section anchor="private-key-format"> <section anchor="private-key-format">
<name>Private Key Format</name> <name>Private Key Format</name>
<t>An <tt>ML-DSA.KeyGen seed (xi)</tt> represents the <bcp14>RECOMMENDED </bcp14> format for storing <t>An <tt>ML-DSA.KeyGen seed (xi)</tt> represents the <bcp14>RECOMMENDED </bcp14> format for storing
and transmitting ML-DSA private keys. This format is explicitly permitted and transmitting ML-DSA private keys. This format is explicitly permitted
by <xref target="FIPS204"/> as an acceptable representation of a keypair. In par ticular, by <xref target="FIPS204"/> as an acceptable representation of a keypair. In par ticular,
generating the seed in one cryptographic module and then importing or generating the seed in one cryptographic module and then importing or
exporting it into another cryptographic module is allowed. The internal exporting it into another cryptographic module is allowed. The internal
key generation function <tt>ML-DSA.KeyGen_internal(xi)</tt> can be accessed for key-generation function <tt>ML-DSA.KeyGen_internal(xi)</tt> can be accessed for
this purpose.</t> this purpose.</t>
<t>Note also that unlike other private key compression methods in other algorithms, <t>Note also that unlike other private key compression methods in other algorithms,
expanding a private key from a seed is a one-way function, meaning that once a expanding a private key from a seed is a one-way function, meaning that once a
full key is expanded from seed and the seed discarded, the seed cannot be full key is expanded from seed and the seed discarded, the seed cannot be
re-created even if the full expanded private key is available. For this reason recreated, even if the full expanded private key is available. For this reason,
it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the seed , it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the seed ,
even when also exporting the expanded private key. ML-DSA seed extraction can be even when also exporting the expanded private key. ML-DSA seed extraction can be
implemented by including the seed xi randomly generated at line 1 of Algorithm 1 implemented by including the seed xi that is randomly generated at line 1 of Alg orithm 1
<tt>ML-DSA.KeyGen</tt> in the returned output.</t> <tt>ML-DSA.KeyGen</tt> in the returned output.</t>
<t>When encoding an ML-DSA private key in a OneAsymmetricKey object, any <t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> ob ject, any
of these three formats may be used, though the seed format is of these three formats may be used, though the seed format is
<bcp14>RECOMMENDED</bcp14> for storage efficiency.</t> <bcp14>RECOMMENDED</bcp14> for storage efficiency.</t>
</section> </section>
<section anchor="private-key-consistency-testing"> <section anchor="private-key-consistency-testing">
<name>Private Key Consistency Testing</name> <name>Private Key Consistency Testing</name>
<t>When receiving a private key that contains both the seed and the <t>When receiving a private key that contains both the seed and the
expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency chec k to expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency chec k to
ensure that the sender properly generated the private key. Recipients ensure that the sender properly generated the private key. Recipients
that do not perform this seed consistency check avoid keygen that do not perform this seed consistency check avoid keygen
and compare operations, but are unable to ensure that the <tt>seed</tt> and and compare operations, but are unable to ensure that the <tt>seed</tt> and
<tt>expandedKey</tt> match.</t> <tt>expandedKey</tt> match.</t>
<t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</t t> are not consistent, <t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</t t> are not consistent,
the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t> the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t>
<t>The seed consistency check consists of regenerating the expanded form from <t>The seed consistency check consists of regenerating the expanded form from
the seed via <tt>ML-DSA.KeyGen_internal</tt> and ensuring it is bytewise equal t o the seed via <tt>ML-DSA.KeyGen_internal</tt>, and ensuring it is bytewise equal to
the value presented in the private key.</t> the value presented in the private key.</t>
<t><xref target="example-bad"/> includes some examples of inconsistent s eeds and expanded private <t><xref target="example-bad"/> includes some examples of inconsistent s eeds and expanded private
keys.</t> keys.</t>
</section> </section>
<section anchor="sec-disallow-hash"> <section anchor="sec-disallow-hash">
<name>Rationale for disallowing HashML-DSA</name> <name>Rationale for Disallowing HashML-DSA</name>
<t>The HashML-DSA mode defined in Section 5.4 of <xref target="FIPS204"/ > <bcp14>MUST NOT</bcp14> be <t>The HashML-DSA mode defined in Section 5.4 of <xref target="FIPS204"/ > <bcp14>MUST NOT</bcp14> be
used; in other words, public keys identified by used; in other words, public keys identified by
<tt>id-hash-ml-dsa-44-with-sha512</tt>, <tt>id-hash-ml-dsa-65-with-sha512</tt>, and <tt>id-hash-ml-dsa-44-with-sha512</tt>, <tt>id-hash-ml-dsa-65-with-sha512</tt>, and
<tt>id-hash-ml-dsa-87-with-sha512</tt> <bcp14>MUST NOT</bcp14> be in X.509 certi ficates used for <tt>id-hash-ml-dsa-87-with-sha512</tt> <bcp14>MUST NOT</bcp14> be in X.509 certi ficates used for
CRLs, OCSP, certificate issuance and related PKIX protocols. This restriction CRLs, OCSP, certificate issuance, and related PKIX protocols. This restriction
is primarily to increase interoperability.</t> is primarily to increase interoperability.</t>
<t>ML-DSA and HashML-DSA are incompatible algorithms that require <t>ML-DSA and HashML-DSA are incompatible algorithms that require
different <tt>Verify()</tt> routines. This introduces the complexity of different <tt>Verify()</tt> routines. This introduces the complexity of
informing the verifier whether to use <tt>ML-DSA.Verify()</tt> or informing the verifier whether to use <tt>ML-DSA.Verify()</tt> or
<tt>HashML-DSA.Verify()</tt>. Additionally, since <tt>HashML-DSA.Verify()</tt>. Additionally, since
the same OIDs are used to identify the ML-DSA the same OIDs are used to identify the ML-DSA
public keys and ML-DSA signature algorithms, an implementation would public keys and ML-DSA signature algorithms, an implementation would
need to commit a given public key to be either of type <tt>ML-DSA</tt> or need to commit a given public key to be either of type <tt>ML-DSA</tt> or
<tt>HashML-DSA</tt> at the time of certificate creation. This is anticipated <tt>HashML-DSA</tt> at the time of certificate creation. This is anticipated
to cause operational issues in contexts where the operator does not to cause operational issues in contexts where the operator does not
know whether the key will need to produce pure or pre-hashed signatures know whether the key will need to produce pure or pre-hashed signatures
at key generation time. The External μ (mu) mode described in <xref target="exte rnalmu"/> at key-generation time. The External <u>μ</u> mode described in <xref target="ex ternalmu"/>
avoids all of these operational concerns.</t> avoids all of these operational concerns.</t>
<t>A minor security reason for disallowing HashML-DSA is that the design of the <t>A minor security reason for disallowing HashML-DSA is that the design of the
ML-DSA algorithm provides enhanced resistance against collision attacks, ML-DSA algorithm provides enhanced resistance against collision attacks,
compared with HashML-DSA or conventional RSA or ECDSA signature algorithms. compared with HashML-DSA or conventional RSA or ECDSA signature algorithms.
Specifically, ML-DSA prepends the SHAKE256 hash of the public key (<tt>tr</tt>) Specifically, ML-DSA prepends the SHAKE256 hash of the public key (<tt>tr</tt>)
to the message to-be-signed prior to hashing, as described in to the message to-be-signed prior to hashing, as described in
line 6 of Algorithm 7 of <xref target="FIPS204"/>. This means that in the unlike ly line 6 of Algorithm 7 of <xref target="FIPS204"/>. This means that in the unlike ly
discovery of a collision attack against the SHA-3 family, an attacker discovery of a collision attack against the SHA-3 family, an attacker
would have to perform a public-key-specific collision search in order would have to perform a public-key-specific collision search in order
to find message pairs such that <tt>H(tr || m1) = H(tr || m2)</tt> since a to find message pairs such that <tt>H(tr || m1) = H(tr || m2)</tt>, because a
direct hash collision <tt>H(m1) = H(m2)</tt> will not suffice. direct hash collision <tt>H(m1) = H(m2)</tt> will not suffice.
HashML-DSA removes this enhanced security property. HashML-DSA removes this enhanced security property.
In spite of its lack of targeted collision protection, the practical In spite of its lack of targeted collision protection, the practical
security risk of using HashML-DSA in X.509 signatures would be security risk of using HashML-DSA in X.509 signatures would be
immaterial. That is because a hash of the issuing CA's public key immaterial. This is because a hash of the issuing CA's public key
is already included in the Authority Key Identifier (AKI) extension which is already included in the Authority Key Identifier (AKI) extension, which
is signed as part of the tbsCertificate structure. is signed as part of the tbsCertificate structure.
