<?xml version='1.0'encoding='utf-8'?>encoding='UTF-8'?> <!DOCTYPE rfc [ <!ENTITY nbsp " "> <!ENTITY zwsp "​"> <!ENTITY nbhy "‑"> <!ENTITY wj "⁠"> ]><?xml-stylesheet type="text/xsl" href="rfc2629.xslt" ?> <!-- generated by https://github.com/cabo/kramdown-rfc version 1.7.29 (Ruby 3.4.4) --><rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft-ietf-lamps-dilithium-certificates-13" number="9881" updates="" obsoletes="" xml:lang="en" category="std" consensus="true" submissionType="IETF" tocInclude="true" sortRefs="true" symRefs="true" version="3"><!-- xml2rfc v2v3 conversion 3.30.2 --><front> <title abbrev="ML-DSA in Certificates">Internet X.509 Public Key Infrastructure--- Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algorithm (ML-DSA)</title> <seriesInfoname="Internet-Draft" value="draft-ietf-lamps-dilithium-certificates-13"/>name="RFC" value="9881"/> <author initials="J." surname="Massimo" fullname="Jake Massimo"> <organization>AWS</organization> <address> <postal><country>US</country><country>United States of America</country> </postal> <email>jakemas@amazon.com</email> </address> </author> <author initials="P." surname="Kampanakis" fullname="Panos Kampanakis"> <organization>AWS</organization> <address> <postal><country>US</country><country>United States of America</country> </postal> <email>kpanos@amazon.com</email> </address> </author> <author initials="S." surname="Turner" fullname="Sean Turner"> <organization>sn3rd</organization> <address> <email>sean@sn3rd.com</email> </address> </author> <author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan"> <organization>Cloudflare</organization> <address> <email>bas@cloudflare.com</email> </address> </author> <date year="2025"month="September" day="30"/>month="October"/> <area>SEC</area><workgroup>LAMPS WG</workgroup> <keyword>ML-DSA Certificate X.509 PKIX</keyword><workgroup>lamps</workgroup> <keyword>ML-DSA</keyword> <keyword>Certificate</keyword> <keyword>X.509</keyword> <keyword>PKIX</keyword> <abstract><?line 147?><t>Digital signatures are used within X.509certificates,certificates and Certificate Revocation Lists (CRLs), and to sign messages. This document specifies the conventions for using FIPS 204, the Module-Lattice-Based Digital Signature Algorithm (ML-DSA) in Internet X.509 certificates andcertificate revocation lists.CRLs. The conventions for the associated signatures, subject public keys, and private key are also described.</t> </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-certificates.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 mailing list (<eref target="mailto:spasm@ietf.org"/>), which is archived at <eref target="https://mailarchive.ietf.org/arch/browse/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> <middle><?line 156?><section anchor="introduction"> <name>Introduction</name> <t>The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a quantum-resistant digital signature scheme standardized by the US National Institute of Standards and Technology (NIST) PQC project <xref target="NIST-PQC"/> in <xref target="FIPS204"/>. This document specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX) certificates and Certificate Revocation Lists (CRLs) at three security levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.</t> <t><xref target="FIPS204"/> defines two variants of ML-DSA:apure anda pre-hash variant.pre-hash. Only the former is specified in this document. See <xref target="sec-disallow-hash"/> for the rationale. The pure variant of ML-DSA supports the typical pre-hash flow. Refer to <xref target="externalmu"/> for more details.</t> <t>Prior tostandardisation,standardization, ML-DSA was known as Dilithium. ML-DSA and Dilithium are not compatible.</t> <section anchor="requirements-language"> <name>Requirements Language</name><t>The<t> The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be interpreted as described inBCP 14BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and only when, they appear in all capitals, as shownhere.</t> <?line -18?>here. </t> </section> </section> <section anchor="oids"> <name>Identifiers</name> <!-- [rfced] The AlgorithmIdentifier type defined in [RFC5912] includes an "&" character before "Params". Please review and let us know if the ampersand should be included in the first block of sourcecode. In addition, the first line extends 3 characters beyond the margin. Please let us know how the line can be broken. Current: AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= SEQUENCE { algorithm ALGORITHM-TYPE.id({AlgorithmSet}), parameters ALGORITHM-TYPE. Params({AlgorithmSet}{@algorithm}) OPTIONAL } From [RFC5912]: AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= SEQUENCE { algorithm ALGORITHM-TYPE.&id({AlgorithmSet}), parameters ALGORITHM-TYPE. &Params({AlgorithmSet}{@algorithm}) OPTIONAL } --> <t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC5912"/> as follows:</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= SEQUENCE { algorithm ALGORITHM-TYPE.id({AlgorithmSet}), parameters ALGORITHM-TYPE. Params({AlgorithmSet}{@algorithm}) OPTIONAL} ]]></artwork>}]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t>The fields in AlgorithmIdentifier have the following meanings:</t> <ul spacing="normal"> <li> <t><tt>algorithm</tt> identifies the cryptographic algorithm with an object identifier (OID).</t> </li> <li> <t><tt>parameters</tt>, which are optional, are the associated parameters for the algorithm identifier in the algorithm field.</t> </li> </ul> <t>TheNIST registeredNIST-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) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) } id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) } id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19)} ]]></artwork>}]]></sourcecode> <t>The contents of the <tt>parameters</tt> component for each <tt>algorithm</tt> <bcp14>MUST</bcp14> be absent.</t> </section> <section anchor="ml-dsa-signatures-in-pkix"> <name>ML-DSA Signatures in PKIX</name> <t>ML-DSA is a digital signature scheme built upon the Fiat-Shamir-with-aborts framework <xref target="Fiat-Shamir"/>. The security is based upon the hardness of lattice problems over module lattices <xref target="Dilithium"/>. ML-DSA provides three parameter sets for the NIST PQC security categories 2,33, and 5.</t> <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 certificate, a signature is encoded with an algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute that contains the actual signature.</t><artwork><![CDATA[<!-- [rfced] The following sentences makes it seem like this ASN.1 is copied from [RFC5280], but this exact source code doesn't appear to be in [RFC5280]. Perhaps the intent is to indicate the use "1988 ASN.1 syntax"? Current: As shown in the ASN.1 representation from [RFC5280] below, in an X.509 certificate, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature. Certificate ::= SIGNED{ TBSCertificate } SIGNED{ToBeSigned} ::= SEQUENCE { toBeSigned ToBeSigned, algorithmIdentifier SEQUENCE { algorithm SIGNATURE-ALGORITHM. &id({SignatureAlgorithms}), parameters SIGNATURE-ALGORITHM. &Params({SignatureAlgorithms} {@algorithmIdentifier.algorithm}) OPTIONAL }, signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value( {SignatureAlgorithms} {@algorithmIdentifier.algorithm})) }]]></artwork>Same issue occurs here: Current: Signatures are also used in the CRL list ASN.1 representation from [RFC5280] below. In a X.509 CRL, a signature is encoded with an algorithm identifier in the signatureAlgorithm attribute and a signatureValue attribute that contains the actual signature. CertificateList ::= SIGNED{ TBSCertList } --> <sourcecode type="asn.1"><![CDATA[ Certificate ::= SIGNED{ TBSCertificate } SIGNED{ToBeSigned} ::= SEQUENCE { toBeSigned ToBeSigned, algorithmIdentifier SEQUENCE { algorithm SIGNATURE-ALGORITHM. &id({SignatureAlgorithms}), parameters SIGNATURE-ALGORITHM. &Params({SignatureAlgorithms} {@algorithmIdentifier.algorithm}) OPTIONAL }, signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value( {SignatureAlgorithms} {@algorithmIdentifier.algorithm})) }]]></sourcecode> <t>Signatures are also used in the CRL list ASN.1 representation from <xref target="RFC5280"/> below. Inaan X.509 CRL, a signature is encoded with an algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute that contains the actual signature.</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ CertificateList ::= SIGNED{ TBSCertList} ]]></artwork>}]]></sourcecode> <t>The following <tt>SIGNATURE-ALGORITHM</tt> ASN.1 classes are for ML-DSA-44, ML-DSA-65, and ML-DSA-87:</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-44 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-44 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } } sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-65 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-65 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } } sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-87 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 }} ]]></artwork>}]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t>The identifiers defined in <xref target="oids"/> can be used as the <tt>AlgorithmIdentifier</tt> in the <tt>signatureAlgorithm</tt> field in the sequence <tt>Certificate</tt>/<tt>CertificateList</tt> and in the <tt>signature</tt> field in the sequence <tt>TBSCertificate</tt>/<tt>TBSCertList</tt> in certificates and CRLs, respectively, <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>AlgorithmIdentifier</tt> <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> <t>The <tt>signatureValue</tt> field contains the corresponding ML-DSA signature computed upon the ASN.1DER encodedDER-encoded <tt>tbsCertificate</tt>/<tt>tbsCertList</tt> <xref target="RFC5280"/>. The optional context string (ctx) parameter as defined in Section 5.2 of <xref target="FIPS204"/> is left to its default value: the empty string.</t> <t>Conforming Certification Authority (CA) implementations <bcp14>MUST</bcp14> specify the algorithms explicitly by using the OIDs specified in <xref target="oids"/> when encoding ML-DSA signatures in certificates and CRLs. Conforming client implementations that process certificates and CRLs using ML-DSA <bcp14>MUST</bcp14> recognize the corresponding OIDs. Encoding rules for ML-DSA signature values are specified in <xref target="oids"/>.</t> </section> <section anchor="ML-DSA-PublicKey"> <name>ML-DSA Public Keys in PKIX</name> <t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has the <tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE { algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}}, subjectPublicKey BIT STRING} ]]></artwork>}]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning:</t> <ul spacing="normal"> <li> <t><tt>algorithm</tt> is the algorithm identifier and parameters for the public key (see above).