JOSE and COSE Encoding for Dilithium

Notational Conventions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in .

Terminology The following terminology is used throughout this document: PK : The public key for the signature scheme. SK : The secret key for the signature scheme. signature : The digital signature output. message : The input to be signed by the signature scheme. sha256 : The SHA-256 hash function defined in . shake256 : The SHAKE256 hash function defined in .

CRYSTALS-Dilithium

Overview This section of the document describes the lattice signature scheme CRYSTALS-Dilithium (CRYDI). The scheme is based on "Fiat-Shamir with Aborts"[Lyu09, Lyu12] utlizing a matrix of polynomials for key material, and a vector of polynomials for signatures. The parameter set is strategically chosen such that the signing algorithm is large enough to maintain zero-knowledge properties but small enough to prevent forgery of signatures. An example implementation and test vectors are provided. CRYSTALS-Dilithium is a post-quantum approach to digital signatures that is an algorithmic apprach that seeks to ensure key pair and signing properties that is a strong implementation meeting Existential Unforgeability under Chosen Message Attack (EUF-CMA) properties, while ensuring that the security levels reached meet security needs for resistance to both classical and quantum attacks. The algoritm itself is based on hard problems over module lattices, specifically Ring Learning with Errors (Ring-LWE). For all security levels the only operations required are variants of Keccak and number theoretic transforms (NTT) for the ring Zq[X]/(X256+1). This ensures that to increase or decrease the security level involves only the change of parameters rather than re-implementation of a related algorithm. While based on Ring-LWE, CRYSTALS-Dilithium has less algebraic structure than direct Ring-LWE implementations and more closely resembles the unstructured lattices used in Learning with Errors (LWE). This brings a theorectical protection against future algebraic attacks on Ring-LWE that may be developed. Given the use of module lattices, this family of approaches is often referred to as MLWE. CRYSTALS-Dilithium, brings several advantages over other approaches to signature suites:

Post-quantum in nature - use of lattices and other approaches that should remain hard problems even when under attack utilizing quantum approaches
Simple implementation while maintaining security - a danger in many possible approaches to cryptography is that it may be possible inadvertently introduce errors in code that lead to weakness or decreases in security level
Signature and public key size - compared to other post-quantum approaches a reasonable key size has been achieved that also preserves desired security properties
Conservative parameter space - parameterization is utilized for the purposes of defining the sizes of matrices in use, and thereby the number of polynomials described by the key material.
Parameter set adjustment for greater security - increasing this matrix size increases the number of polynomials, and thereby the security level
Performance and optimization - the approach makes use of well known transforms that can be highly optimized, especially with use of hardware optimizations without being so large that it cannot be deployed in embedded or IoT environments without some degree of optimization.

The primary known disadvantage to CRYSTALS-Dilithium is the size of keys and signatures, especially as compared to classical approaches for digital signing.

Parameters Unlike certain other approaches such as Ed25519 that have a large set of parameters, CRYSTALS-Dilithium uses distinct numbers of paramters to increase or decrease the security level according to the required level for a particular scenario. Under CRYSTALS-Dilithium, the key parameter specification determines the size of the matrix and thereby the number of polynomials that describe the lattice. For use according to this specification we do not recommend a parameter set of less than 3, which should be sufficient to maintain 128 bits of security for all known classical and quantum attacks. Under a parameter set at NIST level 3, a 6x5 matrix is utilized that thereby consists of 30 polynomials.

Parameter sets Parameter sets are identified by the corresponding NIST level per the table below

NIST Level	Matrix Size	memory in bits
2	4x4	97.8
3	6x5	138.7
5	8x7	187.4

Core Operations Core operations used by the signature scheme should be implemented according to the details in . Core operations include key generation, sign, and verify.