Even when it is a SHA-1 hash, general second pre-images against Even when it is a SHA-1 hash, general second pre-images against
the AKI hash of existing issuing CAs would be impractical.</t> the AKI hash of existing issuing CAs would be impractical.</t>
</section> </section>
</section> </section>
<section anchor="security-considerations"> <section anchor="security-considerations">
<name>Security Considerations</name> <name>Security Considerations</name>
<t>The Security Considerations section of <xref target="RFC5280"/> applies to this <t>The Security Considerations section of <xref target="RFC5280"/> applies to this
specification as well.</t> specification as well.</t>
<t>The ML-DSA signature scheme is strongly unforgeable under chosen messag e <t>The ML-DSA signature scheme is strongly unforgeable under chosen messag e
attacks (SUF-CMA). For the purpose of estimating security strength, it has attacks (SUF-CMA). For the purpose of estimating security strength, it has
been assumed that the attacker has access to signatures for no more been assumed that the attacker has access to signatures for no more
than 2^{64} chosen messages.</t> than 2^{64} chosen messages.</t>
<t>ML-DSA depends on high quality random numbers that are suitable for <t>ML-DSA depends on high quality random numbers that are suitable for
use in cryptography. The use of inadequate pseudo-random number use in cryptography. The use of inadequate pseudo-random number
generators (PRNGs) to generate such values can significantly undermine generators (PRNGs) to generate such values can significantly undermine
various security properties. For instance, using an inadequate PRNG various security properties. For instance, using an inadequate PRNG
for key generation, might allow an attacker to efficiently recover for key generation might allow an attacker to efficiently recover
the private key by trying a small set of possibilities, rather than the private key by trying a small set of possibilities, rather than
brute force search the whole keyspace. The generation of random brute-force searching the whole keyspace. The generation of random
numbers of a sufficient level of quality for use in cryptography numbers of a sufficient level of quality for use in cryptography
is difficult; see Section 3.6.1 of <xref target="FIPS204"/> for some additional is difficult; see Section 3.6.1 of <xref target="FIPS204"/> for some additional
information.</t> information.</t>
<t>In the design of ML-DSA, care has been taken to make side-channel <t>In the design of ML-DSA, care has been taken to make side-channel
resilience easier to achieve. For instance, ML-DSA does not depend resilience easier to achieve. For instance, ML-DSA does not depend
on Gaussian sampling. Implementations must still take great care on Gaussian sampling. Implementations must still take great care
not to leak information via various side channels. While deliberate not to leak information via various side channels. While deliberate
design decisions such as these can help to deliver a greater ease design decisions such as these can help to deliver a
of secure implementation - particularly against side-channel secure implementation with greater ease -- particularly against side-channel
attacks - it does not necessarily provide resistance to more attacks -- it does not necessarily provide resistance to more
powerful attacks such as differential power analysis. Some amount powerful attacks such as differential power analysis. Some amount
of side-channel leakage has been demonstrated in parts of the of side-channel leakage has been demonstrated in parts of the
signing algorithm (specifically the bit-unpacking function), from signing algorithm (specifically the bit-unpacking function), from
which a demonstration of key recovery has been made over a large which a demonstration of key recovery has been made over a large
sample of signatures. Masking countermeasures exist for sample of signatures. Masking countermeasures exist for
ML-DSA, but come with a performance overhead.</t> ML-DSA, but comes with performance overhead.</t>
<t>ML-DSA offers both deterministic and randomized signing. Signatures <t>ML-DSA offers both deterministic and randomized signing. Signatures
generated with either mode are compatible and a verifyer can't tell generated with either mode are compatible and a verifier can't tell
them apart. In the deterministic case, a signature only depends them apart. In the deterministic case, a signature only depends
on the private key and the message to be signed. This makes on the private key and the message to be signed. This makes
the implementation easier to test and does not require the implementation easier to test and does not require
a randomness source during signing. In the randomized case, a randomness source during signing. In the randomized case,
signing mixes in a 256-bit random string from an approved random bit signing mixes in a 256-bit random string from an approved random bit
generator (RBG). When randomized, ML-DSA is easier to harden generator (RBG). When randomized, ML-DSA is easier to harden
against fault and hardware side-channel attacks.</t> against fault and hardware side-channel attacks.</t>
<t>A security property also associated with digital
<t>A security property that is also associated with digital
signatures is non-repudiation. Non-repudiation refers to the signatures is non-repudiation. Non-repudiation refers to the
assurance that the owner of a signature key pair that was assurance that the owner of a signature keypair that was
capable of generating an existing signature corresponding to capable of generating an existing signature corresponding to
certain data cannot convincingly deny having signed the data, certain data cannot convincingly deny having signed the data,
unless its private key was compromised. unless its private key was compromised.
The digital signature scheme ML-DSA possess three security The digital signature scheme ML-DSA possesses three security
properties beyond unforgeability, that are associated with properties beyond unforgeability, that are associated with
non-repudiation. These are exclusive ownership, message-bound non-repudiation. These are exclusive ownership, message-bound
signatures, and non-resignability. These properties are based signatures, and non-resignability. These properties are based
tightly on the assumed collision resistance of the hash tightly on the assumed collision resistance of the hash
function used (in this case SHAKE-256). A full discussion function used (in this case SHAKE-256). A full discussion
of these properties in ML-DSA can be found at <xref target="CDFFJ21"/>.</t> of these properties in ML-DSA can be found at <xref target="CDFFJ21"/>.</t>
</section> </section>
</middle> </middle>
<back> <back>
<references anchor="sec-combined-references"> <references anchor="sec-combined-references">
skipping to change at line 608 skipping to change at line 617
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ITU-T Recommendation" value="X.680"/>
<seriesInfo name="ISO/IEC" value="8824-1:2021"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/>
</reference> </reference>
<reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690"> <reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690">
<front> <front>
<title>Information Technology -- Abstract Syntax Notation One (ASN.1 ): ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title> <title>Information Technology -- ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ITU-T Recommendation" value="X.690"/>
<seriesInfo name="ISO/IEC" value="8825-1:2021"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/>
</reference> </reference>
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer
-security-objects-register/algorithm-registration"> <reference anchor="FIPS204" target="https://nvlpubs.nist.gov/nistpubs/FI
PS/NIST.FIPS.204.pdf">
<front> <front>
<title>Computer Security Objects Register</title> <title>Module-Lattice-Based Digital Signature Standard</title>
<author initials="" surname="NIST" fullname="National Institute of S <author>
tandards and Technology"> <organization abbrev="NIST">National Institute of Standards and Te
<organization/> chnology</organization>
</author> </author>
<date year="2024" month="August" day="20"/> <date day="13" year="2024" month="August"/>
</front> </front>
<seriesInfo name="NIST FIPS" value="204"/>
<seriesInfo name="DOI" value="10.6028/NIST.FIPS.204 "/>
</reference> </reference>
<reference anchor="FIPS204">
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer
-security-objects-register/algorithm-registration">
<front> <front>
<title>Module-lattice-based digital signature standard</title> <title>Computer Security Objects Register (CSOR)</title>
<author> <author>
<organization/> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date month="August" year="2024"/> <date year="2025" month="June" day="13"/>
</front>
<seriesInfo name="DOI" value="10.6028/nist.fips.204"/>
<refcontent>National Institute of Standards and Technology (U.S.)</ref
content>
</reference>
<reference anchor="RFC2119">
<front>
<title>Key words for use in RFCs to Indicate Requirement Levels</tit
le>
<author fullname="S. Bradner" initials="S." surname="Bradner"/>
<date month="March" year="1997"/>
<abstract>
<t>In many standards track documents several words are used to sig
nify the requirements in the specification. These words are often capitalized. T
his document defines these words as they should be interpreted in IETF documents
. This document specifies an Internet Best Current Practices for the Internet Co
mmunity, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author fullname="B. Leiba" initials="B." surname="Leiba"/>
<date month="May" year="2017"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying that
only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
<reference anchor="RFC5912">
<front>
<title>New ASN.1 Modules for the Public Key Infrastructure Using X.5
09 (PKIX)</title>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<date month="June" year="2010"/>
<abstract>
<t>The Public Key Infrastructure using X.509 (PKIX) certificate fo
rmat, and many associated formats, are expressed using ASN.1. The current ASN.1
modules conform to the 1988 version of ASN.1. This document updates those ASN.1
modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire c
hanges to any of the formats; this is simply a change to the syntax. This docume
nt is not an Internet Standards Track specification; it is published for informa
tional purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5912"/>
<seriesInfo name="DOI" value="10.17487/RFC5912"/>
</reference>
<reference anchor="RFC5280">
<front>
<title>Internet X.509 Public Key Infrastructure Certificate and Cert
ificate Revocation List (CRL) Profile</title>
<author fullname="D. Cooper" initials="D." surname="Cooper"/>
<author fullname="S. Santesson" initials="S." surname="Santesson"/>
<author fullname="S. Farrell" initials="S." surname="Farrell"/>
<author fullname="S. Boeyen" initials="S." surname="Boeyen"/>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<author fullname="W. Polk" initials="W." surname="Polk"/>
<date month="May" year="2008"/>
<abstract>
<t>This memo profiles the X.509 v3 certificate and X.509 v2 certif
icate revocation list (CRL) for use in the Internet. An overview of this approac
h and model is provided as an introduction. The X.509 v3 certificate format is d
escribed in detail, with additional information regarding the format and semanti
cs of Internet name forms. Standard certificate extensions are described and two
Internet-specific extensions are defined. A set of required certificate extensi
ons is specified. The X.509 v2 CRL format is described in detail along with stan
dard and Internet-specific extensions. An algorithm for X.509 certification path
validation is described. An ASN.1 module and examples are provided in the appen
dices. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5280"/>
<seriesInfo name="DOI" value="10.17487/RFC5280"/>
</reference>
<reference anchor="RFC5958">
<front>
<title>Asymmetric Key Packages</title>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="August" year="2010"/>