</t> </li> <li> <t><tt>subjectPublicKey</tt> contains the public key.</t> </li> </ul> <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> type, 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>SubjectPublicKeyInfo</tt> type in an 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 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><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ pk-ml-dsa-44 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-44 -- KEY no ASN.1 wrapping -- CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-44-PrivateKey } -- defined in Section 6 pk-ml-dsa-65 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-65 -- KEY no ASN.1 wrapping -- CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-65-PrivateKey } -- defined in Section 6 pk-ml-dsa-87 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-87 -- KEY no ASN.1 wrapping -- CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-87-PrivateKey } -- defined in Section 6 ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312)) ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952)) ML-DSA-87-PublicKey ::= OCTET STRING (SIZE(2592)) ]]></artwork>(2592))]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t><xref target="RFC5958"/> specifies the Asymmetric Key Package's <tt>OneAsymmetricKey</tt> type for encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded as a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-key"/>.</t> <t>When the ML-DSA private key appears outside of an Asymmetric Key Package in an environment that uses ASN.1 encoding, it can be encoded using one of thethe<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 public key.</t> <t><xref target="examples"/> contains example ML-DSA public keys encoded using the textual encoding defined in <xref target="RFC7468"/>.</t> </section> <section anchor="key-usage-bits"> <name>Key Usage Bits</name> <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="RFC5280"/>. If the <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>SubjectPublicKeyInfo</tt>, then the subject public key can only be used for verifying digital signatures on certificates or CRLs, or those used in an entity authentication service, a data origin authentication service, an integrity service, and/or a non-repudiation service that protects against the signing entity falsely denying some action. This means that the <tt>keyUsage</tt>extentionextension <bcp14>MUST</bcp14> have at least one of the following bits set:</t><artwork><![CDATA[ digitalSignature nonRepudiation keyCertSign cRLSign ]]></artwork><ul spacing="normal"> <li>digitalSignature</li> <li>nonRepudiation</li> <li>keyCertSign</li> <li>cRLSign</li> </ul> <t>ML-DSA subject public keys cannot be used to establish keys or encrypt data, so the <tt>keyUsage</tt>extentionextension <bcp14>MUST NOT</bcp14> have any of the following bits set:</t><artwork><![CDATA[ keyEncipherment, dataEncipherment, keyAgreement, encipherOnly, and decipherOnly. ]]></artwork><ul spacing="normal"> <li>keyEncipherment</li> <li>dataEncipherment</li> <li>keyAgreement</li> <li>encipherOnly</li> <li>decipherOnly</li> </ul> <t>Requirements about the <tt>keyUsage</tt> extension bits defined in <xref target="RFC5280"/> still apply.</t> </section> <section anchor="priv-key"> <name>Private Key Format</name> <t><xref target="FIPS204"/> specifies two formats for an ML-DSA private key: a 32-octet seed (xi) and an (expanded) private key. The expanded private key (and public key) 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 encode a private 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 key to be included as well. For illustration, the ASN.1 structure <tt>OneAsymmetricKey</tt> is replicated below.</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ OneAsymmetricKey ::= SEQUENCE { version Version, privateKeyAlgorithm SEQUENCE { algorithm PUBLIC-KEY.&id({PublicKeySet}), parameters PUBLIC-KEY.&Params({PublicKeySet} {@privateKeyAlgorithm.algorithm}) OPTIONAL} privateKey OCTET STRING (CONTAINING PUBLIC-KEY.&PrivateKey({PublicKeySet} {@privateKeyAlgorithm.algorithm})), attributes [0] Attributes OPTIONAL, ..., [[2: publicKey [1] BIT STRING (CONTAINING PUBLIC-KEY.&Params({PublicKeySet} {@privateKeyAlgorithm.algorithm}) OPTIONAL ]], ...} ]]></artwork>}]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5958"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>.</t> </aside> <t>For ML-DSA private keys, the <tt>privateKey</tt> field in <tt>OneAsymmetricKey</tt> contains one of the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> format is a fixed32 byte32-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 vary in size by security level:</t><artwork><![CDATA[<sourcecode type="asn.1"><![CDATA[ ML-DSA-44-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (2560)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (2560)) } } ML-DSA-65-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4032)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4032)) } } ML-DSA-87-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4896)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4896)) }} ]]></artwork>}]]></sourcecode> <aside> <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compatible with the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> </aside> <t>The <tt>CHOICE</tt> allows three representations of the private key:</t> <ol spacing="normal" type="1"><li> <t>The <tt>seed</tt> format (tag <tt>[0]</tt>) contains just the 32-byte seed value (xi) from which both the expanded private key and public key can be derived using <tt>ML-DSA.KeyGen_internal(xi)</tt>.</t> </li> <li> <t>The <tt>expandedKey</tt> format contains the expanded private key that was derived from the seed.</t> </li> <li> <t>The <tt>both</tt> format contains both the seed and expanded private key, allowing forforinteroperability; some may want to use and retain the seed and others may only support expanded private keys.</t> </li> </ol> <t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> object, any of these three formats may be used, though the seed format is <bcp14>RECOMMENDED</bcp14> for storage efficiency.</t> <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>publicKey</tt> field will hold the encoded public key as defined in <xref target="ML-DSA-PublicKey"/>.</t> <aside> <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. Both the expanded private key and the public key can be deterministically derived from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt>. Alternatively, the public 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-only format, they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during import operations.</t> </aside> <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-specific 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 <tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, rather than any 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 textual encoding defined in <xref target="RFC7468"/>.</t> </section> <section anchor="iana-considerations"> <name>IANA Considerations</name> <t>For the ASN.1 module in <xref target="asn1"/>, IANAis requested to assign anhas assigned the following object identifier (OID)for the module identifier (TBD1) with a Description of "id-mod-x509-ml-dsa-2025". The OID for the module should be allocatedin the "SMI Security for PKIX Module Identifier" registry(1.3.6.1.5.5.7.0).</t>(1.3.6.1.5.5.7.0): </t> <table anchor="oid"> <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 anchor="operational-considerations"> <name>Operational Considerations</name> <section anchor="private-key-format"> <name>Private Key Format</name> <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 by <xref target="FIPS204"/> as an acceptable representation of a keypair. In particular, generating the seed in one cryptographic module and then importing or exporting it into another cryptographic module is allowed. The internal key generation function <tt>ML-DSA.KeyGen_internal(xi)</tt> can be accessed for this purpose.</t> <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 full key is expanded from seed and the seed discarded, the seed cannot bere-createdrecreated, even if the full expanded private key is available. For thisreasonreason, 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 implemented by including the seed xi that is randomly generated at line 1 of Algorithm 1 <tt>ML-DSA.KeyGen</tt> in the returned output.</t> <t>When encoding an ML-DSA private key in a OneAsymmetricKey object, any of these three formats may be used, though the seed format is <bcp14>RECOMMENDED</bcp14> for storage efficiency.</t> </section> <section anchor="private-key-consistency-testing"> <name>Private Key Consistency Testing</name> <t>When receiving a private key that contains both the seed and the expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency check to ensure that the sender properly generated the private key. Recipients that do not perform this seed consistency check avoid keygen and compare operations, but are unable to ensure that the <tt>seed</tt> and <tt>expandedKey</tt> match.</t> <t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</tt> are not consistent, the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t> <t>The seed consistency check consists of regenerating the expanded form from the seed via<tt>ML-DSA.KeyGen_internal</tt><tt>ML-DSA.KeyGen_internal</tt>, and ensuring it is bytewise equal to the value presented in the private key.</t> <t><xref target="example-bad"/> includes some examples of inconsistent seeds and expanded private keys.</t> </section> <section anchor="sec-disallow-hash"> <name>Rationale fordisallowingDisallowing HashML-DSA</name> <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 <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 certificates used for CRLs, OCSP, certificateissuanceissuance, and related PKIX protocols. This restriction is primarily to increase interoperability.</t> <t>ML-DSA and HashML-DSA are incompatible algorithms that require different <tt>Verify()</tt> routines. This introduces the complexity of informing the verifier whether to use <tt>ML-DSA.Verify()</tt> or <tt>HashML-DSA.Verify()</tt>. Additionally, since the same OIDs are used to identify the ML-DSA 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 <tt>HashML-DSA</tt> at the time of certificate creation. This is anticipated to cause operational issues in contexts where the operator does not know whether the key will need to produce pure or pre-hashed signatures atkey generationkey-generation time. The External μ (mu) mode described in <xref target="externalmu"/> avoids all of these operational concerns.