Using CRYDI with JOSE This sections is based on CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE)

CRYDI Key Representations A new key type (kty) value "MLWE" is defined for public key algorithms that use base 64 encoded strings of the underlying binary material as private and public keys and that support cryptographic sponge functions. "MLWE" refers to for keys related to the family of algorithms that utilize Learning With Errors approaches to Post-quantum lattice module based cryptography It has the following parameters:

The parameter "kty" MUST be "MLWE".
The parameter "alg" MUST be specified, and its value MUST be one of the values specified in the table below

alg	Description
CRYDI5	CRYSTALS-Dilithium paramter set 5
CRYDI3	CRYSTALS-Dilithium paramter set 3
CRYDI2	CRYSTALS-Dilithium paramter set 2

The parameter "pset" MAY be specfied to indicate the not only paramter set in use for the algorithm, but SHOULD also reflect the targeted NIST level for the algorithm in combination with the specified paramter set. For "alg" "CRYDI" one of the described parameter sets "2", "3", or "5" MUST be specified. Parameter set "3" or above SHOULD be used with "CRYDI" for any situation requiring at least 128bits of security against both quantum and classical attacks
The parameter "x" MUST be present and contain the public key encoded using the base64url encoding.
The parameter "d" MUST be present for private keys and contain the private key encoded using the base64url encoding. This parameter MUST NOT be present for public keys.

Sizes of various key and signature material is as follows (for "pset" value "2")

Variable	Paramter Name	Paramter Set	Size	base64url encoded size
Signature	sig	2	3293	4393
Public Key	x	2	1952	2605
Private Key	d	2	4000	5337

When calculating JWK Thumbprints , the four public key fields are included in the hash input in lexicographic order: "kty", "alg", and "x".

CRYDI Algorithms In order to reduce the complexity of the key representation and signature representations we register a unique algorithm name per pset. This allows us to omit registering the pset term, and reduced the likelyhood that it will be misused. These alg values are used in both key representations and signatures.

kty	alg	Paramter Set
MLWE	CRYDI5	5
MLWE	CRYDI3	3
MLWE	CRYDI2	2

Public Key Per section 5.1 of :

The public key, containing p and t1, is stored as the concatenation of the bit-packed representations of p and t1 in this order. Therefore, it has a size of 32 + 288 kbytes.

The public key is represented as x and encoded using base64url encoding as described in . Example public key using only required fields: =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kty": "MLWE", "alg": "CRYDI3", "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ 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oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\ elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\ 5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\ pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\ 6F2LKTBMJWg9o/0blvilMH9EPblcLeF/bR1AZTUD6ZFdi2TxN6Epn3QVqeG/qPm1EBTF\ Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\ ZpFl+sGV3Gip3tKlS7PKQkTqI6DMwxEbdrvtdY1sHZagpclLDisA/yFT4RR2m3VNJR9P\ 6Nx3teqN1eg6RXmD/MlKCdWrlcjZ/6yeIQYwbr9CjItY/tLQX2gtAR1SXOh99UUBVv+Z\ E03VOZ+Ecsc78lSB9G/6n6CFzlbk/HgAF+cu0yMbGnEM8W3mTUspS4JBACwk5w0XWNNQ\ DWVEdgzuLGhPq+hYExDjVZrLELhkH8YgZA+7RXXUZHM/joNOGHUhpUG/bFo3ktnaILCu\ xsOXMUbDC3VcitFFHsGK1svtcERDFxk1HA8pGa59jT0do6n3wEbnBDU1soKNFtpmcVkE\ Ul3XpvuoW3BgCwJzBUCWvPs47DJRgGxO11bSaEYYlhTVaaShcvzgz46AkqO+Q7TjckDP\ /8uzsSQk0AbuhxWFQpSiBP8OZ/U=" } Example public key including optional fields: =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kid": "key-0", "kty": "MLWE", "alg": "CRYDI3", "key_ops": ["verify"], "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\ 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Private Key Per section 5.1 of :

The secret key contains p,K,tr,s1,s2 and t0 and is also stored as a bit-packed representation of these quantities in the given order. Consequently, a secret key requires 64 + 48 + 32((k+l) * dlog (2n+ 1)e + 14k) bytes. For the weak, medium and high security level this is equal to 112 + 576k+ 128l bytes. With the very high security parameters one needs 112 + 544k + 96l = 3856 bytes.