<abstract>
<t>This document defines the syntax for private-key information an
d a content type for it. Private-key information includes a private key for a sp
ecified public-key algorithm and a set of attributes. The Cryptographic Message
Syntax (CMS), as defined in RFC 5652, can be used to digitally sign, digest, aut
henticate, or encrypt the asymmetric key format content type. This document obso
letes RFC 5208. [STANDARDS-TRACK]</t>
</abstract>
</front> </front>
<seriesInfo name="RFC" value="5958"/>
<seriesInfo name="DOI" value="10.17487/RFC5958"/>
</reference> </reference>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2
119.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8
174.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
912.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
280.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
958.xml"/>
</references> </references>
<references anchor="sec-informative-references"> <references anchor="sec-informative-references">
<name>Informative References</name> <name>Informative References</name>
<reference anchor="Dilithium" target="https://pq-crystals.org/dilithium/ data/dilithium-specification-round3-20210208.pdf"> <reference anchor="Dilithium" target="https://pq-crystals.org/dilithium/ data/dilithium-specification-round3-20210208.pdf">
<front> <front>
<title>CRYSTALS-Dilithium Algorithm Specifications and Supporting Do cumentation</title> <title>CRYSTALS-Dilithium Algorithm Specifications and Supporting Do cumentation (Version 3.1)</title>
<author initials="S." surname="Bai"> <author initials="S." surname="Bai">
<organization/> <organization/>
</author> </author>
<author initials="L." surname="Ducas"> <author initials="L." surname="Ducas">
<organization/> <organization/>
</author> </author>
<author initials="E." surname="Kiltz">
<organization/>
</author>
<author initials="T." surname="Lepoint"> <author initials="T." surname="Lepoint">
<organization/> <organization/>
</author> </author>
<author initials="V." surname="Lyubashevsky"> <author initials="V." surname="Lyubashevsky">
<organization/> <organization/>
</author> </author>
<author initials="P." surname="Schwabe"> <author initials="P." surname="Schwabe">
<organization/> <organization/>
</author> </author>
<author initials="G." surname="Seiler"> <author initials="G." surname="Seiler">
<organization/> <organization/>
</author> </author>
<author initials="D." surname="Stehlé"> <author initials="D." surname="Stehlé">
<organization/> <organization/>
</author> </author>
<date year="2021"/> <date day="8" month="2" year="2021"/>
</front> </front>
</reference> </reference>
<reference anchor="Fiat-Shamir" target="https://www.iacr.org/archive/asi acrypt2009/59120596/59120596.pdf"> <reference anchor="Fiat-Shamir" target="https://www.iacr.org/archive/asi acrypt2009/59120596/59120596.pdf">
<front> <front>
<title>Fiat-Shamir with aborts: Applications to lattice and factorin g-based signatures</title> <title>Fiat-Shamir with aborts: Applications to lattice and factorin g-based signatures</title>
<author initials="V." surname="Lyubashevsky"> <author initials="V." surname="Lyubashevsky">
<organization/> <organization/>
</author> </author>
<date year="2009"/> <date year="2009"/>
</front> </front>
<seriesInfo name="International Conference on the Theory and Applicati on of Cryptology and Information Security" value=""/> <refcontent>International Conference on the Theory and Application of Cryptology and Information Security</refcontent>
</reference> </reference>
<reference anchor="CDFFJ21" target="https://eprint.iacr.org/2020/1525.pd
f"> <!-- Note: IEEE version of [CDFFJ21]
<reference anchor="CDFFJ21" target="https://ieeexplore.ieee.org/document
/9519420">
<front> <front>
<title>BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures</title> <title>BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures</title>
<author initials="C." surname="Cremers"> <author initials="C." surname="Cremers">
<organization/> <organization/>
</author> </author>
<author initials="S." surname="Düzlü"> <author initials="S." surname="Düzlü">
<organization/> <organization/>
</author> </author>
<author initials="R." surname="Fiedler"> <author initials="R." surname="Fiedler">
<organization/> <organization/>
</author> </author>
<author initials="M." surname="Fischlin"> <author initials="M." surname="Fischlin">
<organization/> <organization/>
</author> </author>
<author initials="C." surname="Janson"> <author initials="C." surname="Janson">
<organization/> <organization/>
</author> </author>
<date year="2021"/> <date year="2021"/>
</front> </front>
<seriesInfo name="In Proceedings of the 42nd IEEE Symposium on Securit <seriesInfo name="DOI" value="10.1109/SP40001.2021.00093"/>
y and Privacy" value=""/> <refcontent>2021 IEEE Symposium on Security and Privacy (SP), pp. 1696
-1714</refcontent>
</reference>
-->
<reference anchor="CDFFJ21" target="https://eprint.iacr.org/2020/1525.pd
f">
<front>
<title>BUFFing signature schemes beyond unforgeability and the case
of post-quantum signatures</title>
<author initials="C." surname="Cremers">
<organization/>
</author>
<author initials="S." surname="Düzlü">
<organization/>
</author>
<author initials="R." surname="Fiedler">
<organization/>
</author>
<author initials="M." surname="Fischlin">
<organization/>
</author>
<author initials="C." surname="Janson">
<organization/>
</author>
<date month="October" year="2023"/>
</front>
<refcontent>Cryptology ePrint Archive, Paper 2020/1525</refcontent>
</reference> </reference>
<reference anchor="NIST-PQC" target="https://csrc.nist.gov/Projects/post -quantum-cryptography"> <reference anchor="NIST-PQC" target="https://csrc.nist.gov/Projects/post -quantum-cryptography">
<front> <front>
<title>Post-Quantum Cryptography Project</title> <title>Post-Quantum Cryptography (PQC)</title>
<author> <author>
<organization>National Institute of Standards and Technology (NIST )</organization> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date year="2016" month="December" day="20"/> <date year="2025" month="July" day="28"/>
</front> </front>
</reference> </reference>
<reference anchor="FIPS204-ExternalMuFAQ" target="https://csrc.nist.gov/ csrc/media/Projects/post-quantum-cryptography/documents/faq/fips204-sec6-0319202 5.pdf"> <reference anchor="FIPS204-ExternalMuFAQ" target="https://csrc.nist.gov/ csrc/media/Projects/post-quantum-cryptography/documents/faq/fips204-sec6-0319202 5.pdf">
<front> <front>
<title>FIPS 204 Section 6 FAQ</title> <title>FIPS 204 Section 6 FAQ</title>
<author> <author>
<organization>National Institute of Standards and Technology (NIST )</organization> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date year="2025"/> <date year="2025"/>
</front> </front>
</reference> </reference>
<reference anchor="RFC7468"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7
<front> 468.xml"/>
<title>Textual Encodings of PKIX, PKCS, and CMS Structures</title> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3
<author fullname="S. Josefsson" initials="S." surname="Josefsson"/> 647.xml"/>
<author fullname="S. Leonard" initials="S." surname="Leonard"/>
<date month="April" year="2015"/>
<abstract>
<t>This document describes and discusses the textual encodings of
the Public-Key Infrastructure X.509 (PKIX), Public-Key Cryptography Standards (P
KCS), and Cryptographic Message Syntax (CMS). The textual encodings are well-kno
wn, are implemented by several applications and libraries, and are widely deploy
ed. This document articulates the de facto rules by which existing implementatio
ns operate and defines them so that future implementations can interoperate.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="7468"/>
<seriesInfo name="DOI" value="10.17487/RFC7468"/>
</reference>
<reference anchor="RFC3647">
<front>
<title>Internet X.509 Public Key Infrastructure Certificate Policy a
nd Certification Practices Framework</title>
<author fullname="S. Chokhani" initials="S." surname="Chokhani"/>
<author fullname="W. Ford" initials="W." surname="Ford"/>
<author fullname="R. Sabett" initials="R." surname="Sabett"/>
<author fullname="C. Merrill" initials="C." surname="Merrill"/>
<author fullname="S. Wu" initials="S." surname="Wu"/>
<date month="November" year="2003"/>
<abstract>
<t>This document presents a framework to assist the writers of cer
tificate policies or certification practice statements for participants within p
ublic key infrastructures, such as certification authorities, policy authorities
, and communities of interest that wish to rely on certificates. In particular,
the framework provides a comprehensive list of topics that potentially (at the w
riter's discretion) need to be covered in a certificate policy or a certificatio
n practice statement. This document supersedes RFC 2527.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3647"/>
<seriesInfo name="DOI" value="10.17487/RFC3647"/>
</reference>
</references> </references>
</references> </references>
<?line 726?>
<section anchor="asn1"> <section anchor="asn1">
<name>ASN.1 Module</name> <name>ASN.1 Module</name>
<t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-DSA. Note that <t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-DSA. Note that
as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see
<xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> .</t> <xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> .</t>
<sourcecode markers="true"><![CDATA[ <sourcecode type="asn.1" markers="true"><![CDATA[
X509-ML-DSA-2025 X509-ML-DSA-2025
{ iso(1) identified-organization(3) dod(6) { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-x509-ml-dsa-2025(TBD1) } id-mod-x509-ml-dsa-2025(119) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL; EXPORTS ALL;
IMPORTS IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM PUBLIC-KEY, SIGNATURE-ALGORITHM
FROM AlgorithmInformation-2009 -- [RFC 5912] FROM AlgorithmInformation-2009 -- [RFC 5912]
{ iso(1) identified-organization(3) dod(6) internet(1) { iso(1) identified-organization(3) dod(6) internet(1)
skipping to change at line 974 skipping to change at line 925
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-87 } PUBLIC-KEYS { pk-ml-dsa-87 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 }
} }
END END
]]></sourcecode> ]]></sourcecode>
</section> </section>
<section anchor="security-strengths"> <section anchor="security-strengths">
<name>Security Strengths</name> <name>Security Strengths</name>
<t>Instead of defining the strength of a quantum algorithm <t>Instead of defining the strength of a quantum algorithm
in a traditional manner using the imprecise notion of bits using the common but imprecise notion of bits
of security, NIST has instead elected to define security of security, NIST has instead elected to define security
levels by picking a reference scheme, which NIST expects levels by picking a reference scheme, which NIST expects
to offer notable levels of resistance to both quantum and to offer notable levels of resistance to both quantum and
classical attack. To wit, an algorithm that achieves NIST PQC classical attacks. To wit, an algorithm that achieves NIST PQC
security level 1 must require computational resources to security level 1 must require computational resources to
break the relevant security property, which are greater than break the relevant security property, which are greater than
those required for a brute-force key search on AES-128. those required for a brute-force key search on AES-128.
Levels 3 and 5 use AES-192 and AES-256 as reference respectively. Levels 3 and 5 use AES-192 and AES-256 as references, respectively.
Levels 2 and 4 use collision search for SHA-256 and SHA-384 Levels 2 and 4 use collision search for SHA-256 and SHA-384
as reference.</t> as references.</t>
<t>The parameter sets defined for NIST security levels 2, 3 and 5 <t>The parameter sets defined for NIST security levels 2, 3, and 5
are listed in the Figure 1, along with the resulting signature are listed in Figure 1, along with the resulting signature
size, public key, and private key sizes in bytes. size, public key, and private key sizes in bytes.