</t> <t>A minor security reason for disallowing HashML-DSA is that the design of the ML-DSA algorithm provides enhanced resistance against collision attacks, 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>) 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 unlikely discovery of a collision attack against the SHA-3 family, an attacker 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> sincem2)</tt>, because a direct hash collision <tt>H(m1) = H(m2)</tt> will not suffice. HashML-DSA removes this enhanced security property. In spite of its lack of targeted collision protection, the practical security risk of using HashML-DSA in X.509 signatures would be immaterial.ThatThis is because a hash of the issuing CA's public key is already included in the Authority Key Identifier (AKI)extensionextension, which is signed as part of the tbsCertificate structure. Even when it is a SHA-1 hash, general second pre-images against the AKI hash of existing issuing CAs would be impractical.</t> </section> </section> <section anchor="security-considerations"> <name>Security Considerations</name> <t>The Security Considerations section of <xref target="RFC5280"/> applies to this specification as well.</t> <t>The ML-DSA signature scheme is strongly unforgeable under chosen message attacks (SUF-CMA). For the purpose of estimating security strength, it has been assumed that the attacker has access to signatures for no more than 2^{64} chosen messages.</t> <t>ML-DSA depends on high quality random numbers that are suitable for use in cryptography. The use of inadequate pseudo-random number generators (PRNGs) to generate such values can significantly undermine various security properties. For instance, using an inadequate PRNG for key generation, might allow an attacker to efficiently recover the private key by trying a small set of possibilities, rather thanbrute forcebrute-force search the whole keyspace. The generation of random 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 information.</t> <!-- [rfced] May we rephrase this as "deliver a secure implementation with greater ease"? In addition, to what does "it" refer - perhaps it should be "they"? Original: While deliberate design decisions such as these can help to deliver a greater ease of secure implementation - particularly against side-channel attacks - it does not necessarily provide resistance to more powerful attacks such as differential power analysis. --> <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 on Gaussian sampling. Implementations must still take great care not to leak information via various side channels. While deliberate design decisions such as these can help to deliver a greater ease of secure implementation--- particularly against side-channel attacks--- it does not necessarily provide resistance to more powerful attacks such as differential power analysis. Some amount of side-channel leakage has been demonstrated in parts of the signing algorithm (specifically the bit-unpacking function), from which a demonstration of key recovery has been made over a large sample of signatures. Masking countermeasures exist for ML-DSA, butcomecomes withaperformance overhead.</t> <t>ML-DSA offers both deterministic and randomized signing. Signatures generated with either mode are compatible and averifyerverifier can't tell them apart. In the deterministic case, a signature only depends on the private key and the message to be signed. This makes the implementation easier to test and does not require a randomness source during signing. In the randomized case, signing mixes in a 256-bit random string from an approved random bit generator (RBG). When randomized, ML-DSA is easier to harden against fault and hardware side-channel attacks.</t> <!-- [rfced] Should "key pair" be "keypair" here as used elsewhere in the document? Original: Non-repudiation refers to the assurance that the owner of a signature key pair that was capable of generating an existing signature corresponding to certain data cannot convincingly deny having signed the data, unless its private key was compromised. --> <t>A security property that is also associated with digital signatures is non-repudiation. Non-repudiation refers to the assurance that the owner of a signature key pair that was capable of generating an existing signature corresponding to certain data cannot convincingly deny having signed the data, unless its private key was compromised. The digital signature scheme ML-DSApossesspossesses three security properties beyond unforgeability, that are associated with non-repudiation. These are exclusive ownership, message-bound signatures, and non-resignability. These properties are based tightly on the assumed collision resistance of the hash function used (in this case SHAKE-256). A full discussion of these properties in ML-DSA can be found at <xref target="CDFFJ21"/>.</t> </section> </middle> <back> <references anchor="sec-combined-references"> <name>References</name> <references anchor="sec-normative-references"> <name>Normative References</name> <reference anchor="X680" target="https://www.itu.int/rec/T-REC-X.680"> <front> <title>Information Technology -- Abstract Syntax Notation One (ASN.1): Specification of basic notation</title> <author> <organization>ITU-T</organization> </author> <date year="2021" month="February"/> </front> <seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/> </reference> <reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690"> <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> <author> <organization>ITU-T</organization> </author> <date year="2021" month="February"/> </front> <seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/> </reference><reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer-security-objects-register/algorithm-registration"> <front> <title>Computer Security Objects Register</title> <author initials="" surname="NIST" fullname="National Institute of Standards and Technology"> <organization/> </author> <date year="2024" month="August" day="20"/> </front> </reference> <reference anchor="FIPS204"> <front> <title>Module-lattice-based digital signature standard</title> <author> <organization/> </author> <date month="August" year="2024"/> </front> <seriesInfo name="DOI" value="10.6028/nist.fips.204"/> <refcontent>National Institute of Standards and Technology (U.S.)</refcontent> </reference> <reference anchor="RFC2119"> <front> <title>Key words<!-- [rfced] [FIPS204] FYI: We have updated the date foruse in RFCs to Indicate Requirement Levels</title> <author fullname="S. Bradner" initials="S." surname="Bradner"/> <date month="March" year="1997"/> <abstract> <t>In many standards track documents several words are usedthis reference from August 2023 tosignify the requirements inAugust 2024. We also replaced thespecification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices fororiginal URL (https://csrc.nist.gov/projects/post-quantum-cryptography) with theInternet Community, 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</title> <author fullname="B. Leiba" initials="B." surname="Leiba"/> <date month="May" year="2017"/> <abstract> <t>RFC 2119 specifies common key wordsone thatmay be used in protocol specifications. This document aimspoints toreducetheambiguity by clarifying that only UPPERCASE usagemost recent version ofthe 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>FIPS 204 (https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.204.pdf). --> <referenceanchor="RFC5912">anchor="FIPS204" target="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.204.pdf"> <front><title>New ASN.1 Modules for the Public Key Infrastructure Using X.509 (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 format, 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 changes to any<title>Module-Lattice-Based Digital Signature Standard</title> <author> <organization abbrev="NIST">National Institute ofthe formats; this is simply a change to the syntax. This document is not an InternetStandardsTrack specification; it is published for informational purposes.</t> </abstract>and Technology</organization> </author> <date day="13" year="2024" month="August"/> </front> <seriesInfoname="RFC" value="5912"/>name="NIST FIPS" value="204"/> <seriesInfo name="DOI"value="10.17487/RFC5912"/>value="10.6028/NIST.FIPS.204 "/> </reference><reference anchor="RFC5280"> <front> <title>Internet X.509 Public Key Infrastructure Certificate and Certificate 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<!-- [rfced] [CSOR] FYI: We updated theX.509 v3 certificate and X.509 v2 certificate revocation list (CRL)date foruse in the Internet. An overview ofthisapproach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regardingreference from 20 August 2024 to 13 June 2025 to match theformat and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples aredate providedinat theappendices. [STANDARDS-TRACK]</t> </abstract> </front> <seriesInfo name="RFC" value="5280"/> <seriesInfo name="DOI" value="10.17487/RFC5280"/> </reference>URL. --> <referenceanchor="RFC5958">anchor="CSOR" target="https://csrc.nist.gov/projects/computer-security-objects-register/algorithm-registration"> <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 and a content type for it. Private-key information includes a private key for a specified public-key algorithm and a set<title>Computer Security Objects Register (CSOR)</title> <author> <organization abbrev="NIST">National Institute ofattributes. The Cryptographic Message Syntax (CMS), as defined in RFC 5652, can be used to digitally sign, digest, authenticate, or encrypt the asymmetric key format content type. This document obsoletes RFC 5208. [STANDARDS-TRACK]</t> </abstract>Standards and Technology</organization> </author> <date year="2025" month="June" day="13"/> </front><seriesInfo name="RFC" value="5958"/> <seriesInfo name="DOI" value="10.17487/RFC5958"/></reference> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2119.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8174.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5912.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5280.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5958.xml"/> </references> <references anchor="sec-informative-references"> <name>Informative References</name> <reference anchor="Dilithium" target="https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf"> <front> <title>CRYSTALS-Dilithium Algorithm Specifications and SupportingDocumentation</title>Documentation (Version 3.1)</title> <author initials="S." surname="Bai"> <organization/> </author> <author initials="L." surname="Ducas"> <organization/> </author> <author initials="E." surname="Kiltz"> <organization/> </author> <author initials="T." surname="Lepoint"> <organization/> </author> <author initials="V." surname="Lyubashevsky"> <organization/> </author> <author initials="P." surname="Schwabe"> <organization/> </author> <author initials="G." surname="Seiler"> <organization/> </author> <author initials="D." surname="Stehlé"> <organization/> </author> <date day="8" month="2" year="2021"/> </front> </reference> <reference anchor="Fiat-Shamir" target="https://www.iacr.org/archive/asiacrypt2009/59120596/59120596.pdf"> <front> <title>Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures</title> <author initials="V." surname="Lyubashevsky"> <organization/> </author> <date year="2009"/> </front><seriesInfo name="International<refcontent>International Conference on the Theory and Application of Cryptology and InformationSecurity" value=""/>Security</refcontent> </reference> <!