The private key is represented as d and encoded using base64url encoding as described in . Example private key using only required fields: =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kty": "MLWE", "alg": "CRYDI3", "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ 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l48YW2/cyS3LvmISQn9KPWK7yEpNQnV0vurn3ZFOGO0eDjSXUjI+xIrRia5GQ1yb31ma\ nJnf2PdHcMmVr0wu4lMGno7a14nMRdnXkBU8bVOp8wF6Toz59hBJ3a/F+mP4/a19Ixra\ wiVVeEPgoi9QQ9NcLgQEFCoskA+EpcLK0FxV2rYI9JFNF/nDxP5nmGtnkmlFaLo+pleH\ CJYS0OTGKQr6X+Y65NOllx5nNwsnWkIUkCodoSt4Givdoe/S9JNIu8tW+jTBae2hNr9c\ glErCNKDYe1+T+Ldyr9rfOKm9LKNyTBsodgF4KI/hFh9Iv/i55DTWtqjpN0eQnPTB3/6\ +7KzTfSE9il5UMcP3zKKC2mAQvtyYxF3k0m24ZTwPs2LAPJkr/xtPH3BnGE/UfUDmvDS\ TBp9m049Nh9oDZvI4HKsY8auiyENk0ys67F9GTHhOYM0FgHyP5qk4/IR5YC3lnq7xx6i\ owebEJAy63htMytq+xd3cJyZR0lWBUOqvSpd/A==" } Example private key using optional fields: =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kid": "key-0", "kty": "MLWE", "alg": "CRYDI3", "key_ops": ["sign"], "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ 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CRYDI Signature Representation For the purpose of using the CRYSTALS-Dilithium Signature Algorithm (CRYDI) for signing data using "JSON Web Signature (JWS)" , algorithm "CRYDI" is defined here, to be applied as the value of the "alg" parameter. The following key subtypes are defined here for use with CRYDI:

"paramter"	CRYDI Paramter Set
5	CRYDI5
3	CRYDI3
2	CRYDI2

The key type used with these keys is "MLWE" and the algorithm used for signing is "CRYDI". These subtypes MUST NOT be used for key agreement. The CRYDI variant used is determined by the subtype of the key (CRYDI3 for "pset 3" and CRYDI2 for "pset 2"). Implementations need to check that the key type is "MLWE" for JOSE and that the pset of the key is a valid subtype when creating a signature. The CRYDI digital signature is generated as follows:

Generate a digital signature of the JWS Signing Input using CRYDI with the desired private key, as described in Section 3.2. The signature bit string is the concatenation of a bit packed representation of z and encodings of h and c in this order.
The resulting octet sequence is the JWS Signature.

When using a JWK for this algorithm, the following checks are made:

The "kty" field MUST be present, and it MUST be "MLWE" for JOSE.
The "alg" field MUST be present, and it MUST represent the algorith and parameter set.
If the "key_ops" field is present, it MUST include "sign" when creating an CRYDI signature.
If the "key_ops" field is present, it MUST include "verify" when verifying an CRYDI signature.
If the JWK "use" field is present, its value MUST be "sig".