Note that these are the sizes of the raw keys, not including Note that these are the sizes of the raw keys, not including
ASN.1 encoding overhead from OneAsymmetricKey and SubjectPublicKeyInfo ASN.1 encoding overhead from <tt>OneAsymmetricKey</tt> and <tt>SubjectPublicKeyI nfo</tt>
wrappers. Private key sizes are shown for both the seed format wrappers. Private key sizes are shown for both the seed format
and expanded format.</t> and expanded format.</t>
<figure anchor="ML-DSAParameters"> <table anchor="ML-DSAParameters">
<name>ML-DSA Parameters</name> <name>ML-DSA Parameters</name>
<artwork><![CDATA[ <thead>
|=======+=======+=====+========+========+==========+==========| <tr>
| Level | (k,l) | eta | Sig. | Public | Private | Private | <th>Level</th>
| | | | (B) | Key(B) | Seed(B) | Expand(B)| <th>(k,l)</th>
|=======+=======+=====+========+========+==========+==========| <th>eta</th>
| 2 | (4,4) | 2 | 2420 | 1312 | 32 | 2560 | <th>Sig. (B)</th>
| 3 | (6,5) | 4 | 3309 | 1952 | 32 | 4032 | <th>Public Key(B)</th>
| 5 | (8,7) | 2 | 4627 | 2592 | 32 | 4896 | <th>Private Seed(B)</th>
|=======+=======+=====+========+========+==========+==========| <th>Private Expand(B)</th>
]]></artwork> </tr>
</figure> </thead>
<tbody>
<tr>
<td>2</td>
<td>(4,4)</td>
<td>2</td>
<td>2420</td>
<td>1312</td>
<td>32</td>
<td>2560</td>
</tr>
<tr>
<td>3</td>
<td>(6,5)</td>
<td>4</td>
<td>3309</td>
<td>1952</td>
<td>32</td>
<td>4032</td>
</tr>
<tr>
<td>5</td>
<td>(8,7)</td>
<td>2</td>
<td>4627</td>
<td>2592</td>
<td>32</td>
<td>4896</td>
</tr>
</tbody>
</table>
</section> </section>
<section anchor="examples"> <section anchor="examples">
<name>Examples</name> <name>Examples</name>
<t>This appendix contains examples of ML-DSA private keys, public keys, <t>This appendix contains examples of ML-DSA private keys, public keys,
certificates, and inconsistent seed and expanded private keys.</t> certificates, and inconsistent seed and expanded private keys.</t>
<section anchor="example-private"> <section anchor="example-private">
<name>Example Private Keys</name> <name>Example Private Keys</name>
<t>The following examples show ML-DSA private keys in different formats, <t>The following examples show ML-DSA private keys in different formats,
all derived from the same seed <tt>000102...1e1f</tt>. For each security level, all derived from the same seed <tt>000102...1e1f</tt>. For each security level,
we show the seed-only format (using a context-specific <tt>[0]</tt> primitive we show the seed-only format (using a context-specific <tt>[0]</tt> primitive
tag with an implicit encoding of <tt>OCTET STRING</tt>), the <tt>expanded</tt> f ormat, tag with an implicit encoding of <tt>OCTET STRING</tt>), the <tt>expanded</tt> f ormat,
and <tt>both</tt> formats together.</t> and <tt>both</tt> formats together.</t>
<aside>
<t>NOTE: All examples use the same seed value, showing how the same seed <t>NOTE: All examples use the same seed value, showing how the same seed
produces different expanded private keys for each security level.</t> produces different expanded private keys for each security level.</t>
</aside>
<section anchor="ml-dsa-44-private-key-examples"> <section anchor="ml-dsa-44-private-key-examples">
<name>ML-DSA-44 Private Key Examples</name> <name>ML-DSA-44 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format"> <section anchor="seed-format">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format"> <section anchor="expanded-format">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
skipping to change at line 1103 skipping to change at line 1087
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178 OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178
9dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff9a 9dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff9a
613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe623 613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe623
skipping to change at line 1194 skipping to change at line 1178
495679adaed70167b50866713a53109db7b6f7d81304ecdfd83b319b1ef24830 495679adaed70167b50866713a53109db7b6f7d81304ecdfd83b319b1ef24830
6b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a893 6b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a893
2878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926b4 2878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926b4
e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe75 e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe75
27e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafca8 27e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafca8
6be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a56 6be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a56
46601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa1063 46601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa1063
98f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c7217 98f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c7217
b0689e21d8eb0ff69668` } b0689e21d8eb0ff69668` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format"> <section anchor="both-format">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp
vsk5zg9/d/jbVkTc2jZr/kc0vZX0Nf+aYTqlSqQcLGlMBDKaB7H6u0j1KjCfEaGJ vsk5zg9/d/jbVkTc2jZr/kc0vZX0Nf+aYTqlSqQcLGlMBDKaB7H6u0j1KjCfEaGJ
j4SOIyL/5iPsgQ2zvuM2hYVKiCadoyDVEgv8/omhjjD3EU2DqkBKZGtsmXOJhg0S j4SOIyL/5iPsgQ2zvuM2hYVKiCadoyDVEgv8/omhjjD3EU2DqkBKZGtsmXOJhg0S
Ui7gAG4jhIGRhmGbJg0RhmTUpigiGESCQCiYFGFIpmFMQkihkgjCOClRJEgIoSXC Ui7gAG4jhIGRhmGbJg0RhmTUpigiGESCQCiYFGFIpmFMQkihkgjCOClRJEgIoSXC
skipping to change at line 1351 skipping to change at line 1336
306b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a8 306b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a8
932878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926 932878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926
b4e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe b4e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe
7527e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafc 7527e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafc
a86be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a a86be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a
5646601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa10 5646601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa10
6398f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c72 6398f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c72
17b0689e21d8eb0ff69668` } 17b0689e21d8eb0ff69668` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-dsa-65-private-key-examples"> <section anchor="ml-dsa-65-private-key-examples">
<name>ML-DSA-65 Private Key Examples</name> <name>ML-DSA-65 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-1"> <section anchor="seed-format-1">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-1"> <section anchor="expanded-format-1">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i
WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj
zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r
8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy 8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy
IkQQiGhghkYBJ0dWcYCHBmaGQzJEQSIENjhmdQKCNjQkQyIFc2QQZFVUdyJ1VoFD IkQQiGhghkYBJ0dWcYCHBmaGQzJEQSIENjhmdQKCNjQkQyIFc2QQZFVUdyJ1VoFD
skipping to change at line 1469 skipping to change at line 1454
j4Q32BOw8SLy+xdgO2k+2cOPF8/VC4FebZ38DtLM8Z9jmSdKFCDyNaWdi/ckNF4U j4Q32BOw8SLy+xdgO2k+2cOPF8/VC4FebZ38DtLM8Z9jmSdKFCDyNaWdi/ckNF4U
5F2eS+iTTfw/qSZ422HXEYv1PLiiIlszX36uUOP5QSN2KNt22Oo493pyrzomyB/k 5F2eS+iTTfw/qSZ422HXEYv1PLiiIlszX36uUOP5QSN2KNt22Oo493pyrzomyB/k
NSOzNVNaXR23w480EIK7VzTQieiuMJz9o6C8tc1bCXETyO35YWqk9uZjG5ElJ2+z NSOzNVNaXR23w480EIK7VzTQieiuMJz9o6C8tc1bCXETyO35YWqk9uZjG5ElJ2+z
9oCjQ0HD22aNxsrUX8k7JwjKKvdczOc0/RkcUAidrVOYL92uAlMf+T4fIf85X8Ch 9oCjQ0HD22aNxsrUX8k7JwjKKvdczOc0/RkcUAidrVOYL92uAlMf+T4fIf85X8Ch
KHTt8GtvlkfpWnMkWGxx39kdkB1iGFgZD+zQDM0RC7rFn5bLiEw8k5lHSKVvQSg7 KHTt8GtvlkfpWnMkWGxx39kdkB1iGFgZD+zQDM0RC7rFn5bLiEw8k5lHSKVvQSg7
/EH7iQUhU6iUWIw8uQF/PWYybJhWN+V1rLgSNGNCZUAl1gLeO6lAwZrBpjPf/al3 /EH7iQUhU6iUWIw8uQF/PWYybJhWN+V1rLgSNGNCZUAl1gLeO6lAwZrBpjPf/al3
tSm4AT4ZwdbQaA9NrmLJJEUK5mqrgvIUcwYdqz1iskf5B+NVGTmtP1Rl6dCKgr/q tSm4AT4ZwdbQaA9NrmLJJEUK5mqrgvIUcwYdqz1iskf5B+NVGTmtP1Rl6dCKgr/q
F+6htrK5I3V0d/mTAAsvQ7cPKKqrH+miatH9M2FhbAsOJC/nZgS3AzofMOl+KPUm F+6htrK5I3V0d/mTAAsvQ7cPKKqrH+miatH9M2FhbAsOJC/nZgS3AzofMOl+KPUm
yjyID+K42dGwyf8YizHLnZdCWsq5shbZimrjVeWD2nHohk7j0WsHWXlhkO9UXB5i yjyID+K42dGwyf8YizHLnZdCWsq5shbZimrjVeWD2nHohk7j0WsHWXlhkO9UXB5i
v++Sr2yhR7EyRNbIkvyO8iOrP0P5JML0Zgl+6A== v++Sr2yhR7EyRNbIkvyO8iOrP0P5JML0Zgl+6A==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f625949 OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f625949
fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0cb3 fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0cb3
cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c65 cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c65
skipping to change at line 1606 skipping to change at line 1591
edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac59f edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac59f
96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d6632 96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d6632
6c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b529 6c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b529
b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f907 b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f907
e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b70f e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b70f
28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca3c 28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca3c
880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e886 880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e886
4ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223ab 4ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223ab
3f43f924c2f466097ee8` } 3f43f924c2f466097ee8` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-1"> <section anchor="both-format-1">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIP/gIBADALBglghkgBZQMEAxIEgg/qMIIP5gQgAAECAwQFBgcICQoLDA0ODxAR MIIP/gIBADALBglghkgBZQMEAxIEgg/qMIIP5gQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8Egg/ASGg9kZeOMes93biwRzSC0riKX2JZSf2PWKVh5pa9 EhMUFRYXGBkaGxwdHh8Egg/ASGg9kZeOMes93biwRzSC0riKX2JZSf2PWKVh5pa9
TCfYU/ppuBmQI+jNZ43Z+r+QR2Rv/QyzzH95WAWnHnDSNxsFY+PNM0YUnIyevPI7 TCfYU/ppuBmQI+jNZ43Z+r+QR2Rv/QyzzH95WAWnHnDSNxsFY+PNM0YUnIyevPI7
Ck5akA7qnGVieQp8Y+OGY9qi3dtuSA3EBaHnAZSLdIQe9cwcPyvzJ5culRBRDNU3 Ck5akA7qnGVieQp8Y+OGY9qi3dtuSA3EBaHnAZSLdIQe9cwcPyvzJ5culRBRDNU3