-- [rfced] [CDFFJ21] Please review. The original date for this reference is 2021. The version of this paper in the Cryptology ePrint Archive was updated in October 2023 (see the "Note" at this URL: https://eprint.iacr.org/2020/1525). The 2021 version is available for free from IEEE - https://ieeexplore.ieee.org/document/9519420 Should this reference point to the updated (2023) version at the Cryptology ePrint Archive or to the 2021 version of this paper? --> <!-- Note: IEEE version of [CDFFJ21] --> <reference anchor="CDFFJ21"target="https://eprint.iacr.org/2020/1525.pdf">target="https://ieeexplore.ieee.org/document/9519420"> <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 year="2021"/> </front> <seriesInfoname="In Proceedings of the 42ndname="DOI" value="10.1109/SP40001.2021.00093"/> <refcontent>2021 IEEE Symposium on Security andPrivacy" value=""/>Privacy (SP), pp. 1696-1714</refcontent> </reference> <!-- Note: Cryptology ePrint Archive version of [CDFFJ21] <reference anchor="CDFFJ21" target="https://eprint.iacr.org/2020/1525.pdf"> <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> --> <!-- [rfced] [NIST-PQC] FYI: We have updated the date for this reference from 20 December 2016 to 28 July 2025 to match the date provided at the URL. --> <reference anchor="NIST-PQC" target="https://csrc.nist.gov/Projects/post-quantum-cryptography"> <front> <title>Post-Quantum CryptographyProject</title>(PQC)</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology (NIST)</organization>Technology</organization> </author> <dateyear="2016" month="December" day="20"/>year="2025" month="July" day="28"/> </front> </reference> <reference anchor="FIPS204-ExternalMuFAQ" target="https://csrc.nist.gov/csrc/media/Projects/post-quantum-cryptography/documents/faq/fips204-sec6-03192025.pdf"> <front> <title>FIPS 204 Section 6 FAQ</title> <author><organization>National<organization abbrev="NIST">National Institute of Standards andTechnology (NIST)</organization>Technology</organization> </author> <date year="2025"/> </front> </reference><reference anchor="RFC7468"> <front> <title>Textual Encodings of PKIX, PKCS, and CMS Structures</title> <author fullname="S. Josefsson" initials="S." surname="Josefsson"/> <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 (PKCS), and Cryptographic Message Syntax (CMS). The textual encodings are well-known, are implemented by several applications and libraries, and are widely deployed. This document articulates the de facto rules by which existing implementations 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 and 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 certificate policies or certification practice statements for participants within public 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 writer's discretion) need to be covered in a certificate policy or a certification practice statement. This document supersedes RFC 2527.</t> </abstract> </front> <seriesInfo name="RFC" value="3647"/> <seriesInfo name="DOI" value="10.17487/RFC3647"/> </reference><xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7468.xml"/> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3647.xml"/> </references> </references><?line 726?><section anchor="asn1"> <name>ASN.1 Module</name> <t>This appendix includes the ASN.1 module <xref target="X680"/> for the ML-DSA. Note that as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rules; see <xref target="X690"/>. This module imports objects from <xref target="RFC5912"/>.</t> <sourcecode type="asn.1" markers="true"><![CDATA[ X509-ML-DSA-2025 { iso(1) identified-organization(3) dod(6) 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 EXPORTS ALL; IMPORTS PUBLIC-KEY, SIGNATURE-ALGORITHM FROM AlgorithmInformation-2009 -- [RFC 5912] { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-algorithmInformation-02(58) } ; -- -- ML-DSA Identifiers -- nistAlgorithms OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithms(4) } sigAlgs OBJECT IDENTIFIER ::= { nistAlgorithms 3 } id-ml-dsa-44 OBJECT IDENTIFIER ::= { sigAlgs 17 } id-ml-dsa-65 OBJECT IDENTIFIER ::= { sigAlgs 18 } id-ml-dsa-87 OBJECT IDENTIFIER ::= { sigAlgs 19 } -- -- Public Key Algorithms -- PublicKeys PUBLIC-KEY ::= { -- This expands PublicKeys from [RFC 5912] pk-ml-dsa-44 | pk-ml-dsa-65 | pk-ml-dsa-87, ... } -- -- ML-DSA Public Keys -- pk-ml-dsa-44 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-44 -- KEY no ASN.1 wrapping; 1312 octets -- PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-44-PrivateKey } ML-DSA-44-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (2560)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (2560)) } } pk-ml-dsa-65 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-65 -- KEY no ASN.1 wrapping; 1952 octets -- PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-65-PrivateKey } ML-DSA-65-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4032)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4032)) } } pk-ml-dsa-87 PUBLIC-KEY ::= { IDENTIFIER id-ml-dsa-87 -- KEY no ASN.1 wrapping; 2592 octets -- PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } PRIVATE-KEY ML-DSA-87-PrivateKey } ML-DSA-87-PrivateKey ::= CHOICE { seed [0] OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4896)), both SEQUENCE { seed OCTET STRING (SIZE (32)), expandedKey OCTET STRING (SIZE (4896)) } } ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312)) ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952)) ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2602)) -- -- Signature Algorithms -- SignatureAlgorithms SIGNATURE-ALGORITHM ::= { -- This expands SignatureAlgorithms from [RFC 5912] sa-ml-dsa-44 | sa-ml-dsa-65 | sa-ml-dsa-87, ... } -- -- ML-DSA Signature Algorithm Identifiers -- sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-44 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-44 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } } sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-65 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-65 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } } sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= { IDENTIFIER id-ml-dsa-87 PARAMS ARE absent PUBLIC-KEYS { pk-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } } END ]]></sourcecode> </section> <section anchor="security-strengths"> <name>Security Strengths</name><t>Instead<!-- [rfced] Please consider whether "traditional" has a universal meaning as used here: Instead of defining the strength of a quantum algorithm in a traditional manner using the imprecise notion of bits of security, NIST has instead elected to define security levels by picking a reference scheme, which NIST expects to offer notable levels of resistance to both quantum and classical attack. --> <t>Instead of defining the strength of a quantum algorithm in a traditional manner using the imprecise notion of bits of security, NIST has instead elected to define security levels by picking a reference scheme, which NIST expects to offer notable levels of resistance to both quantum and classical attacks. To wit, an algorithm that achieves NIST PQC security level 1 must require computational resources to break the relevant security property, which are greater than those required for a brute-force key search on AES-128. Levels 3 and 5 use AES-192 and AES-256 asreferencereferences, respectively. Levels 2 and 4 use collision search for SHA-256 and SHA-384 asreference.</t>references.</t> <t>The parameter sets defined for NIST security levels 2,33, and 5 are listed intheFigure 1, along with the resulting signature size, public key, and private key sizes in bytes. Note that these are the sizes of the raw keys, not including ASN.1 encoding overhead from OneAsymmetricKey and SubjectPublicKeyInfo wrappers. Private key sizes are shown for both the seed format and expanded format.</t><figure<table anchor="ML-DSAParameters"> <name>ML-DSA Parameters</name><artwork><![CDATA[ |=======+=======+=====+========+========+==========+==========| | Level | (k,l) | eta | Sig. | Public | Private | Private | | | | | (B) | Key(B) | Seed(B) | Expand(B)| |=======+=======+=====+========+========+==========+==========| | 2 | (4,4) | 2 | 2420 | 1312 | 32 | 2560 | | 3 | (6,5) | 4 | 3309 | 1952 | 32 | 4032 | | 5 | (8,7) | 2 | 4627 | 2592 | 32 | 4896 | |=======+=======+=====+========+========+==========+==========| ]]></artwork> </figure><thead> <tr> <th>Level</th> <th>(k,l)</th> <th>eta</th> <th>Sig. (B)</th> <th>Public Key(B)</th> <th>Private Seed(B)</th> <th>Private Expand(B)</th> </tr> </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 anchor="examples"> <name>Examples</name> <t>This appendix contains examples of ML-DSA private keys, public keys, certificates, and inconsistent seed and expanded private keys.</t> <section anchor="example-private"> <name>Example Private Keys</name> <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, 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> format, and <tt>both</tt> formats together.</t> <aside> <t>NOTE: All examples use the same seed value, showing how the same seed produces different expanded private keys for each security level.</t> </aside> <section anchor="ml-dsa-44-private-key-examples"> <name>ML-DSA-44 Private Key Examples</name> <t>Each of the examples includes the textual encoding <xref target="RFC7468"/> followed by the so-called "pretty print"; the private keys are the same.