Example signature using only required fields, represented in compact form: eyJhbGciOiJQUzM4NCIsImtpZCI6ImJpbGJvLmJhZ2dpbnNAaG9iYml0b24uZX hhbXBsZSJ9 . SXTigJlzIGEgZGFuZ2Vyb3VzIGJ1c2luZXNzLCBGcm9kbywgZ29pbmcgb3V0IH lvdXIgZG9vci4gWW91IHN0ZXAgb250byB0aGUgcm9hZCwgYW5kIGlmIHlvdSBk b24ndCBrZWVwIHlvdXIgZmVldCwgdGhlcmXigJlzIG5vIGtub3dpbmcgd2hlcm UgeW91IG1pZ2h0IGJlIHN3ZXB0IG9mZiB0by4 . cu22eBqkYDKgIlTpzDXGvaFfz6WGoz7fUDcfT0kkOy42miAh2qyBzk1xEsnk2I pN6-tPid6VrklHkqsGqDqHCdP6O8TTB5dDDItllVo6_1OLPpcbUrhiUSMxbbXU vdvWXzg-UD8biiReQFlfz28zGWVsdiNAUf8ZnyPEgVFn442ZdNqiVJRmBqrYRX e8P_ijQ7p8Vdz0TTrxUeT3lm8d9shnr2lfJT8ImUjvAA2Xez2Mlp8cBE5awDzT 0qI0n6uiP1aCN_2_jLAeQTlqRHtfa64QQSUmFAAjVKPbByi7xho0uTOcbH510a 6GYmJUAfmWjwZ6oD4ifKo8DYM-X72Eaw The same example decoded for readability: =============== NOTE: '\\' line wrapping per RFC 8792 =============== { "header": { "alg": "CRYDI3", "kid": "did:example:123#key-0" }, "payload": "It's a dangerous business, Frodo, going out your door.\ \ You step onto the road, and if you don't keep your feet, there's\ \ no knowing where you might be swept off to.", "signature": 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Using CRYDI with COSE The approach taken here matches the work done to support secp256k1 in JOSE and COSE in . The following tables map terms between JOSE and COSE for signatures.

Name	Value	Description	Recommended
CRYDI5	TBD	CRYSTALS-Dilithium with parameter set 5	No
CRYDI3	TBD	CRYSTALS-Dilithium with parameter set 3	No
CRYDI2	TBD	CRYSTALS-Dilithium with parameter set 2	No

The following tables map terms between JOSE and COSE for key types.

Name	Value	Description	Recommended
MLWE	TBD	kty for Learning with Errors based Signatures	No

Security Considerations The following considerations SHOULD apply to all parmeter sets described in this specification, unless otherwise noted. Care should be taken to ensure "kty" and intended use match, the algorithms described in this document share many properties with other cryptographic approaches from related families that are used for purposes other than digital signatures.

Validating public keys All algorithms in that operate on public keys require first validating those keys. For the sign, verify and proof schemes, the use of KeyValidate is REQUIRED.

Side channel attacks Implementations of the signing algorithm SHOULD protect the secret key from side-channel attacks. Multiple best practices exist to protect against side-channel attacks. Any implementation of the the CRYSTALS-Dilithium signing algorithms SHOULD utilize the following best practices at a minimum:

Constant timing - the implementation should ensure that constant time is utilized in operations
Sequence and memory access persistance - the implemention SHOULD execute the exact same sequence of instructions (at a machine level) with the exact same memory access independent of which polynomial is being operated on.
Uniform sampling - uniform sampling is the default in CRYSTALS-Dilithium to prevent information leakage, however care should be given in implementations to preserve the property of uniform sampling in implementation.
Secrecy of S1 - utmost care must be given to protection of S1 and to prevent information or power leakage. As is the case with most proposed lattice based approaches to date, fogery and other attacks may succeed, for example, with Dilithium through leakage of S1 through side channel mechanisms.

Randomness considerations It is recommended that the all nonces are from a trusted source of randomness.