XswIVXF3EYciIYYjgQAEJHeAYUdQB1AXFwNVBFFRJUcYOARhdXIiRBCIaGCGRgEn XswIVXF3EYciIYYjgQAEJHeAYUdQB1AXFwNVBFFRJUcYOARhdXIiRBCIaGCGRgEn
skipping to change at line 1699 skipping to change at line 1683
F2A7aT7Zw48Xz9ULgV5tnfwO0szxn2OZJ0oUIPI1pZ2L9yQ0XhTkXZ5L6JNN/D+p F2A7aT7Zw48Xz9ULgV5tnfwO0szxn2OZJ0oUIPI1pZ2L9yQ0XhTkXZ5L6JNN/D+p
JnjbYdcRi/U8uKIiWzNffq5Q4/lBI3Yo23bY6jj3enKvOibIH+Q1I7M1U1pdHbfD JnjbYdcRi/U8uKIiWzNffq5Q4/lBI3Yo23bY6jj3enKvOibIH+Q1I7M1U1pdHbfD
jzQQgrtXNNCJ6K4wnP2joLy1zVsJcRPI7flhaqT25mMbkSUnb7P2gKNDQcPbZo3G jzQQgrtXNNCJ6K4wnP2joLy1zVsJcRPI7flhaqT25mMbkSUnb7P2gKNDQcPbZo3G
ytRfyTsnCMoq91zM5zT9GRxQCJ2tU5gv3a4CUx/5Ph8h/zlfwKEodO3wa2+WR+la ytRfyTsnCMoq91zM5zT9GRxQCJ2tU5gv3a4CUx/5Ph8h/zlfwKEodO3wa2+WR+la
cyRYbHHf2R2QHWIYWBkP7NAMzRELusWflsuITDyTmUdIpW9BKDv8QfuJBSFTqJRY cyRYbHHf2R2QHWIYWBkP7NAMzRELusWflsuITDyTmUdIpW9BKDv8QfuJBSFTqJRY
jDy5AX89ZjJsmFY35XWsuBI0Y0JlQCXWAt47qUDBmsGmM9/9qXe1KbgBPhnB1tBo jDy5AX89ZjJsmFY35XWsuBI0Y0JlQCXWAt47qUDBmsGmM9/9qXe1KbgBPhnB1tBo
D02uYskkRQrmaquC8hRzBh2rPWKyR/kH41UZOa0/VGXp0IqCv+oX7qG2srkjdXR3 D02uYskkRQrmaquC8hRzBh2rPWKyR/kH41UZOa0/VGXp0IqCv+oX7qG2srkjdXR3
+ZMACy9Dtw8oqqsf6aJq0f0zYWFsCw4kL+dmBLcDOh8w6X4o9SbKPIgP4rjZ0bDJ +ZMACy9Dtw8oqqsf6aJq0f0zYWFsCw4kL+dmBLcDOh8w6X4o9SbKPIgP4rjZ0bDJ
/xiLMcudl0JayrmyFtmKauNV5YPaceiGTuPRawdZeWGQ71RcHmK/75KvbKFHsTJE /xiLMcudl0JayrmyFtmKauNV5YPaceiGTuPRawdZeWGQ71RcHmK/75KvbKFHsTJE
1siS/I7yI6s/Q/kkwvRmCX7o 1siS/I7yI6s/Q/kkwvRmCX7o
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f` } 15161718191a1b1c1d1e1f` }
skipping to change at line 1840 skipping to change at line 1824
9f96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d66 9f96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d66
326c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b5 326c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b5
29b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f9 29b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f9
07e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b7 07e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b7
0f28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca 0f28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca
3c880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e8 3c880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e8
864ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223 864ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223
ab3f43f924c2f466097ee8` } ab3f43f924c2f466097ee8` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-dsa-87-private-key-examples"> <section anchor="ml-dsa-87-private-key-examples">
<name>ML-DSA-87 Private Key Examples</name> <name>ML-DSA-87 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-2"> <section anchor="seed-format-2">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-2"> <section anchor="expanded-format-2">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX
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tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ
SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR
WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS
skipping to change at line 1976 skipping to change at line 1959
bEvuv0b8EiIsCy7M1hWdWuqOVU16CWUrBr98ppmnGZ5xbQXdVTBBqPKzA9I2qbq6 bEvuv0b8EiIsCy7M1hWdWuqOVU16CWUrBr98ppmnGZ5xbQXdVTBBqPKzA9I2qbq6
r7n6Uo8oosoqp4C5QDg8CZqmWgB0uD/R8Lxbe15Gwl5Ug4s8vPyV+H8dRxs7qJRD r7n6Uo8oosoqp4C5QDg8CZqmWgB0uD/R8Lxbe15Gwl5Ug4s8vPyV+H8dRxs7qJRD
T6WJUv3Ld/FhNyaTMG26To8hbRyOXK/w/oNgpRxgdjZEFp/caoJn8uP5CaYbKmeL T6WJUv3Ld/FhNyaTMG26To8hbRyOXK/w/oNgpRxgdjZEFp/caoJn8uP5CaYbKmeL
zmrpBAOoNrGnt+jNi1TDcIep4URG2V5pCNLu2/zGU+Av33cfcBp5ueWibtCpR4Qg zmrpBAOoNrGnt+jNi1TDcIep4URG2V5pCNLu2/zGU+Av33cfcBp5ueWibtCpR4Qg
cPO1cBdCIRIZ52F2LDfw0KHRuXUP7ld+EggRXGasB+wJHmo/xKpqJTvLqGjt0xVN cPO1cBdCIRIZ52F2LDfw0KHRuXUP7ld+EggRXGasB+wJHmo/xKpqJTvLqGjt0xVN
yvUWL2FehUkKbKNC80xDrGGj6mv+79hQ4ZDrHY2k0otezusWeMAkM+zV1IslNkBC yvUWL2FehUkKbKNC80xDrGGj6mv+79hQ4ZDrHY2k0otezusWeMAkM+zV1IslNkBC
V+jKe+9YVfK4E+0vTECURaMxfJvho1ri+00rh5IbkEvywU21FM7gRSUc/CdjdNsV V+jKe+9YVfK4E+0vTECURaMxfJvho1ri+00rh5IbkEvywU21FM7gRSUc/CdjdNsV
yZ3qFazeGXxutSSYjjm2Moe+uGdoZaqjutG0O4yrFcvyekmHWeMgOr82npckLwsB yZ3qFazeGXxutSSYjjm2Moe+uGdoZaqjutG0O4yrFcvyekmHWeMgOr82npckLwsB
VBSfFKwjPNtzoit/uPCTJb8qzoO7a124oSGitoIUmmkTHMzlIimECxE/x7C8xYQF VBSfFKwjPNtzoit/uPCTJb8qzoO7a124oSGitoIUmmkTHMzlIimECxE/x7C8xYQF
v+h/H5X/wulvxVllZ+lDZN+qbZ1abrma5N30JA== v+h/H5X/wulvxVllZ+lDZN+qbZ1abrma5N30JA==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab41 OCTET_STRING { `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab41
b90258cfa7e90ec97124d8e9ee4e90a16c602f5ec9bc38517dc30e329d5ab276 b90258cfa7e90ec97124d8e9ee4e90a16c602f5ec9bc38517dc30e329d5ab276
73bd85f4c9b0300f776389886750b57c24db3fc012e61ede59753337374fa712 73bd85f4c9b0300f776389886750b57c24db3fc012e61ede59753337374fa712
skipping to change at line 2140 skipping to change at line 2123
b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec091e b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec091e
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ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257e8 ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257e8
ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2c1 ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2c1
4db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287be 4db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287be
b8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b015414 b8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b015414
9f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a69131c 9f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a69131c
cce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364dfaa cce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364dfaa
6d9d5a6eb99ae4ddf424` } 6d9d5a6eb99ae4ddf424` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-2"> <section anchor="both-format-2">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIITXgIBADALBglghkgBZQMEAxMEghNKMIITRgQgAAECAwQFBgcICQoLDA0ODxAR MIITXgIBADALBglghkgBZQMEAxMEghNKMIITRgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EghMgl5K87C8kMGhqgvzPPC9f9mXncderQbkCWM+n6Q7J EhMUFRYXGBkaGxwdHh8EghMgl5K87C8kMGhqgvzPPC9f9mXncderQbkCWM+n6Q7J
cSTY6e5OkKFsYC9eybw4UX3DDjKdWrJ2c72F9MmwMA93Y4mIZ1C1fCTbP8AS5h7e cSTY6e5OkKFsYC9eybw4UX3DDjKdWrJ2c72F9MmwMA93Y4mIZ1C1fCTbP8AS5h7e
WXUzNzdPpxJJkVSa8kNJbQY3yzvgWllII1v3mHX4ltj+DKswyElI201jFaqvFgrG WXUzNzdPpxJJkVSa8kNJbQY3yzvgWllII1v3mHX4ltj+DKswyElI201jFaqvFgrG
JDZkIgFIFhEJESyUAokiRSxiuEUARSoIlnCQEm4Uk3DURhCERFFYlpEMqSmCskHJ JDZkIgFIFhEJESyUAokiRSxiuEUARSoIlnCQEm4Uk3DURhCERFFYlpEMqSmCskHJ
skipping to change at line 2251 skipping to change at line 2233
LszWFZ1a6o5VTXoJZSsGv3ymmacZnnFtBd1VMEGo8rMD0japurqvufpSjyiiyiqn LszWFZ1a6o5VTXoJZSsGv3ymmacZnnFtBd1VMEGo8rMD0japurqvufpSjyiiyiqn
gLlAODwJmqZaAHS4P9HwvFt7XkbCXlSDizy8/JX4fx1HGzuolENPpYlS/ct38WE3 gLlAODwJmqZaAHS4P9HwvFt7XkbCXlSDizy8/JX4fx1HGzuolENPpYlS/ct38WE3
JpMwbbpOjyFtHI5cr/D+g2ClHGB2NkQWn9xqgmfy4/kJphsqZ4vOaukEA6g2sae3 JpMwbbpOjyFtHI5cr/D+g2ClHGB2NkQWn9xqgmfy4/kJphsqZ4vOaukEA6g2sae3
6M2LVMNwh6nhREbZXmkI0u7b/MZT4C/fdx9wGnm55aJu0KlHhCBw87VwF0IhEhnn 6M2LVMNwh6nhREbZXmkI0u7b/MZT4C/fdx9wGnm55aJu0KlHhCBw87VwF0IhEhnn
YXYsN/DQodG5dQ/uV34SCBFcZqwH7Akeaj/EqmolO8uoaO3TFU3K9RYvYV6FSQps YXYsN/DQodG5dQ/uV34SCBFcZqwH7Akeaj/EqmolO8uoaO3TFU3K9RYvYV6FSQps
o0LzTEOsYaPqa/7v2FDhkOsdjaTSi17O6xZ4wCQz7NXUiyU2QEJX6Mp771hV8rgT o0LzTEOsYaPqa/7v2FDhkOsdjaTSi17O6xZ4wCQz7NXUiyU2QEJX6Mp771hV8rgT
7S9MQJRFozF8m+GjWuL7TSuHkhuQS/LBTbUUzuBFJRz8J2N02xXJneoVrN4ZfG61 7S9MQJRFozF8m+GjWuL7TSuHkhuQS/LBTbUUzuBFJRz8J2N02xXJneoVrN4ZfG61
JJiOObYyh764Z2hlqqO60bQ7jKsVy/J6SYdZ4yA6vzaelyQvCwFUFJ8UrCM823Oi JJiOObYyh764Z2hlqqO60bQ7jKsVy/J6SYdZ4yA6vzaelyQvCwFUFJ8UrCM823Oi
K3+48JMlvyrOg7trXbihIaK2ghSaaRMczOUiKYQLET/HsLzFhAW/6H8flf/C6W/F K3+48JMlvyrOg7trXbihIaK2ghSaaRMczOUiKYQLET/HsLzFhAW/6H8flf/C6W/F
WWVn6UNk36ptnVpuuZrk3fQk WWVn6UNk36ptnVpuuZrk3fQk
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f` } 15161718191a1b1c1d1e1f` }
skipping to change at line 2419 skipping to change at line 2401
1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61 1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61
a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257 a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257
e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2 e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2
c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287 c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287
beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154 beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154
149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913 149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913
1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df 1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df
aa6d9d5a6eb99ae4ddf424` } aa6d9d5a6eb99ae4ddf424` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
</section> </section>
<section anchor="example-public"> <section anchor="example-public">
<name>Example Public Keys</name> <name>Example Public Keys</name>
<t>The following is the ML-DSA-44 public key corresponding to the privat e <t>The following is the ML-DSA-44 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
skipping to change at line 2459 skipping to change at line 2440
7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV 7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV
oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn
j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl
Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI
bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/ bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/
XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br
IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP
cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO
t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo
7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI= 7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI=
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17 BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17
89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156 89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156
93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3 93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3
826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7 826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7
62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55 62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55
skipping to change at line 2508 skipping to change at line 2489
299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21 299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21