</t> <section anchor="seed-format"> <name>Seed Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ GhscHR4f -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } OCTET_STRING { [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 5161718191a1b1c1d1e1f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp 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} } OCTET_STRING { OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178 9dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff9a 613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe623 ec810db3bee33685854a88269da320d5120bfcfe89a18e30f7114d83aa404a64 6b6c997389860d12522ee0006e2384819186619b260d118664d4a62822184482 402898146148a6614c4248a19208c2382951244808a125c2083108c471201409 14836c18a78084106ec9c07022b56408b0610c07049812445188695900462293 2041062e42b64c01164914284c41a85180460a5116515a0820022244dc9849d1 3251e13065d3c08592a85112a1640039220946621cc70cd9086dd00626524085 80443091062c50c80924c5841a966d4a982c99066da4443220a7645a326e11b5 7020926124138e04852c0a4872c8a051d3082a99208058242024074e59148810 a46460c06de0b28d1b1909203422c024410943710a212061a2015222521b8080 9a340013934dd3322922170a9892691a14512027219cc02062a2814818691a85 4d8344695b2041031242cb184601a90d0c023183b0215a224ac89205d9906904 306a4b064ad2b2011c404081423252327254a6405a18100c321292c280521262 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e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe75 27e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafca8 6be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a56 46601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa1063 98f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c7217 b0689e21d8eb0ff69668` } }} ]]></artwork>}]]></artwork> </section> <section anchor="both-format"> <name>Both Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp vsk5zg9/d/jbVkTc2jZr/kc0vZX0Nf+aYTqlSqQcLGlMBDKaB7H6u0j1KjCfEaGJ j4SOIyL/5iPsgQ2zvuM2hYVKiCadoyDVEgv8/omhjjD3EU2DqkBKZGtsmXOJhg0S Ui7gAG4jhIGRhmGbJg0RhmTUpigiGESCQCiYFGFIpmFMQkihkgjCOClRJEgIoSXC CDEIxHEgFAkUg2wYp4CEEG7JwHAitWQIsGEMBwSYEkRRiGlZAEYikyBBBi5CtkwB FkkUKExBqFGARgpRFlFaCCACIkTcmEnRMlHhMGXTwIWSqFESoWQAOSIJRmIcxwzZ 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CeXRaFZ3gpNSnwKG0BXDtTmWGWQqMz6eWT1uP1NTmUII6eajMoUdf2UlIqkouRfi fi1tQhN9/i6/pvscZ7JsAlRShoX369vjFaaOqi2naeip9C0+YAB8cTMJJrLAAS2D 6tTk/R7YcszRlyIB0rAn81RawtMM14vB10D+zLxvwqBEbG4w6sUfWmkJiqLUR/II W05OS5LMwmkh0t5HhRjNCQziZ66i0nraV/2ItJdtifuEPNzPSadsomeeaAG/p/sD GJb7UGKXBLmSOTa7XdOFMREhyt+xGZXlm3MDTPZ+0Dq4E4Z2SNAlgoCH6Umpr9Fr ldctmbHtyiV6rBMv+3oHCa7VqcD/BfsPK78oQJ7te19YAb6WTO0Bnhy3hR04UfEC kGdOGf+wCLMBxKz2QaK7FCFuHWnKv1K17yJ0lrDzB5moVdEX+tN0Sm+jNQPqeYtS 3dfuVCZgnb/NPwwTsWTWwFH37UoRlxmnEuOI0yhAIIH/E1S1VNLCN6/tOxUcS6jp 9L3rhJmjBm4mu8aeivCJ3scXMdHcUp6rF+9zdHNMD+R1SUyDg2vdNKA7m8iZFHFg Yb+5jsbmHD7UQ47cryUkPGRwhrnqcBiw2aigsAzssAq94kmNacIzYQGncsvk9XFS P1G9BYgs3zWLhJzBQKofryJCOhKFHODjP9SJdaSVn6XF/kGMk5CBkatudBt3v+As vWmO55XEZtYVYZ5kQTgsbqwBg07pq3POqAu+I1x42pG9ebb4L4mXhdaHANOT5nXC Ik1rehrSEyBJVnmtrtcBZ7UIZnE6UxCdt7b32BME7N/YOzGbHvJIMGtFrSnn3cyG PaxWBItdaeoXUBH3YUwAqGqGPN4YcqiTKHi5rH4axb2kmXtyBk8M119MgU4DTeEa y5ATz36pJrTn6qzgcMe6IYjvrS5DHhIj1F3QXE2EA8LkXO5kE+y+dSfoc+RVxOYQ phg5qswL1W0kg+ePKYtmpHjrL1WMuvyoa+hHuusCxbIWyM2I/qTfJJsJ5nCiBwOr rCSwqRq8SlZGYBRCuhC+z9MJk4gAUdB/VqBak3nnqOa+/uPyL6oQY5j3cGAG5C6b 4e+J0lwnLxGpUJXFh9cTcyKE3p29PHIXsGieIdjrD/aWaA== -----END PRIVATE KEY----- ]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } OCTET_STRING { SEQUENCE { OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 15161718191a1b1c1d1e1f` } OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d1 789dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff 9a613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe6 23ec810db3bee33685854a88269da320d5120bfcfe89a18e30f7114d83aa404a 646b6c997389860d12522ee0006e2384819186619b260d118664d4a628221844 82402898146148a6614c4248a19208c2382951244808a125c2083108c4712014 0914836c18a78084106ec9c07022b56408b0610c070498124451886959004622 932041062e42b64c01164914284c41a85180460a5116515a0820022244dc9849 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encoding <xref target="RFC7468"/> followed by the so-called "pretty print"; the private keys are the same.</t> <section anchor="seed-format-1"> <name>Seed Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ GhscHR4f -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } } OCTET_STRING { [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 5161718191a1b1c1d1e1f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format-1"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r 8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy 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]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { INTEGER { 0 } SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } } OCTET_STRING { [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 5161718191a1b1c1d1e1f` } }} ]]></artwork>}]]></artwork> </section> <section anchor="expanded-format-2"> <name>Expanded Format</name> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX q0G5AljPp+kOyXEk2OnuTpChbGAvXsm8OFF9ww4ynVqydnO9hfTJsDAPd2OJiGdQ tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS IJkpEwVpXDRopDKOGSaSWUYQCaRJI0JNEjZhWBBlASiQGjNMmYYx06JJCYIlQxQo wDiBAxVNWyiGCIdIIzFSlCIlw8BNpJghmEAg0UKGy0BwW7BxnJYswRIGU0YJDEUC FEZukbQhVLCM5EZCmiCMASElE0EFWkAiE8kMoBhAUsIwyzQsS8hoG6RgSYSEYzAp SqBpW4AE0jgKFCZM4rJEi6IRJEZJxBRSC0JxA7IQkiiAASSI4wgRCgUoGcSBACAi 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482732a81a87f724f8d2e780b3a39d451a380f75c2d680cc7213eab1d4a59d39 4ae3810a1c90818d52f93fb203e2d8b1b5fa8f60b2d585d9135d648846f138b8 6953242d2bb1f2ecdf389b4de7651817b8e4e64b333f1aac523a93f2748a9c38 ffbc29ced457b6f9781b08a67a1975d031ccd71545c0037434056c2434d13e6c 4beebf46fc12222c0b2eccd6159d5aea8e554d7a09652b06bf7ca699a7199e71 6d05dd553041a8f2b303d236a9babaafb9fa528f28a2ca2aa780b940383c099a a65a0074b83fd1f0bc5b7b5e46c25e54838b3cbcfc95f87f1d471b3ba894434f a58952fdcb77f161372693306dba4e8f216d1c8e5caff0fe8360a51c60763644 169fdc6a8267f2e3f909a61b2a678bce6ae90403a836b1a7b7e8cd8b54c37087 a9e14446d95e6908d2eedbfcc653e02fdf771f701a79b9e5a26ed0a947842070 f3b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec09 1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61 a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257 e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2 c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287 beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154 149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913 1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df aa6d9d5a6eb99ae4ddf424` } } }} ]]></artwork>}]]></artwork> </section> </section> </section> <section anchor="example-public"> <name>Example Public Keys</name> <t>The following is the ML-DSA-44 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIFMjALBglghkgBZQMEAxEDggUhANeytHJUquDbReeTDUqY0sl9jxOX0Xidr6Fw JLMW6b7JT8mUbULxm3mnQTu6oz5xSctC7VEVaTrAQfrLmIretf4OHYYxGEmVtZLD l9IpTi4U+QqkFLo4JomaxD9MzKy8JumoMrlRGNXLQzy++WYLABOOCBf2HnYsonTD atVU6yKqwRYuSrAay6HjjE79j4C2WzM9D3LlXf5xzpweu5iJ58VhBsD9c4A6Kuz+ r97XqjyyztpU0SvYzTanjPl1lDtHq9JeiArEUuV0LtHo0agq+oblkMdYwVrk0oQN kryhpQkPQElll/yn2LlRPxob2m6VCqqY3kZ1B9Sk9aTwWZIWWCw1cvYu2okFqzWB ZwxKAnd6M+DKcpX9j0/20aCjp2g9ZfX19/xg2gI+gmxfkhRMAvfRuhB1mHVT6pNn /NdtmQt/qZzUWv24g21D5Fn1GH3wWEeXCaAepoNZNfpwRgmQzT3BukAbqUurHd5B rGerMxncrKBgSNTE7vJ+4TqcF9BTj0MPLWQtwkFWYN54h32NirxyUjl4wELkKF9D GYRsRBJiQpdoRMEOVWuiFbWnGeWdDGsqltOYWQcf3MLN51JKe+2uVOhbMY6FTo/i svPt+slxkSgnCq/R5QRMOk/a/Z/zH5B4S46ORZYUSg2vWGUR09mWK56pWvGXtOX8 YPKx7RXeOlvvX4m9x52RBR2bKBbnT6VFMe/cHL501EiFf0drzVjyHAtlOzt2pOB2 plWaMCcYVVzGP3SFmqurkl8COGHKjND3utsocfZ9VTJtdFETWtRfShumkRj7ssij DuyTku8/l3Bmya3VxxDMZHsVFNIX2VjHAXw+kP0gwE5nS5BIbpNwoxoAHTL0c5ee SQZ0nn5Hf6C3RQj4pfI3gxK4PCW9OIygsP/3R4uvQrcWZ+2qyXxGsSlkPlhuWwVa DCEZRtTzbmdb7Vhg+gQqMV2YJhZNapI3w1pfv0lUkKW9TfJIuVxKrneEtgVnMWas QkW1tLCCoJ6TI+YvIHjFt2eDRG3v1zatOjcC1JsImESQCmGDM5e8RBmzDXqXoLOH wZEUdMTUG1PjKpd6y28Op122W7OeWecB52lX3vby1EVZwxp3EitSBOO1whnxaIsU 7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/ XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo 7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI= -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17 89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156 93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3 826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7 62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55 dfe71ce9c1ebb9889e7c56106c0fd73803a2aecfeafded7aa3cb2ceda54d12bd 8cd36a78cf975943b47abd25e880ac452e5742ed1e8d1a82afa86e590c758c15 ae4d2840d92bca1a5090f40496597fca7d8b9513f1a1bda6e950aaa98de46750 7d4a4f5a4f0599216582c3572f62eda8905ab3581670c4a02777a33e0ca7295f d8f4ff6d1a0a3a7683d65f5f5f7fc60da023e826c5f92144c02f7d1ba1075987 553ea9367fcd76d990b7fa99cd45afdb8836d43e459f5187df058479709a01ea 6835935fa70460990cd3dc1ba401ba94bab1dde41ac67ab3319dcaca06048d4c 4eef27ee13a9c17d0538f430f2d642dc2415660de78877d8d8abc72523978c04 2e4285f4319846c44126242976844c10e556ba215b5a719e59d0c6b2a96d3985 9071fdcc2cde7524a7bedae54e85b318e854e8fe2b2f3edfac9719128270aafd 1e5044c3a4fdafd9ff31f90784b8e8e4596144a0daf586511d3d9962b9ea95af 197b4e5fc60f2b1ed15de3a5bef5f89bdc79d91051d9b2816e74fa54531efdc1 cbe74d448857f476bcd58f21c0b653b3b76a4e076a6559a302718555cc63f748 59aabab925f023861ca8cd0f7badb2871f67d55326d7451135ad45f4a1ba6911 8fbb2c8a30eec9392ef3f977066c9add5c710cc647b1514d217d958c7017c3e9 0fd20c04e674b90486e9370a31a001d32f473979e4906749e7e477fa0b74508f 8a5f2378312b83c25bd388ca0b0fff7478baf42b71667edaac97c46b129643e5 86e5b055a0c211946d4f36e675bed5860fa042a315d9826164d6a9237c35a5fb f495490a5bd4df248b95c4aae7784b605673166ac4245b5b4b082a09e9323e62 f2078c5b76783446defd736ad3a3702d49b089844900a61833397bc4419b30d7 a97a0b387c1911474c4d41b53e32a977acb6f0ea75db65bb39e59e701e76957d ef6f2d44559c31a77122b5204e3b5c219f1688b14ed0bc0b801b3e6e82dcd43e 9c0e9f41744cd9815bd1bc8820d8bb123f04facd1b1b685dd5a2b1b8dbbf3ed9 33670f095a180b4f192d08b10b8fabbdfcc2b24518e32eea0a5e0c904ca84478 0083f3b0cd2d0b8b6af67bc355b9494025dc7b0a78fa80e3a2dbfeb51328851d 6078198e9493651ae787ec0251f922ba30e9f51df62a6d72784cf3dd20539317 6dfa324a512bd94970a36dd34a514a86791f0eb36f0145b09ab64651b4a0313b 299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21 6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358 fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208 3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8 815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e 938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b 0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95 eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31 5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9 784cf05c830b3242c8312` }} ]]></artwork>}]]></artwork> <t>The following is the ML-DSA-65 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg BrHDT1uguILyY3giL7NvIoPCQ/D/618btBSgpw1V49QKVrbLyIrh8Dt7KILZje6i jhRcne39jq8c7y7ZSosFD4lk9G0eoNDCpD4N2mGCrb9PbtF1tnQiV4Wb8i86QX7P H52JMXteU51YevFrnhMT4EUU/6ZLqLP/K4Mh+IEcs/sCLI9kTnCkuAovv+5gSrtz eQkeqObFx038AoNma0DAeThwAoIEoTa/XalWjreY00kDi9sMEeA0ReeEfLUGnHXP KKxgHHeZ2VghDdvLIm5Rr++fHeR7Bzhz1tP5dFa+3ghQgudKKYss1I9LMJMVXzZs j6YBxq+FjfoywISRsqKYh/kDNZSaXW7apnmIKjqV1r9tlwoiH0udPYy/OEr4GqyV 4rMpTgR4msg3J6XcBFWflq9B2KBTUW/u7rxSdG62qygZ4JEIcQ2DXwEfpjBlhyrT NNXN/7KyMQUH6S/Jk64xfal/TzCc2vD2ftmdkCFVdgg4SflTskbX/ts/22dnmFCl rUBOZBR/t89Pau3dBa+0uDSWjR/ogBSWDc5dlCI2Um4SpHjWnl++aXAxCzCMBoRQ GM/HsqtDChOmsax7sCzMuz2RGsLxEGhhP74Cm/3OAs9c04lQ7XLIOUTt+8dWFa+H +GTAUfPFVFbFQShjpAwG0dq1Yr3/BXG408ORe70wCIC7pemYI5uV+pG31kFtTzmL