IANA Considerations The following has NOT YET been added to the "JSON Web Key Types" registry:

Name: "MLWE"
Description: MLWE family post-quantum signature algorithm key pairs
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): Section 3.1 of this document (TBD)

The following has NOT YET been added to the "JSON Web Key Parameters" registry:

Parameter Name: "pset"
Parameter Description: The parameter set of the crypto system
Parameter Information Class: Public
Used with "kty" Value(s): "MLWE"
Change Controller: IESG
Specification Document(s): Section 2 of this document (TBD)

The following has NOT YET been added to the "JSON Web Key Parameters" registry:

Parameter Name: "d"
Parameter Description: The private key
Parameter Information Class: Private
Used with "kty" Value(s): "MLWE"
Change Controller: IESG
Specification Document(s): Section 2 of RFC 8037

The following has NOT YET been added to the "JSON Web Key Parameters" registry:

Parameter Name: "x"
Parameter Description: The public key
Parameter Information Class: Public
Used with "kty" Value(s): "MLWE"
Change Controller: IESG
Specification Document(s): Section 2 of RFC 8037

The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry:

Algorithm Name: "CRYDI2"
Algorithm Description: CRYDI2 signature algorithms
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): Section 3.1 of this document (TBD)
Algorithm Analysis Documents(s): (TBD)

The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry:

Algorithm Name: "CRYDI3"
Algorithm Description: CRYDI3 signature algorithms
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): Section 3.1 of this document (TBD)
Algorithm Analysis Documents(s): (TBD)

The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry:

Algorithm Name: "CRYDI5"
Algorithm Description: CRYDI5 signature algorithms
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): Section 3.1 of this document (TBD)
Algorithm Analysis Documents(s): (TBD)

Appendix

General References

JSON Web Signature (JWS) - RFC7515
JSON Web Encryption (JWE) - RFC7516
JSON Web Key (JWK) - RFC7517
JSON Web Algorithms (JWA) - RFC7518
JSON Web Token (JWT) - RFC7519
JSON Web Key Thumbprint - RFC7638
JWS Unencoded Payload Option - RFC7797
CFRG Elliptic Curve ECDH and Signatures - RFC8037
CRYSTALS-Dilithium - Dilithium

Appendix A. Acknowledgements We would like to especially thank Gabe Cohen for close attention to and contribution to test vectors, and David Balenson for careful review of approach. We would also like to thank Michael B. Jones for guidance in authoring.

Appendix B. Document History -01

Added Acknowledgements
Added Document History
Changed key type to MLWE
Updated test vectors

-00

Created draft-ietf-cose-dilithium-00 from draft-ietf-cose-post-quantum-signatures-01 following working group feedback