6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358 6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358
fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208 fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208
3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8 3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8
815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e 815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e
938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b 938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b
0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95 0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95
eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31 eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31
5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9 5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9
784cf05c830b3242c8312` } 784cf05c830b3242c8312` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-DSA-65 public key corresponding to the privat e <t>The following is the ML-DSA-65 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il
YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK
xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv
DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax
GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V
Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa
gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ
tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg
skipping to change at line 2557 skipping to change at line 2539
/am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U /am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U
1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r 1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r
utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL
avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+ avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+
SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ
poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC
HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO
IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj
8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF 8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF
HgLy6ERP HgLy6ERP
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594 BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594
9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d 9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d
51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515 51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515
11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c 11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c
2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce 2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce
skipping to change at line 2626 skipping to change at line 2608
48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336 48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336
24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607 24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607
61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec 61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec
79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6 79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6
6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0 6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0
3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914 3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914
66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475 66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475
b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79 b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79
c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210 c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210
4bc460a051e02f2e8444f` } 4bc460a051e02f2e8444f` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-DSA-87 public key corresponding to the privat e <t>The following is the ML-DSA-87 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP
p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt
X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4 X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4
6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY 6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY
ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz
ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv
WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2 WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2
eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z
skipping to change at line 2688 skipping to change at line 2671
citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH
8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4 8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4
P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8 P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8
WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR
gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl
kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO
r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22 r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22
1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT 1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT
SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG
5VvgYiIvi6kKl0BzMmsxISrs4KNKYA== 5VvgYiIvi6kKl0BzMmsxISrs4KNKYA==
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4 BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4
1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46 1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46
a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079 a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079
54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712 54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712
0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f 0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f
skipping to change at line 2777 skipping to change at line 2760
7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846 7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846
c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557 c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557
23ee0c7f4736ce6e6665c5aca32a481c53839bc259167b013d0423395eeb9aaa 23ee0c7f4736ce6e6665c5aca32a481c53839bc259167b013d0423395eeb9aaa
ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce
2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa 2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa
1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270 1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270
4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f 4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f
faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0 faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0
09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407 09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407
3326b31212aece0a34a60` } 3326b31212aece0a34a60` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-certificates"> <section anchor="example-certificates">
<name>Example Certificates</name> <name>Example Certificates</name>
<aside> <aside>
<t>The example certificates in this section have key usage bits set to <t>The example certificates in this section have key usage bits set to
<tt>digitalSignature</tt>, <tt>keyCertSign</tt>, and <tt>cRLSign</tt> to lessen the number of <tt>digitalSignature</tt>, <tt>keyCertSign</tt>, and <tt>cRLSign</tt> to lessen the number of
examples, i.e., brevity. Certificate Policies (CPs) <xref target="RFC3647"/> examples, i.e., brevity. Certificate Policies (CPs) <xref target="RFC3647"/>
for production CAs should consider whether this combination is for production CAs should consider whether this combination is
appropriate.</t> appropriate.</t>
</aside> </aside>
<t>The following is a self-signed certificate for the ML-DSA-44 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-44 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[ <sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P
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F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG
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skipping to change at line 2878 skipping to change at line 2860
J/11Up4pEegRS/c+Li2OUvQr9Jxi8XGIdEJZY1T8oVpzDJf3C29gpARWSDAXrFn0 J/11Up4pEegRS/c+Li2OUvQr9Jxi8XGIdEJZY1T8oVpzDJf3C29gpARWSDAXrFn0
lgZHnqFyebeC1uDW8r/wGtYmI2EC53+FlOF5AFcH+3LzObZzerqwror4UMOA+B5c lgZHnqFyebeC1uDW8r/wGtYmI2EC53+FlOF5AFcH+3LzObZzerqwror4UMOA+B5c
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omIXALO1EiDbpu38gERRLkC84eMhRBQjKcdmlcBFsmilt3cfIofypuhMRiIFjIke omIXALO1EiDbpu38gERRLkC84eMhRBQjKcdmlcBFsmilt3cfIofypuhMRiIFjIke
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IjNzkTyrPI06yMvxaHGajwUtLWCReJOG/uXhswbX7EviVYyqCR4vzDLDVXAulxo/ IjNzkTyrPI06yMvxaHGajwUtLWCReJOG/uXhswbX7EviVYyqCR4vzDLDVXAulxo/
OsHaQhMX8xYOLXontx7SNCBlu/EEBww5QklKUldgd5igr7bDxsvZ6vHy/wcNIzY3 OsHaQhMX8xYOLXontx7SNCBlu/EEBww5QklKUldgd5igr7bDxsvZ6vHy/wcNIzY3
RUdidnuDkpSm1hIoLz4/SW2Tm6C2u9La5evu7xAfIy1ul8LE3/P0AAAAAAAAAAAA RUdidnuDkpSm1hIoLz4/SW2Tm6C2u9La5evu7xAfIy1ul8LE3/P0AAAAAAAAAAAA
AAAAABcmOEM= AAAAABcmOEM=
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
skipping to change at line 3083 skipping to change at line 3065
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5e1b306d7ec4be2558caa091e2fcc32c355702e971a3f3ac1da421317f3160e2 5e1b306d7ec4be2558caa091e2fcc32c355702e971a3f3ac1da421317f3160e2
d7a27b71ed2342065bbf104070c3942494a5257607798a0afb6c3c6cbd9eaf1f d7a27b71ed2342065bbf104070c3942494a5257607798a0afb6c3c6cbd9eaf1f
2ff070d233637454762767b839294a6d612282f3e3f496d939ba0b6bbd2dae5e 2ff070d233637454762767b839294a6d612282f3e3f496d939ba0b6bbd2dae5e
beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` } beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` }
} }]]></artwork>
]]></artwork>
<t>The following is a self-signed certificate for the ML-DSA-65 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-65 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[
<sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
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3mP63SrwFrEZF3+j2XGi2Sdxc/zlW2d0WvC3wh1Zfb65Pmoy80HEmlqL6eglCI0f 3mP63SrwFrEZF3+j2XGi2Sdxc/zlW2d0WvC3wh1Zfb65Pmoy80HEmlqL6eglCI0f
KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1 KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1
skipping to change at line 3206 skipping to change at line 3189
7E3OGjBH4my94VaNx6O8HIEhtY6zq2X18IkRvwUhO9dLIUZqYNAgC5n/8NQrxRqi 7E3OGjBH4my94VaNx6O8HIEhtY6zq2X18IkRvwUhO9dLIUZqYNAgC5n/8NQrxRqi
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uWXH6mJ0D04Edb/ut+2n5xL5VDde/rXlzntbCYTwxa4BbJmYjwQCiKVzDeknXdMj uWXH6mJ0D04Edb/ut+2n5xL5VDde/rXlzntbCYTwxa4BbJmYjwQCiKVzDeknXdMj
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+BH4UnmFmQY7SGZyeHuDvFNzdNIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYNDxMc +BH4UnmFmQY7SGZyeHuDvFNzdNIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYNDxMc
IA== IA==
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
skipping to change at line 3459 skipping to change at line 3442
2485fc1811bdd5e8a9c4dcadc4afeaa15aafbdf8f2b527f8062d170bf235138c 2485fc1811bdd5e8a9c4dcadc4afeaa15aafbdf8f2b527f8062d170bf235138c
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1f810584539f81f81ad421c3f031dbc0376c6be761223f663910a9edd1143e3b 1f810584539f81f81ad421c3f031dbc0376c6be761223f663910a9edd1143e3b
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00000000000000000000000000000000000060d0f131c20` } 00000000000000000000000000000000000060d0f131c20` }
} }]]></artwork>
]]></artwork>
<t>The following is a self-signed certificate for the ML-DSA-87 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-87 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[
<sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
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skipping to change at line 3622 skipping to change at line 3606
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lIn7fepvuNyI+PK9UyvX0am7R29bxNyCTNJHQuVJv93WrokJX7IHOaZXyY7T4bMj lIn7fepvuNyI+PK9UyvX0am7R29bxNyCTNJHQuVJv93WrokJX7IHOaZXyY7T4bMj
yw0yMsWOanzDyh0y7OGhDgXiJS42y2XU0UH/JGGEZbZlEpfNNNOPYcYvMfuOlwww yw0yMsWOanzDyh0y7OGhDgXiJS42y2XU0UH/JGGEZbZlEpfNNNOPYcYvMfuOlwww
ZTIl7tStk6k0AtZ77tHmw2iu5730yoXlTrKxe72lAdDQlvXLTkdXXw+oxg+O078n ZTIl7tStk6k0AtZ77tHmw2iu5730yoXlTrKxe72lAdDQlvXLTkdXXw+oxg+O078n
Zt5jdDQgFMXYxyqanZgc5scGn3X4Q/uXgZ0QSlhPErGjtIC5/XdAUraYJZNo6lu3 Zt5jdDQgFMXYxyqanZgc5scGn3X4Q/uXgZ0QSlhPErGjtIC5/XdAUraYJZNo6lu3
r2dYCUIfo6xun+6+QnoT7OXpb+hc04Ky4QYHq5EYd60H50ogBiHTzC2QLcqDbpK4 r2dYCUIfo6xun+6+QnoT7OXpb+hc04Ky4QYHq5EYd60H50ogBiHTzC2QLcqDbpK4
rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
skipping to change at line 3936 skipping to change at line 3920
8f2bd532bd7d1a9bb476f5bc4dc824cd24742e549bfddd6ae89095fb20739a65 8f2bd532bd7d1a9bb476f5bc4dc824cd24742e549bfddd6ae89095fb20739a65
7c98ed3e1b323cb0d3232c58e6a7cc3ca1d32ece1a10e05e2252e36cb65d4d14 7c98ed3e1b323cb0d3232c58e6a7cc3ca1d32ece1a10e05e2252e36cb65d4d14
1ff24618465b6651297cd34d38f61c62f31fb8e970c30653225eed4ad93a9340 1ff24618465b6651297cd34d38f61c62f31fb8e970c30653225eed4ad93a9340
2d67beed1e6c368aee7bdf4ca85e54eb2b17bbda501d0d096f5cb4e47575f0fa 2d67beed1e6c368aee7bdf4ca85e54eb2b17bbda501d0d096f5cb4e47575f0fa
8c60f8ed3bf2766de6374342014c5d8c72a9a9d981ce6c7069f75f843fb97819 8c60f8ed3bf2766de6374342014c5d8c72a9a9d981ce6c7069f75f843fb97819
d104a584f12b1a3b480b9fd774052b698259368ea5bb7af675809421fa3ac6e9 d104a584f12b1a3b480b9fd774052b698259368ea5bb7af675809421fa3ac6e9
feebe427a13ece5e96fe85cd382b2e10607ab911877ad07e74a200621d3cc2d9 feebe427a13ece5e96fe85cd382b2e10607ab911877ad07e74a200621d3cc2d9
02dca836e92b8ae754b483a8a91b80a0b0c113c48b0f1253c599bb9cf01bdca0 02dca836e92b8ae754b483a8a91b80a0b0c113c48b0f1253c599bb9cf01bdca0
5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000 5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000
0000000000000000000000000000000000000000000040c12151d1e252c` } 0000000000000000000000000000000000000000000040c12151d1e252c` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-bad"> <section anchor="example-bad">
<name>Example Inconsistent Seed and Expanded Private Keys</name> <name>Example Inconsistent Seed and Expanded Private Keys</name>
<aside> <aside>
<t>WARNING: These private keys are purposely bad do not use them in <t>WARNING: These private keys are purposely bad; do not use them in
production systems.</t> production systems.</t>
</aside> </aside>
<t>The following examples demonstrate inconsistent seed and expanded pri vate keys.</t> <t>The following examples demonstrate inconsistent seed and expanded pri vate keys.</t>
<t>Three <tt>ML-DSA-44-PrivateKey</tt> examples of inconsistent seed and <t>Three <tt>ML-DSA-44-PrivateKey</tt> examples of inconsistent seed and
expanded private keys follow:</t> expanded private keys follow:</t>
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1">
<li>
<t>The first <tt>ML-DSA-PrivateKey</tt> example includes the <tt>bot h CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are included. The <tt>seed</tt> and <tt>expanded</tt> values can be checked for inconsistencie s.</t> <t>The first <tt>ML-DSA-PrivateKey</tt> example includes the <tt>bot h CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are included. The <tt>seed</tt> and <tt>expanded</tt> values can be checked for inconsistencie s.</t>
</li> </li>
<li> <li>
<t>The second <tt>ML-DSA-PrivateKey</tt> example includes only <tt>e xpandedKey</tt>. The public key fails to match the <tt>tr</tt> hash value in th e private key.</t> <t>The second <tt>ML-DSA-PrivateKey</tt> example includes only <tt>e xpandedKey</tt>. The public key fails to match the <tt>tr</tt> hash value in th e private key.</t>
</li> </li>
<li> <li>
<t>The third <tt>ML-DSA-PrivateKey</tt> example also includes only < tt>expandedKey</tt>. The private <tt>s_1</tt> and <tt>s_2</tt> vectors imply a < tt>t</tt> vector whose private low bits do not match the <tt>t_0</tt> vector por tion of the private key (its high bits <tt>t_1</tt> are the primary content of t he public key).</t> <t>The third <tt>ML-DSA-PrivateKey</tt> example also includes only < tt>expandedKey</tt>. The private <tt>s_1</tt> and <tt>s_2</tt> vectors imply a < tt>t</tt> vector whose private low bits do not match the <tt>t_0</tt> vector por tion of the private key (its high bits <tt>t_1</tt> are the primary content of t he public key).</t>
</li> </li>
</ol> </ol>
<t>The second and third examples would not be detected by implementation s <t>The second and third examples would not be detected by implementation s
that do not regenerate the public key from the private key, or neglect to that do not regenerate the public key from the private key or, when they do, the
then check consistency of <tt>tr</tt> or <tt>t_0</tt>.</t> y neglect to check consistency of <tt>tr</tt> and <tt>t_0</tt>.</t>
<t>The following is the first example:</t> <t>The following is the first example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L
GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1 GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1
TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65 TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65
3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA 3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA
Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj
lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY
skipping to change at line 4019 skipping to change at line 4004
paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU
AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH
Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa
itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H
2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3 2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3
fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW
YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9 YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9
tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI
2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V 2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V
ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA== ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the second example:</t> <t>The following is the second example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
skipping to change at line 4078 skipping to change at line 4064
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the third example:</t> <t>The following is the third example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
skipping to change at line 4137 skipping to change at line 4124
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
</section> </section>
</section> </section>
<section anchor="externalmu"> <section anchor="externalmu">
<name>Pre-hashing (Externalμ-ML-DSA)</name> <name>Pre-Hashing (Externalμ-ML-DSA)</name>
<t>Some applications require pre-hashing that ease operational <t>Some applications require pre-hashing that ease operational
requirements around large or inconsistently-sized payloads. requirements around large or inconsistently-sized payloads.
When signing with pre-hashing, the signature generation When signing with pre-hashing, the signature-generation
process can be separated into a pre-hash step requiring only the message process can be separated into a pre-hash step requiring only the message
and other public information, and a core signature and other public information, and a core signature
step which uses the public key.</t> step that uses the public key.</t>
<t>In the context of ML-DSA, pre-hashing can be performed with <t>In the context of ML-DSA, pre-hashing can be performed with
the HashML-DSA algorithm defined in Section 5.4 of <xref target="FIPS204"/>. the HashML-DSA algorithm defined in Section 5.4 of <xref target="FIPS204"/>.
ML-DSA itself supports a External μ pre-hashing mode which ML-DSA itself supports an External μ pre-hashing mode, which
externalizes the message pre-hashing originally performed inside externalizes the message pre-hashing originally performed inside
the signing operation. This mode is also laid out in the signing operation. This mode is also laid out in
<xref target="FIPS204-ExternalMuFAQ"/>. This document specifies <xref target="FIPS204-ExternalMuFAQ"/>. This document specifies
only the use of ML-DSA's External μ mode, and not HashML-DSA, only the use of ML-DSA's External μ mode, and not HashML-DSA,
in PKIX for reasons laid out in <xref target="sec-disallow-hash"/>.</t> in PKIX for reasons laid out in <xref target="sec-disallow-hash"/>.</t>
<t>Implementations of ML-DSA using the External μ pre-hashing mode require s the following <t>Implementations of ML-DSA using the External μ pre-hashing mode require s the following
algorithms, which are modified versions of the algorithms presented in <xref tar get="FIPS204"/>. algorithms, which are modified versions of the algorithms presented in <xref tar get="FIPS204"/>.