OtvNMJg+01krTZ731CNv0A9Q2YqlOiNaxBcnIPd9lhcmcpgM/o/3pacCeD7cK6Mb IlkBWhEvx/RoqcL5RkA5AC0w72eLTLeYvBFiFr96mnwYugO3tY/QdRXTEVBJ02FL 56B+dEMAdQ3x0sWHUziQWer8PXhczdMcB2SL7cA6XDuK1G0GTVnBPVc3Ryn8TilT YuKlGRIEUwQovBUir6KP9f4WVeMEylvIwnrQ4MajndTfKJVsFLOMyTaCzv5AK71e gtKcRk5E6103tI/FaN/gzG6OFrrqBeUTVZDxkpTnPoNnsCFtu4FQMLneVZE/CAOc QjUcWeVRXdWvjgiaFeYl6Pbe5jk4bEZJfXomMoh3TeWBp96WKbQbRCQUH5ePuDMS CO/ew8bg3jm8VwY/Pc1sRwNzwIiR6inLx8xtZIO4iJCDrOhqp7UbHCz+birRjZfO NvvFbqQvrpfmp6wRSGRHjDZt8eux57EakJhQT9WXW98fSdxwACtjwXOanSY/utQH P2qfbCuK9LTDMqEDoM/6Xe6y0GLKPCFf02ACa+fFFk9KRCTvdJSIBNZvRkh3Msgg LHlUeGR7TqcdYnwIYCTMo1SkHwh3s48Zs3dK0glcjaU7Bp4hx2ri0gB+FnGe1ACA 0zT32lLp9aWZBDnK8IOpW4M/Aq0QoIwabQ8mDAByhb1KL0dwOlrvRlKH0lOxisIl FDFiEP9WaBSxD4eik9bxmdPDlZmQ0MEmi09Q1fn877vyN70MKLgBgtZll0HxTxC/ uyG7oSq2IKojlvVsBoa06pAXmQIkIWsv6K12xKkUju+ahqNjWmqne8Hc+2+6Wad9 /am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U 1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+ SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj 8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF HgLy6ERP -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } } BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594 9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d 51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515 11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c 2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce a8ba2233d1e56fbc5c5a1e726de63fadd2af016b119177fa3d971a2d9277173f ce55b67745af0b7c21d597dbeb93e6a32f341c49a5a8be9e825088d1f2aa4515 5d6c8ae15367e4eb003b8fdf7851071949739f9fff09023eaf45104d2a84a459 06eed4671a44dc28d27987bb55df69e9e8561f61a80a72699503865fed9b7ee7 2a8e17a19c408144f4b29afef7031c3a6d8571610b42c9f421245a88f197e168 12b031159b65b9687e5b3e934c5225ae98a79ba73d2b399d73510effad19e53b 8450f0ba8fce1012fd98d260a74aaaa13fae249a006b1c34f5ba0b882f263782 22fb36f2283c243f0ffeb5f1bb414a0a70d55e3d40a56b6cbc88ae1f03b7b288 2d98deea28e145c9dedfd8eaf1cef2ed94a8b050f8964f46d1ea0d0c2a43e0dd 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0f77d96172672980cfe8ff7a5a702783edc2ba31b2259015a112fc7f468a9c2f 9464039002d30ef678b4cb798bc116216bf7a9a7c18ba03b7b58fd07515d3115 049d3614be7a07e744300750df1d2c58753389059eafc3d785ccdd31c07648be dc03a5c3b8ad46d064d59c13d57374729fc4e295362e2a5191204530428bc152 2afa28ff5fe1655e304ca5bc8c27ad0e0c6a39dd4df28956c14b38cc93682cef e402bbd5e82d29c464e44eb5d37b48fc568dfe0cc6e8e16baea05e5135590f19 294e73e8367b0216dbb815030b9de55913f08039c42351c59e5515dd5af8e089 a15e625e8f6dee639386c46497d7a263288774de581a7de9629b41b4424141f9 78fb8331208efdec3c6e0de39bc57063f3dcd6c470373c08891ea29cbc7cc6d6 483b8889083ace86aa7b51b1c2cfe6e2ad18d97ce36fbc56ea42fae97e6a7ac1 14864478c366df1ebb1e7b11a9098504fd5975bdf1f49dc70002b63c1739a9d2 63fbad4073f6a9f6c2b8af4b4c332a103a0cffa5deeb2d062ca3c215fd360026 be7c5164f4a4424ef74948804d66f46487732c8202c795478647b4ea71d627c0 86024cca354a41f0877b38f19b3774ad2095c8da53b069e21c76ae2d2007e167 19ed40080d334f7da52e9f5a5990439caf083a95b833f02ad10a08c1a6d0f260 c007285bd4a2f47703a5aef465287d253b18ac22514316210ff566814b10f87a 293d6f199d3c3959990d0c1268b4f50d5f9fcefbbf237bd0c28b80182d665974 1f14f10bfbb21bba12ab620aa2396f56c0686b4ea9017990224216b2fe8ad76c 4a9148eef9a86a3635a6aa77bc1dcfb6fba59a77dfda9b7530dc0ca8648c8d97 3738e01bab8f08b4905e84aa4641bd602410cd97520265f2f231f2b35e15eb2f a04d2bd94d5a77abaf1e0e161010a990087f5b46ea988b2bc0512fda0fa923da dd6c45c5301d09483673265b5ab2e10f4ba520f6bbad564a5c3d5e27bdb080f7 d20e13296a3181954c39c649c943ebe17df5c1f7aae0a8fe126c477585a5d4d6 48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336 24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607 61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec 79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6 6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0 3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914 66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475 b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79 c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210 4bc460a051e02f2e8444f` }} ]]></artwork>}]]></artwork> <t>The following is the ML-DSA-87 public key corresponding to the private 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> <artwork><![CDATA[ -----BEGIN PUBLIC KEY----- MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4 6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2 eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z x7hbrOLO06oSdrph7njtflyltnzdRYqTVAMOaru6v1agojFv7J26g7UdQv0xZ/Hg +QhV1cZlCbIQJl3B5U7ES0O6fPmu8Ri0TYCRLOdRZqZlHhFs6+SSKacGLAmTH3Gr 0ik/dvfvwyFbqXgAA35Y5HC9u7Q8GwQ56vecVNk7RKrJ7+n74VGHTPsqZMvuKMxM D+d3Xl2HDxwC5bLjxQBMmV8kybd5y3U6J30Ocf1CXra8LKVs4SnbUfcHQPMeY5dr 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8JBp5kMucAA1rCoCh5//Ch4b7FIgRxk9lOtd8e/VPuoRRMp4lAhS9eyXJ5BLNm7e T14tMx+tX8KC6ixH6SMUJ3HD3XWoc1dIfe+Z5fGOnZ7WI8F10CiIxR+CwHqA1UcW s8PCvb4unwqbuq6+tNUpNodkBvXADo5LvQpewFeX5iB8WrbIjxpohCG9BaEU9Nfe KsJB+g6L7f9H92Ldy+qpEAT40x6FCVyBBUmUrTgm40S6lgQIEPwLKtHeSM+t4ALG LlpJoHMas4NEvBY23xa/YH1WhV5W1oQAPHGOS62eWgmZefzd7rHEp3ds03o0F8sO GE4p75vA6HR1umY74J4Aq1Yut8D3Fl+WmptCQUGYzPG/8qLI1omkFOznZiknZlaJ 6U25YeuuxWFcvBp4lcaFGslhQy/xEY1GB9Mu+dxzLVEzO+S00OMN3qeE7Ki+R+dB vpwZYx3EcKUu9NwTpPNjP9Q014fBcJd7QX31mOHQ3eUGu3HW8LwX7HDjsDzcGWXL Npk/YzsEcuUNCSOsbGb98dPmRZzBIfD1+U0J6dvPXWkOIyM4OKC6y3xjjRsmUKQw jNFxtoVRJtHaZypu2FqNeMKG+1b0qz0hSXUoBFxjJiyKQq8vmALFO3u4vijnj+C1 zkX7t6GvGjsoqNlLeJDjyILjm8mOnwrXYCW/DdLwApjnFBoiaz187kFPYE0eC6VN EdX+WLzOpq13rS6MHKrPMkWQFLe5EAGx76itFypSP7jjZbV3Ehv5/Yiixgwh6CHX tqy0elqZXkDKztXCI7j+beXhjp0uWJOu/rt6rn/xoUYmDi8RDpOVKCE6ACWjjsea q8hhsl68UJpGdMEyqqy34BRvFO/RHPyvTKpPd1pxbOMl4KQ1pNNJ1yC88TdFCvxF BG/Bofg6nTKXd6cITkqtrnEizpcAWTBSjrPH9/ESmzcoh6NxFVo7ogGiXL8dy2Tn ze4JLDFB+1VQ/j0N2C6HDleLK0ZQCBgRO49laXc8Z3OFtppCt33Lp6z/2V/URS4j qqHTfh2iFR6mWNQKNZayesn4Ep3GzwZDdyYktZ9PRhIw30ccomCHw5QtXGaH32CC g1k1o/h8t2Kww7HQ3aSmUzllvvG3uCkuJUwBTQkP7YV8RMGDnGlMCmTj+tkKEfU0 citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH 8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4 P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8 WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22 1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG 5VvgYiIvi6kKl0BzMmsxISrs4KNKYA== -----END PUBLICKEY----- ]]></artwork>KEY-----]]></artwork> <artwork><![CDATA[ SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } } BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4 1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46 a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079 54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712 0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f 21b3d1b8305850aa42afbb13f1f4d5b9f4835f9d87dfceb162d0ef4a7fdc4cba 1743cd1c87bb4967da16cc8764b6569df8ee5bdcbffe9a4e05748e6fdf225af9 e4eeb7773b62e8f85f9b56b548945551844fbd89806a4ac369bed2d256100f68 8a6ad5e0a709826dc4449e91e23c5506e642361ef5a313712f79bc4b3186861c a85a4bab17e7f943d1b8a333aa3ae7ce16b440d6018f9e04daf5725c7f1a93fa d1a5a27b67895bd249aa91685de20af32c8b7e268c7f96877d0c85001135a4f0 a8f1b8264fa6ebe5a349d8aecad1a16299ccf2fd9c7b85bace2ced3aa1276ba6 1ee78ed7e5ca5b67cdd458a9354030e6abbbabf56a0a2316fec9dba83b51d42f d3167f1e0f90855d5c66509b210265dc1e54ec44b43ba7cf9aef118b44d80912 ce75166a6651e116cebe49229a7062c09931f71abd2293f76f7efc3215ba9780 0037e58e470bdbbb43c1b0439eaf79c54d93b44aac9efe9fbe151874cfb2a64c bee28cc4c0fe7775e5d870f1c02e5b2e3c5004c995f24c9b779cb753a277d0e7 1fd425eb6bc2ca56ce129db51f70740f31e63976b50c7312e9797d78c5b1ac24 a5fa347cc916e0a83f5c3b675cd30b81e3fa10b93444e07397571cce98b28da5 1db9056bc728c5b0b1181e2fbd387b4c79ab1a5fefece37167af772ddad14eb4 c3982da5a59d0e9eb173ec6315091170027a3ab5ef6aa129cb8585727b9358a2 8501d713a72f3f1db31714286f9b6408013af06045d75592fc0b7dd47c73ed9c 75b11e9d7c69f7cadfc3280a9062c5273c43be1c34f87448864cea7b5c97d6d3 2f59bd5f25384653bb5c4faa45bea8b89402843e645b6b9269e2bd988ddacb03 3328ffb060450f7df080053e6969b251e875ecec32cfc592840d69ab69a75e06 b379c535d95266b082f4f09c93162b33b0d9f7307a4eaaa52104437fed66f8ee 3eabbd45d67b25a8133f496468b52baffdbfad93eef1a9818b5e42ec722788a3 d8d3529fc777d2ba570801dfae01ec88302837c1fb9e0355727645ee1046c3f9 15f6ae82dad4fb6b0356a46518ffc834155c3b4fe6dafa6cc8a5ccf53c73a084 9d8d44f7dcf72754e70e1b7dfb447bb4ef49d1a718f6171bbce200950e0ce926 106b151a3e871d5ce49731bd6650a9b0ca972da1c5f136d44820ea6383c08f3b 384cf2338e789c513f618cc5694a6f0cee104511e1ed7c5f23a1ebfd8a0db842 4553240156dbf622831b0c643d1c551b6f3f7a98d29b85c2de05a65fa615eee1 6495bd90737672115b53e91c5d90028cf3f1a93953a153de53b44084e9ccff6b 736693926daefebb2d77aa5ad689b92f31686669df16d1715cc58f7a2cfb72dd 1a51e92f825993a74022be7e9eb6054654457094d14928f20215e7b222ac56b5 1adbec8d8bdb6983979a7e3a21b44b5d1518ca97d0b5195f51ed6a24350c8974 7e1edea51b448e3e9147054ce927873c90db394d86888e07dff177593d6f79e1 52302204aeb03be2386af3e24078bd028b1689f5e147c9f452c8ceb02ec59cc9 db63a03576ceeafe98239023897da0236630a53c0de7f435a19869792fab36e7 b9e635760f09069e6432e700035ac2a02879fff0a1e1bec522047193d94eb5df 1efd53eea1144ca78940852f5ec9727904b366ede4f5e2d331fad5fc282ea2c4 7e923142771c3dd75a87357487def99e5f18e9d9ed623c175d02888c51f82c07 a80d54716b3c3c2bdbe2e9f0a9bbaaebeb4d52936876406f5c00e8e4bbd0a5ec 05797e6207c5ab6c88f1a688421bd05a114f4d7de2ac241fa0e8bedff47f762d dcbeaa91004f8d31e85095c81054994ad3826e344ba96040810fc0b2ad1de48c fade002c62e5a49a0731ab38344bc1636df16bf607d56855e56d684003c718e4 bad9e5a099979fcddeeb1c4a7776cd37a3417cb0e184e29ef9bc0e87475ba663 be09e00ab562eb7c0f7165f969a9b42414198ccf1bff2a2c8d689a414ece7662 927665689e94db961ebaec5615cbc1a7895c6851ac961432ff1118d4607d32ef 9dc732d51333be4b4d0e30ddea784eca8be47e741be9c19631dc470a52ef4dc1 3a4f3633fd434d787c170977b417df598e1d0dde506bb71d6f0bc17ec70e3b03 cdc1965cb36993f633b0472e50d0923ac6c66fdf1d3e6459cc121f0f5f94d09e 9dbcf5d690e23233838a0bacb7c638d1b2650a4308cd171b6855126d1da672a6 ed85a8d78c286fb56f4ab3d21497528045c63262c8a42af2f9802c53b7bb8be2 8e78fe0b5ce45fbb7a1af1a3b28a8d94b7890e3c882e39bc98e9f0ad76025bf0 dd2f00298e7141a226b3d7cee414f604d1e0ba54d11d5fe58bccea6ad77ad2e8 c1caacf32459014b7b91001b1efa8ad172a523fb8e365b577121bf9fd88a2c60 c21e821d7b6acb47a5a995e40caced5c223b8fe6de5e18e9d2e5893aefebb7aa e7ff1a146260e2f110e939528213a0025a38ec79aabc861b25ebc509a4674c13 2aaacb7e0146f14efd11cfcaf4caa4f775a716ce325e0a435a4d349d720bcf13 7450afc45046fc1a1f83a9d329777a7084e4aadae7122ce97005930528eb3c7f 7f1129b372887a371155a3ba201a25cbf1dcb64e7cdee092c3141fb5550fe3d0 dd82e870e578b2b46500818113b8f6569773c677385b69a42b77dcba7acffd95 fd4452e23aaa1d37e1da2151ea658d40a3596b27ac9f8129dc6cf0643772624b 59f4f461230df471ca26087c3942d5c6687df6082835935a3f87cb762b0c3b1d 0dda4a6533965bef1b7b8292e254c014d090fed857c44c1839c694c0a64e3fad 90a11f534722b6ee1574f2e149d55d744de4887024e08511431c062750e16c74 ab9f3242f2db3ffb12a8d6107faa229d6f6373b07f36d3932b3bdb04c19dd64e add7f93c3c564c358a1c81dcf1c9c31e5b06568f97544c17dc15698c5cb38983 a9afc42783faa773a52c9d8260690be9e3156aa5bc1509dea3f69587695cd6ff 172ba83e6a6d8a7d6bbebbbcda3672731983f89bc5831dc37c3f3c5c56facc69 7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846 c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557 23ee0c7f4736ce6e6665c5aca32a481c53839bc259167b013d0423395eeb9aaa ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce 2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa 1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270 4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0 09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407 3326b31212aece0a34a60` }} ]]></artwork>}]]></artwork> </section> <section anchor="example-certificates"> <name>Example Certificates</name> <aside> <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 examples, i.e., brevity. Certificate Policies (CPs) <xref target="RFC3647"/> for production CAs should consider whether this combination is appropriate.