The nomenclature used here has been modified from the NIST FAQ <xref target="FIP S204-ExternalMuFAQ"/> The nomenclature used here has been modified from the NIST FAQ <xref target="FIP S204-ExternalMuFAQ"/>
for clarity.</t> for clarity.</t>
<t>Pre-hash operation:</t> <t>Pre-hash operation:</t>
<figure anchor="fig-externalmu-ml-dsa-external"> <figure anchor="fig-externalmu-ml-dsa-external">
<name>Computeμ prehash operation</name> <name>Computeμ Pre-Hash Operation</name>
<artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
Computeμ(pk, M, ctx): Computeμ(pk, M, ctx):
# Referred to as 'Externalμ-ML-DSA.Prehash(pk, M, ctx)' # Referred to as 'Externalμ-ML-DSA.Prehash(pk, M, ctx)'
# in the FIPS 204 FAQ. # in the FIPS 204 FAQ.
# M is the message, a bit-string # M is the message, a bit-string
# μ and ctx are byte-strings. # μ and ctx are byte-strings.
# ctx is the context string, which defaults to the empy string. # ctx is the context string, which defaults to the empty string.
μ = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) || μ = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) ||
IntegerToBytes(|ctx|, 1) || ctx) || M, 64) IntegerToBytes(|ctx|, 1) || ctx) || M, 64)
# The functions `BytesToBits` and `IntegerToBytes` are defined in FIPS 204. # The functions `BytesToBits` and `IntegerToBytes` are defined
return μ # in FIPS 204.
]]></artwork> return μ]]></sourcecode>
</figure> </figure>
<t>Sign operations:</t> <t>Sign operations:</t>
<figure anchor="fig-externalmu-ml-dsa-internal"> <figure anchor="fig-externalmu-ml-dsa-internal">
<name>The operations for signing μ</name> <name>The Operations for Signing μ</name>
<artwork><![CDATA[
<sourcecode type="pseudocode"><![CDATA[
Signμ(sk, μ): Signμ(sk, μ):
# Referred to as 'Externalμ-ML-DSA.Sign(sk, μ)' # Referred to as 'Externalμ-ML-DSA.Sign(sk, μ)'
# in the FIPS 204 FAQ. # in the FIPS 204 FAQ.
if |μ| != 64 then if |μ| != 64 then
return error # return an error indication if the input μ is not return error # return an error indication if the input μ is not
# 64 bytes. # 64 bytes.
end if end if
skipping to change at line 4204 skipping to change at line 4193
# set rnd to all zeroes # set rnd to all zeroes
if rnd = NULL then if rnd = NULL then
return error # return an error indication if random bit return error # return an error indication if random bit
# generation failed # generation failed
end if end if
sigma = Signμ_internal(sk, μ, rnd, isExternalμ=true) sigma = Signμ_internal(sk, μ, rnd, isExternalμ=true)
return sigma return sigma
ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false): ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false):
# μ can be passed as an argument instead of M' # μ is passed to the function via the argument M'.
# defaulting is Externalμ to false means that # Defaulting Externalμ to false means that
# this modified version of Sign_internal can be used # this modified version of Sign_internal can be used
# in place of the original without interfering with # in place of the original without interfering with
# functioning of pure ML-DSA mode. # functioning of pure ML-DSA mode.
# ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced with
# ... identical to FIPS 204 Algorithm 7, but with Line 6
# replaced with
6: if (isExternalμ): 6: if (isExternalμ):
μ = M' μ = M'
else: else:
μ = H(BytesToBits(tr) || M', 64) μ = H(BytesToBits(tr) || M', 64)]]></sourcecode>
]]></artwork>
</figure> </figure>
<t>There is no need to specify an External μ <tt>Verify()</tt> routine bec ause <t>There is no need to specify an External μ <tt>Verify()</tt> routine bec ause
this is identical to the original <tt>ML-DSA.Verify()</tt>. This makes External this is identical to the original <tt>ML-DSA.Verify()</tt>. This makes External
μ mode simply an internal optimization of the signer, and μ mode simply an internal optimization of the signer, and
allows an ML-DSA key to sometimes be used with the "one-shot" <tt>Sign()</tt> allows an ML-DSA key to sometimes be used with the "one-shot" <tt>Sign()</tt>
API and sometimes the External μ API without any interoperability concens.</t> API and to sometimes be used with the External μ API without any interoperabilit y concerns.</t>
<t>The External μ mode requires the <tt>Computeμ</tt> routine to have acce ss to the <t>The External μ mode requires the <tt>Computeμ</tt> routine to have acce ss to the
hash of the signer's public key which may not be available in some architectures , hash of the signer's public key, which may not be available in some architecture s,
or require fetching it. That may allow for mismatches between <tt>tr</tt> and <t t>sk</tt>. or require fetching it. That may allow for mismatches between <tt>tr</tt> and <t t>sk</tt>.
At worst, this will produce a signature which will fail to verify under the At worst, this will produce a signature that will fail to verify under the
intended public key since a compliant <tt>Verify()</tt> routine will intended public key since a compliant <tt>Verify()</tt> routine will
independently compute <tt>tr</tt> from the public key. That independently compute <tt>tr</tt> from the public key. This
is not believed to be a security concern since <tt>μ</tt> is never used as-is is not believed to be a security concern since <tt>μ</tt> is never used as-is
within <tt>ML-DSA.Sign_internal()</tt> (Algorithm 7 in <xref target="FIPS204"/>) . Rather, within <tt>ML-DSA.Sign_internal()</tt> (Algorithm 7 in <xref target="FIPS204"/>) . Rather,
it is hashed with values unknown to an attacker on lines 7 and 15. it is hashed with values unknown to an attacker on lines 7 and 15.
Thus, a signing oracle exposing <tt>Signμ()</tt> does not leak any bits of the s ecret Thus, a signing oracle exposing <tt>Signμ()</tt> does not leak any bits of the s ecret
key. The External μ mode also requires SHAKE256 to be available to the key. The External μ mode also requires SHAKE256 to be available to the
<tt>Computeμ</tt> routine.</t> <tt>Computeμ</tt> routine.</t>
</section> </section>
<section numbered="false" anchor="acknowledgments"> <section numbered="false" anchor="acknowledgments">
<name>Acknowledgments</name> <name>Acknowledgments</name>
<t>The authors wish to thank the following people for their contributions <t>The authors wish to thank the following people for their
to this document: Corey Bonnell, Dierdre Connolly, Viktor Dukhovni, Russ Housley contributions to this document: <contact fullname="Corey Bonnell"/>,
, <contact fullname="Dierdre Connolly"/>, <contact fullname="Viktor
Alicja Kario, Mike Ounsworth, and Daniel Van Geest.</t> Dukhovni"/>, <contact fullname="Russ Housley"/>, <contact
<t>In addition, we would like to thank those who contributed to the privat fullname="Alicja Kario"/>, <contact fullname="Mike Ounsworth"/>, and
e <contact fullname="Daniel Van Geest"/>.</t>
key format discussion: Tony Arcieri, Bob Beck, Dmitry Belyavskiy, David <t>In addition, we would like to thank those who contributed to the
Benjamin, Daniel Bernstein, Uri Blumenthal, Theo Buehler, Stephen Farrell, private key format discussion: <contact fullname="Tony Arcieri"/>,
Jean-Pierre Fiset, Scott Fluhrer, Alex Gaynor, John Gray, Peter Gutmann, <contact fullname="Bob Beck"/>, <contact fullname="Dmitry Belyavskiy"/>,
David Hook, Tim Hudson, Paul Kehrer, John Kemp, Watson Ladd, Adam Langley, <contact fullname="David Benjamin"/>, <contact fullname="Daniel
John Mattsson, Damien Miller, Robert Relyea, Michael Richardson, Bernstein"/>, <contact fullname="Uri Blumenthal"/>, <contact
Markku-Juhani O. Saarinen, Rich Salz, Roland Shoemaker, Sophie Schmieg, fullname="Theo Buehler"/>, <contact fullname="Stephen Farrell"/>,
Simo Sorce, Michael St. Johns, Falko Strenzke, Filippo Valsorda, Loganaden <contact fullname="Jean-Pierre Fiset"/>, <contact fullname="Scott
Velvindron, Carl Wallace, and Wei-Jun Wang.</t> Fluhrer"/>, <contact fullname="Alex Gaynor"/>, <contact fullname="John
Gray"/>, <contact fullname="Peter Gutmann"/>, <contact fullname="David
Hook"/>, <contact fullname="Tim Hudson"/>, <contact fullname="Paul
Kehrer"/>, <contact fullname="John Kemp"/>, <contact fullname="Watson
Ladd"/>, <contact fullname="Adam Langley"/>, <contact fullname="John
Mattsson"/>, <contact fullname="Damien Miller"/>, <contact
fullname="Robert Relyea"/>, <contact fullname="Michael Richardson"/>,
<contact fullname="Markku-Juhani O. Saarinen"/>, <contact fullname="Rich
Salz"/>, <contact fullname="Roland Shoemaker"/>, <contact
fullname="Sophie Schmieg"/>, <contact fullname="Simo Sorce"/>, <contact
fullname="Michael St. Johns"/>, <contact fullname="Falko Strenzke"/>,
<contact fullname="Filippo Valsorda"/>, <contact fullname="Loganaden
Velvindron"/>, <contact fullname="Carl Wallace"/>, and <contact
fullname="Wei-Jun Wang"/>.</t>
</section> </section>
</back>
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<!-- [rfced] Please review <tt> throughout the document for correctness and cons
istent use. Please see the list of <tt> use at the following location:
https://www.rfc-editor.org/authors/rfc9881tt2.txt
The list has been alphabetized and entries are listed only once (that is, if <tt
> is used multiple times for the same term, it is only listed once).
-->
<!-- [rfced] Please review each artwork element and let us know if any should
be marked as sourcecode (or another element) instead.
Please let us know if any instances of <artwork> should be <sourcecode> and whet
her type="" should be set. The current list of types is available at
<https://www.rfc-editor.org/rpc/wiki/doku.php?id=sourcecode-types>. If it does
not contain an applicable type, then feel free to let us know. Note that it is
also acceptable to leave the "type" attribute not set.
--> -->
</back>
</rfc> </rfc>
 End of changes. 168 change blocks. 
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