</t> </aside> <t>The following is a self-signed certificate for the ML-DSA-44 public key in the previous section. The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P E5fReJ2voXAksxbpvslPyZRtQvGbeadBO7qjPnFJy0LtURVpOsBB+suYit61/g4d hjEYSZW1ksOX0ilOLhT5CqQUujgmiZrEP0zMrLwm6agyuVEY1ctDPL75ZgsAE44I F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG wP1zgDoq7P6v3teqPLLO2lTRK9jNNqeM+XWUO0er0l6ICsRS5XQu0ejRqCr6huWQ x1jBWuTShA2SvKGlCQ9ASWWX/KfYuVE/GhvabpUKqpjeRnUH1KT1pPBZkhZYLDVy 9i7aiQWrNYFnDEoCd3oz4Mpylf2PT/bRoKOnaD1l9fX3/GDaAj6CbF+SFEwC99G6 EHWYdVPqk2f8122ZC3+pnNRa/biDbUPkWfUYffBYR5cJoB6mg1k1+nBGCZDNPcG6 QBupS6sd3kGsZ6szGdysoGBI1MTu8n7hOpwX0FOPQw8tZC3CQVZg3niHfY2KvHJS 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# organizationName OBJECT_IDENTIFIER { 2.5.4.10 } PrintableString { "IETF" } } } SET { SEQUENCE { # commonName OBJECT_IDENTIFIER { 2.5.4.3 } PrintableString { "LAMPS WG" } } } } SEQUENCE { UTCTime { "200203043210Z" } UTCTime { "400129043210Z" } } SEQUENCE { SET { SEQUENCE { # organizationName OBJECT_IDENTIFIER { 2.5.4.10 } PrintableString { "IETF" } } } SET { SEQUENCE { # commonName OBJECT_IDENTIFIER { 2.5.4.3 } PrintableString { "LAMPS WG" } } } } SEQUENCE { SEQUENCE { OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } } BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f139 7d1789dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed5 115693ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa41 4ba3826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f 61e762ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f7 2e55dfe71ce9c1ebb9889e7c56106c0fd73803a2aecfeafded7aa3cb2ceda54d 12bd8cd36a78cf975943b47abd25e880ac452e5742ed1e8d1a82afa86e590c75 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The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggeyMAsGCWCGSAFlAwQDEgOCB6EASGg9kZeOMes93biwRzSC0riK X2JZSf2PWKVh5pa9TCfQWzjbsu3wHmZO/YG+HqiTaIzmiqLVHFlY+LvG606J7mfS wDIJVNVyEsrHIp/x1urwOSi9UVEfjYjYR3NsfeJzDVl45UEHExYJeIZ3Eb9VOaC/ xMNQwr5XK68O4uL7Fsz+oIAo2ZrEmuu3WTfdzhEc2rYv/zzqi6IjPR5W+8XFoecm 3mP63SrwFrEZF3+j2XGi2Sdxc/zlW2d0WvC3wh1Zfb65Pmoy80HEmlqL6eglCI0f KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1 XfaenoVh9hqApyaZUDhl/tm37nKo4XoZxAgUT0spr+9wMcOm2FcWELQsn0ISRaiP GX4WgSsDEVm2W5aH5bPpNMUiWumKebpz0rOZ1zUQ7/rRnlO4RQ8LqPzhAS/ZjSYK dKqqE/riSaAGscNPW6C4gvJjeCIvs28ig8JD8P/rXxu0FKCnDVXj1ApWtsvIiuHw 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411659ecccfe7f811f852798599063b486672787b83bc537374d200000000000 00000000000000000000000000000000000060d0f131c20` }} ]]></artwork>}]]></artwork> <t>The following is a self-signed certificate for the ML-DSA-87 public key in the previous section. The textual encoding <xref target="RFC7468"/> is followed by the so-called "pretty print"; the certificates are the same.</t> <artwork><![CDATA[ -----BEGIN CERTIFICATE----- MIIdMzCCCwqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMT MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI TEFNUFMgV0cwggoyMAsGCWCGSAFlAwQDEwOCCiEAl5K87C8kMGhqgvzPPC9f9mXn cderQbkCWM+n6Q7JcSSnOzI7m6Iatk12fEM/WlIe/+GPhuRqGIlSxEZ+BItynn/E 0RXn5I2hiW1f4RmxDc3e9iyzB5VAdLQjNuUoNt5h2pQfjTfqaKyBBvq+GQcGea9g CFNxIPcHk7jqnMDm57e0yaXHQhxg8kRRuh6TPbGi7hbHlVnyGz0bgwWFCqQq+7E/ H01bn0g1+dh9/OsWLQ70p/3Ey6F0PNHIe7SWfaFsyHZLZWnfjuW9y//ppOBXSOb9 8iWvnk7rd3O2Lo+F+bVrVIlFVRhE+9iYBqSsNpvtLSVhAPaIpq1eCnCYJtxESeke I8VQbmQjYe9aMTcS95vEsxhoYcqFpLqxfn+UPRuKMzqjrnzha0QNYBj54E2vVyXH 8ak/rRpaJ7Z4lb0kmqkWhd4grzLIt+Jox/lod9DIUAETWk8KjxuCZPpuvlo0nYrs rRoWKZzPL9nHuFus4s7TqhJ2umHueO1+XKW2fN1FipNUAw5qu7q/VqCiMW/snbqD 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]]></artwork>}]]></artwork> </section> <section anchor="example-bad"> <name>Example Inconsistent Seed and Expanded Private Keys</name> <aside> <t>WARNING: These private keys are purposelybadbad; do not use them in production systems.</t> </aside> <t>The following examples demonstrate inconsistent seed and expanded private keys.</t> <t>Three <tt>ML-DSA-44-PrivateKey</tt> examples of inconsistent seed and expanded private keys follow:</t> <ol spacing="normal"type="1"><li>type="1"> <li> <t>The first <tt>ML-DSA-PrivateKey</tt> example includes the <tt>both 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 inconsistencies.</t> </li> <li> <t>The second <tt>ML-DSA-PrivateKey</tt> example includes only <tt>expandedKey</tt>. The public key fails to match the <tt>tr</tt> hash value in the private key.</t> </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 portion of the private key (its high bits <tt>t_1</tt> are the primary content of the public key).</t> </li> </ol> <!-- [rfced] We are having trouble understanding "then" in this sentence. Does it indicate a later step or perhaps it should be deleted altogether? Original: The second and third examples would not be detected by implementations that do not regenerate the public key from the private key, or neglect to then check consistency of tr or t_0. Perhaps A: The second and third examples would not be detected by implementations that do not regenerate the public key from the private key and then neglect then check consistency of tr or t_0. Perhaps B: The second and third examples would not be detected by implementations that do not regenerate the public key from the private key or that neglect to check consistency of tr or t_0. --> <t>The second and third examples would not be detected by implementations that do not regenerate the public key from the private key, or neglect to then check consistency of <tt>tr</tt> or <tt>t_0</tt>.</t> <t>The following is the first example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1 TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65 3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY 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a06arDBhDhmeyDQZFhMtlu575XeFZGdP11IVo4UPSCQKzc/AMxlrjNrQw2wNZJ+t 6JDEJq75MS7q5C7gvPpBd3qdmbNQwLFvyCj8ohXcpqc1Lgw12BFNtm5L2JXXle/7 QmhVrMEkSwJznkd+bOqky9uPbI1Nr1fw0+NJBeqCJtxVvjngV3rE97E1RqzHFxaH QQvju+iK/j03mKXQes6be6UWIrYz8+RhZ4jwlK2nPDklHM0+0p2sNlha3BYl+Fob uXxZug5ze+Lor7aiIiy18xn64MxZ4QBP3pFpKeW3YJKoLcJSexuJlKJ8Ky5WjnJ+ skZeuWRgmW/OYyRcKyyylrgnWv0A2oyBqe8ujjv5MD2Oi1Oq/mxtA+a8IAQ0oqOL F00uc91QcXXoUdXnQ+ZCCeNIUg1shMyx+2v6smyMLuSFEQ3R17Br1Sgw6lu2gD0S XMYOX6h8w0Ww9ml1Huth5xm21mYiPLiejT3vPOyWrJNQ7pg4l/0VGBTG+1zaN5fo paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H 2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3 fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9 tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI 2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA== -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <t>The following is the second example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp EcIo0CBIArNsojYJWoZIy7Rhi0ZixECCGokJEAJNJLJFIBIlJMkFiCiMycBNWUgi CiduwTRkTJBgW0RQgoZJQ4gEQ7KMYDCAoogthKRtjKYp0MaEQgZGiYhRAKmNAUmN 5DgNpAaN05RxQrJsGoRhG6MoQrQoCKBxGsUx4KBMATdlJChiFCiQCRBh2UAiGzNg CQKS0CSBIAQISRhEoyItXIhEFJgIpEZhAZVkCzkKDJRQykBq0rIgwDgBgjCOE7kI kYCEFIgpwBiREjUNoCQi4gQG2cKFBCgSHMmJGAJy0kApwggS2AYqmZRxm7hoI4Qp GiKJFEUR3IJEUJZFDESEwLIEmqYFQ4YsRDJuiEQhIKhMmjBw47gtYyaIAyVJA0OM SKgJyhRyUzROEkMIG6cEWTAi2ZSA4jQigUISnDAqlDQmYQRFJCYoE0YJSjJtESgJ GLglYigRE0ENQbIRkIRMixISosaIycAwIgYG0hiOhIYwkERSEogx2SBxE8UoQwYO AzBgzKaEWCZSTIgBHvclYshf+kOs+kkhfysXLXu8FGIObZgKcaq73wxF6aIG7LFC P+4V3swXYBMAFJ2SI81ubG4fqOQfx8ZJOKtokF/T3NpQ2HCC59DXHRvJsrhMhVI8 qP5srSlK34O+FbEI/3IdDMh7w906dZAYSw6EVmOpH8nhw8U6YdhnQgsE8JI1V1O8 ZaBjaP1BKV/QmSQTLG+R9nlkwUJnSnJcNDkUxM7PWMB0vK9FWMl795EeB6ptCTjy 7iuzwajFldY16ENC/eoB3CSyEa0vwoHPd+WREMerxUvwyG1IC5vidkcdydYDzumM /as+n8+3A3k1YFSepEUPp7M/uRacRLTSX7nEV/SXkc09oD6slglYE8EFEyzNpOY+ SSKM0j2KHzeFbxQtk7kNsJ+Cr4kljGOquAR6gMA2yTV+ogRvjcY1TwxSlfNCu0F9 PP6wsf0zYiwp4Uy72S4TY8ZevUUEt1EjKblnDjLhssZ6VOfxpV+Ln56gToyjpwXm KjxeY3N0r7eutt3qYSzeKPAaIC16pONHItJ90/m4mJTQGf1dTXEZ7+NyO7oQTLi7 CYHgdN46/iANqq6tgmzEXyRNv0Ma+rNO+994JHTS/VcRj2RiFJNO2Zy6OwA+jWej g29vGfxBkQzlFj7jrpnrhNUU63YeY2hOpW+XkdLdSqxuYWi5SMgX91oiKssOjNwD zEr+j2cVfho2O3+u/58XK5iRNnfFod0IXp7kwiBSwa9YGTEWZz3NO/xfNLhV3MbH eIVknp5x9D1K6g9Lcsp+2gV4uhPTGmWNLQYKmmb/ae0b55l6L7HScj04+b+r4Y+O ezzakG5Om16ULI6uspYHDr/TZJR6lAzJeL7Wazd0nm1dzXvoxJREDiuEzs/vuYwL 7fs8QeM1nSzXGX++cgxIqmxrZGXB7mPjVpwq3HREkTcLf3gm/gt3odGdZBAdAyuR gQa0LS73N0flYB/kulDyPt5SHwMagX0VKUpDci6DeHhLbbDPG6norpEdkgG5zpzD AZxvXCfLmNomFEtkIlp8kysw92Hnii1Zodi4PsY0Si9t1H52VwbQC/SnmmqSbDup HYEsjyx5erF5Zwnl0WhWd4KTUp8ChtAVw7U5lhlkKjM+nlk9bj9TU5lCCOnmozKF HX9lJSKpKLkX4n4tbUITff4uv6b7HGeybAJUUoaF9+vb4xWmjqotp2noqfQtPmAA fHEzCSaywAEtg+rU5P0e2HLM0ZciAdKwJ/NUWsLTDNeLwddA/sy8b8KgRGxuMOrF H1ppCYqi1EfyCFtOTkuSzMJpIdLeR4UYzQkM4meuotJ62lf9iLSXbYn7hDzcz0mn bKJnnmgBv6f7AxiW+1BilwS5kjk2u13ThTERIcrfsRmV5ZtzA0z2ftA6uBOGdkjQ JYKAh+lJqa/Ra5XXLZmx7coleqwTL/t6Bwmu1anA/wX7Dyu/KECe7XtfWAG+lkzt AZ4ct4UdOFHxApBnThn/sAizAcSs9kGiuxQhbh1pyr9Ste8idJaw8weZqFXRF/rT dEpvozUD6nmLUt3X7lQmYJ2/zT8ME7Fk1sBR9+1KEZcZpxLjiNMoQCCB/xNUtVTS wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> <t>The following is the third example:</t> <artwork><![CDATA[ -----BEGIN PRIVATE KEY----- MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi wCRBCUNxCiEgYaIBUiJSG4CAmjQAE5NN0zIpIhcKmJJpGhRRICchnMAgYqKBSBhp GoVNg0RpWyBBAxJCyxhGAakNDAIxg7AhWiJKyJIF2ZBpBDBqSwZK0rIBHEBAgUIy UjJyVKZAWhgQDDISksKAUhJiXIIoC7RsA0KNUxAMFAEO4TZSiIQkkQIKY0YmIAYp EcIo0CBIArNsojYJWoZIy7Rhi0ZixECCGokJEAJNJLJFIBIlJMkFiCiMycBNWUgi CiduwTRkTJBgW0RQgoZJQ4gEQ7KMYDCAoogthKRtjKYp0MaEQgZGiYhRAKmNAUmN 5DgNpAaN05RxQrJsGoRhG6MoQrQoCKBxGsUx4KBMATdlJChiFCiQCRBh2UAiGzNg CQKS0CSBIAQISRhEoyItXIhEFJgIpEZhAZVkCzkKDJRQykBq0rIgwDgBgjCOE7kI kYCEFIgpwBiREjUNoCQi4gQG2cKFBCgSHMmJGAJy0kApwggS2AYqmZRxm7hoI4Qp GiKJFEUR3IJEUJZFDESEwLIEmqYFQ4YsRDJuiEQhIKhMmjBw47gtYyaIAyVJA0OM SKgJyhRyUzROEkMIG6cEWTAi2ZSA4jQigUISnDAqlDQmYQRFJCYoE0YJSjJtESgJ GLglYigRE0ENQbIRkIRMixISosaIycAwIgYG0hiOhIYwkERSEogx2SBxE8UoQwYO AzBgzKaEWCZSTIgBH/clYshf+kOs+kkhfysXLXu8FGIObZgKcaq73wxF6aIG7LFC P+4V3swXYBMAFJ2SI81ubG4fqOQfx8ZJOKtokF/T3NpQ2HCC59DXHRvJsrhMhVI8 qP5srSlK34O+FbEI/3IdDMh7w906dZAYSw6EVmOpH8nhw8U6YdhnQgsE8JI1V1O8 ZaBjaP1BKV/QmSQTLG+R9nlkwUJnSnJcNDkUxM7PWMB0vK9FWMl795EeB6ptCTjy 7iuzwajFldY16ENC/eoB3CSyEa0vwoHPd+WREMerxUvwyG1IC5vidkcdydYDzumM /as+n8+3A3k1YFSepEUPp7M/uRacRLTSX7nEV/SXkc09oD6slglYE8EFEyzNpOY+ SSKM0j2KHzeFbxQtk7kNsJ+Cr4kljGOquAR6gMA2yTV+ogRvjcY1TwxSlfNCu0F9 PP6wsf0zYiwp4Uy72S4TY8ZevUUEt1EjKblnDjLhssZ6VOfxpV+Ln56gToyjpwXm KjxeY3N0r7eutt3qYSzeKPAaIC16pONHItJ90/m4mJTQGf1dTXEZ7+NyO7oQTLi7 CYHgdN46/iANqq6tgmzEXyRNv0Ma+rNO+994JHTS/VcRj2RiFJNO2Zy6OwA+jWej g29vGfxBkQzlFj7jrpnrhNUU63YeY2hOpW+XkdLdSqxuYWi5SMgX91oiKssOjNwD zEr+j2cVfho2O3+u/58XK5iRNnfFod0IXp7kwiBSwa9YGTEWZz3NO/xfNLhV3MbH eIVknp5x9D1K6g9Lcsp+2gV4uhPTGmWNLQYKmmb/ae0b55l6L7HScj04+b+r4Y+O ezzakG5Om16ULI6uspYHDr/TZJR6lAzJeL7Wazd0nm1dzXvoxJREDiuEzs/vuYwL 7fs8QeM1nSzXGX++cgxIqmxrZGXB7mPjVpwq3HREkTcLf3gm/gt3odGdZBAdAyuR gQa0LS73N0flYB/kulDyPt5SHwMagX0VKUpDci6DeHhLbbDPG6norpEdkgG5zpzD AZxvXCfLmNomFEtkIlp8kysw92Hnii1Zodi4PsY0Si9t1H52VwbQC/SnmmqSbDup HYEsjyx5erF5Zwnl0WhWd4KTUp8ChtAVw7U5lhlkKjM+nlk9bj9TU5lCCOnmozKF HX9lJSKpKLkX4n4tbUITff4uv6b7HGeybAJUUoaF9+vb4xWmjqotp2noqfQtPmAA fHEzCSaywAEtg+rU5P0e2HLM0ZciAdKwJ/NUWsLTDNeLwddA/sy8b8KgRGxuMOrF H1ppCYqi1EfyCFtOTkuSzMJpIdLeR4UYzQkM4meuotJ62lf9iLSXbYn7hDzcz0mn bKJnnmgBv6f7AxiW+1BilwS5kjk2u13ThTERIcrfsRmV5ZtzA0z2ftA6uBOGdkjQ JYKAh+lJqa/Ra5XXLZmx7coleqwTL/t6Bwmu1anA/wX7Dyu/KECe7XtfWAG+lkzt AZ4ct4UdOFHxApBnThn/sAizAcSs9kGiuxQhbh1pyr9Ste8idJaw8weZqFXRF/rT dEpvozUD6nmLUt3X7lQmYJ2/zT8ME7Fk1sBR9+1KEZcZpxLjiNMoQCCB/xNUtVTS wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= -----END PRIVATEKEY----- ]]></artwork>KEY-----]]></artwork> </section> </section> <section anchor="externalmu"><name>Pre-hashing<name>Pre-Hashing (Externalμ-ML-DSA)</name> <t>Some applications require pre-hashing that ease operational requirements around large or inconsistently-sized payloads. When signing with pre-hashing, the signature generation process can be separated into a pre-hash step requiring only the message and other public information, and a core signature stepwhichthat uses the public key.</t> <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"/>. ML-DSA itself supportsaan External μ pre-hashingmodemode, which externalizes the message pre-hashing originally performed inside the signing operation. This mode is also laid out in <xref target="FIPS204-ExternalMuFAQ"/>. This document specifies 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> <t>Implementations of ML-DSA using the External μ pre-hashing mode requires the following algorithms, which are modified versions of the algorithms presented in <xref target="FIPS204"/>. The nomenclature used here has been modified from the NIST FAQ <xref target="FIPS204-ExternalMuFAQ"/> for clarity.</t> <!-- [rfced] Should "pre-hash" and "prehash" be consistent throughout? For example: Original: Pre-hash operation: ... Figure 2: Computeμ prehash operation --> <t>Pre-hash operation:</t> <figure anchor="fig-externalmu-ml-dsa-external"> <name>Computeμprehash operation</name>Prehash Operation</name> <!-- [rfced] The following lines extended beyond 72 characters. We folded the lines as follows. Please let us know if any corrections are needed. Original: # The functions `BytesToBits` and `IntegerToBytes` are defined in FIPS 204. Current: # The functions `BytesToBits` and `IntegerToBytes` are defined # in FIPS 204. Original: # ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced with Current: # ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced # with --> <artwork><![CDATA[ Computeμ(pk, M, ctx): # Referred to as 'Externalμ-ML-DSA.Prehash(pk, M, ctx)' # in the FIPS 204 FAQ. # M is the message, a bit-string # μ and ctx are byte-strings. # ctx is the context string, which defaults to theempyempty string. μ = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) || IntegerToBytes(|ctx|, 1) || ctx) || M, 64) # The functions `BytesToBits` and `IntegerToBytes` are defined # in FIPS 204. returnμ ]]></artwork>μ]]></artwork> </figure> <t>Sign operations:</t> <figure anchor="fig-externalmu-ml-dsa-internal"> <name>TheoperationsOperations forsigningSigning μ</name> <!-- [rfced] We are having trouble parsing "defaulting is Externalμ to false". Please review. Original: ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false): # μ can be passed as an argument instead of M' # defaulting is Externalμ to false means that # this modified version of Sign_internal can be used # in place of the original without interfering with # functioning of pure ML-DSA mode. --> <artwork><![CDATA[ Signμ(sk, μ): # Referred to as 'Externalμ-ML-DSA.Sign(sk, μ)' # in the FIPS 204 FAQ. if |μ| != 64 then return error # return an error indication if the input μ is not # 64 bytes. end if rnd = rand(32) # for the optional deterministic variant, # set rnd to all zeroes if rnd = NULL then return error # return an error indication if random bit # generation failed end if sigma = Signμ_internal(sk, μ, rnd, isExternalμ=true) return sigma ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false): # μ can be passed as an argument instead of M' # defaulting is Externalμ to false means that # this modified version of Sign_internal can be used # in place of the original without interfering with # the functioning of pure ML-DSA mode. # ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced # with 6: if (isExternalμ): μ = M' else: μ = H(BytesToBits(tr) || M',64) ]]></artwork>64)]]></artwork> </figure> <t>There is no need to specify an External μ <tt>Verify()</tt> routine because this is identical to the original <tt>ML-DSA.Verify()</tt>. This makes External 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> API and to sometimes be used with the External μ API without any interoperabilityconcens.</t>concerns.</t> <t>The External μ mode requires the <tt>Computeμ</tt> routine to have access to the hash of the signer's publickeykey, which may not be available in some architectures, or require fetching it. That may allow for mismatches between <tt>tr</tt> and <tt>sk</tt>. At worst, this will produce a signaturewhichthat will fail to verify under the intended public key since a compliant <tt>Verify()</tt> routine will independently compute <tt>tr</tt> from the public key.ThatThis 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, 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 secret key. The External μ mode also requires SHAKE256 to be available to the <tt>Computeμ</tt> routine.</t> </section> <section numbered="false" anchor="acknowledgments"> <name>Acknowledgments</name> <t>The authors wish to thank the following people for their contributions to this document:Corey Bonnell, Dierdre Connolly, Viktor Dukhovni, Russ Housley, Alicja Kario, Mike Ounsworth,<contact fullname="Corey Bonnell"/>, <contact fullname="Dierdre Connolly"/>, <contact fullname="Viktor Dukhovni"/>, <contact fullname="Russ Housley"/>, <contact fullname="Alicja Kario"/>, <contact fullname="Mike Ounsworth"/>, andDaniel<contact fullname="Daniel VanGeest.</t>Geest"/>.</t> <t>In addition, we would like to thank those who contributed to the private key format discussion:Tony Arcieri, Bob Beck, Dmitry Belyavskiy, David Benjamin, Daniel Bernstein, Uri Blumenthal, Theo Buehler, Stephen Farrell, Jean-Pierre Fiset, Scott Fluhrer, Alex Gaynor, John Gray, Peter Gutmann, David Hook, Tim Hudson, Paul Kehrer, John Kemp, Watson Ladd, Adam Langley, John Mattsson, Damien Miller, Robert Relyea, Michael Richardson, Markku-Juhani<contact fullname="Tony Arcieri"/>, <contact fullname="Bob Beck"/>, <contact fullname="Dmitry Belyavskiy"/>, <contact fullname="David Benjamin"/>, <contact fullname="Daniel Bernstein"/>, <contact fullname="Uri Blumenthal"/>, <contact fullname="Theo Buehler"/>, <contact fullname="Stephen Farrell"/>, <contact fullname="Jean-Pierre Fiset"/>, <contact fullname="Scott 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, Rich Salz, Roland Shoemaker, Sophie Schmieg, Simo Sorce, MichaelSaarinen"/>, <contact fullname="Rich Salz"/>, <contact fullname="Roland Shoemaker"/>, <contact fullname="Sophie Schmieg"/>, <contact fullname="Simo Sorce"/>, <contact fullname="Michael St.Johns, Falko Strenzke, Filippo Valsorda, Loganaden Velvindron, Carl Wallace, and Wei-Jun Wang.</t>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></back><!--##markdown-source: H4sIAAAAAAAAA+S96ZbqSpYm+F9Pob53rSw/6QOahU5kZKUAAWJ0JneHWNF1 NCHEJEDCAT9x81n6b79D/ep8sf7MJIFw93OHqIpeWV0ecf3gGsy27fHb2wbu 7++ZOIiX3lf2XxmWNdext1t7MfvyIHMa+7i3l4HDNr0T7kx3VhTv9k6833ns Pasv/XAXxLMVa7reOg6mgbeL0MQ03LHxzGPbobtfevctK44Dx7svWZHnspXA D2JryQ4Cf23Rhi7N3LRb95WB/oWxbHvnvX5lk7/ZYM2WvR3pwLFiL2LIb7xz +spGscswbuisrRXod3fWNL4PvHh6v7RWm+jeDZZoONiv7p3c+/e8yER7exVE 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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). Note that we did not review each item on the list. These are our notes and questions on the items we checked: a) <tt>expanded</tt> - Should instances of <tt>expanded</tt> be <tt>expandedKey</tt>? For example: For each security level, 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> format, and <tt>both</tt> formats together.</t> b) <tt>seed</tt> - Should occurrences of "seed-only format" be "<tt>seed</tt> format"? For example: For each security level, we show the seed-only format (using a context-specific [0] primitive tag with an implicit encoding of OCTET STRING), the expanded format, and both formats together. b) <tt>OCTET STRING</tt> - seems to be used consistently in <tt> outside of code c) <tt>OneAsymmetricKey</tt> - Below are examples where "OneAsymmetricKey" does not appear in <tt>: <t>When encoding an ML-DSA private key in a OneAsymmetricKey object, any of these three formats may be used, though the seed format is <bcp14>RECOMMENDED</bcp14> for storage efficiency.</t> Note that these are the sizes of the raw keys, not including ASN.1 encoding overhead from OneAsymmetricKey and SubjectPublicKeyInfo wrappers. d) <tt>PUBLIC-KEY</tt> - seems to be used consistently in <tt> outside of code --> <!-- [rfced] Please review each artwork element and let us know if any should be marked as sourcecode (or another element) instead. We updated a number of instances of <artwork> to <sourcecode type="asn.1">. Please review closely and let us know if any corrections are needed. Please let us know if any instances of <artwork> should be <sourcecode> and whether 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. --> <!-- [rfced] Please review the "Inclusive Language" portion of the online Style Guide <https://www.rfc-editor.org/styleguide/part2/#inclusive_language> and let us know if any changes are needed. Updates of this nature typically result in more precise language, which is helpful for readers. Note that our script did not flag any words in particular, but this should still be reviewed as a best practice. --> </back> </rfc>