Appendix C. Test Vectors

MLWE CRYDI5

publicKeyJwk ========== NOTE: '\' line wrapping per RFC 8792 ========== { "kty": "MLWE", "alg": "CRYDI5", "x": "TUlJS05EQU5CZ3NyQmdFRUFRS0NDd2NJQndPQ0NpRUFpM1lBMWZnZGZ3YXJM\ UmlmbTB2MEowZlI3TjdMWDZhdmtDU3pIa3kzVUtwOEFpRmhDSWJIbHFwSHAxUXNESGls\ VXhydDhtd1FhQTFUR1FvanBvbmlKa3ZWaFZTZDFMRUhXeXpPOUVPclFFSXo4S2xVUEpF\ ZUgzWTJCVCtpQ245Z2J1ZGFudFIyYUd6WHY4RFBxb1hXbXRaMFZxV3loUnE2MVFVcmJy\ ZjZPU2ZqMkxOQklBaHRPR3JmVkltRisrN2x6NGUyM2hiQzZCcUFiYU8zZDV4dzdhaUlS\ c1l2Y0tHaHpOOE83dU9xRUxJajViWnJrakgzenJ4bWx4Q2pUVHhHSGlkMy8zNTNXWW5p\ S25FUzJ0Njd1K0Vob3FiaG1nUWdQNFI4cmNpSWMzZFY4THF1S3huZTJ4NHd0bno3cW12\ KzhtdmFQbXVMOHJTUEpTbFpCbHd5V2laMGF5VUV0djVxS0hERGxtYnpscUZIeENOdUxV\ MnRKamd5ZUVSTWNUU0htaFVONk9mZGlPTkdIektFOC9ZTTBjUC9OTS9zaEUwdFE4Rk9w\ RUV6UjhwWE5aamhSWEI5SFdBMTRNNjFMTUZ3VWZ1czYweHNDOFhzQit0NEd6ZU1iNWVy\ L0dIejZBOTJoQjd1RzlmYzdxZTViSjJJWnJ2U3h1Sjh3alFCRDdBaTYxTDRpS1JGeTZK\ VzRsdXB6VWlXTldGSjU5Q1dORHdLbUM3ZTlyN1NROUV4dzNUNFIvVDFEcnVzbThUNEt1\ cTJOOGdGSFJDUmpLanhha0NnRy9DZXphRVV1SVRqS293M3RMQ01QalZSRUNRRTIxV0Er\ UXBic2RpZm1tY1dlVFpEQ2JOb3hyYnJhMGpud1RuVVd3WS94a1FyN2NMV2RabU1JNGtn\ NFpOaFNndlFrMUdqczlrcHozekpBbG5KSDNnckt2U1hqSENvSDgyZ29ubnl5OWtkVWdh\ Qk9vbHRCOWd6eXZCOVZ2NUM2LzJJOTdaYWZFUWU3NVV4eU9Hejh4WHc4L1BGdDA0eHFu\ WGVmSmZSTUhDSEQ2WU9OdVp4L3FraWMwUkNCMTJkeVlYQTZ4TWRKVGtDRzhNTzBwQ2N6\ SnBvdm02Tk5GTTZETGVFd3B0QUxycWhtUjdQUkR3ZGVSVSsrLzVtUGlkRkpaZUlpTWxU\ NXpBN0JJUW1tbDBnNmwvdVhsMG9lN2xkaFlCSnE5Rnc2dDB0azBubWUvUlhSb3dEdVZG\ cUpscnJiZHNEZFdRQXUwL3JZVHNnTGhLck1uMHFUOHBNYUNLNkZpQXdNR3BGT0VsVkFx\ VXVGRTQyejZvcmJzZmNVcDJqdy9ESi83MVRDeW9yWVBxakN1Yno0alFKSWZWMTIyWWpo\ aHpUNWNXTVo4Mm0wdnpkanMxaFFhU3BmUHlTekhjbmQ3NyszT3JKbzNJck81NlBHQzJB\ WEl3OUNhVFExd3F6bC9PZ0xHQmdQWDNHZHZxRHNKRzdqR05rN1BoaHRvMDEzRTB5WldZ\ WUFWUXZ0RHQveUN5NUdXMzNXTm85Znc3TkVFaTJUbGdDMHRNVjJEcDhvNmRGY0gwZTRY\ Q0VoVUxpam1EdEkrYzJrYVd6Ui9qTDZjVHlaMXZEWGhpOEpHUmNaZVIzRGpvN2xpcjln\ OTFTN3ZvTGJMT0R4Q21FNjl0UGVvc1dIbDZYYjJtWXk3M2dicWo0SFFCMEZ1Rjc4QnBL\ YUVlN3dieGhuelg1Ry9EYmZTOEt3eXBJUzl0UkFvd0JzWjFVSTRsMHJCYmNBdDRQTjVx\ RUJ0cFZLeTVYTE0xTVZNL2RLY0RiOVgrQU8wZ3hqdmQyNCt2bVNOeFBSSUh3WkU2UTMr\ WXh4dE85eCtrMkxibWNtdFJjRDkyWDAweUc5cmhJSVRIQnE2cWVjUi90WE85S3dobVJj\ dWM2aXZ0UWlYNUV6MkhtN3c5cDRZWVd1aGNEZ3M3VlBZUDdnLy9SM042V0FiL0pnMHhp\ TVpsVXpqTTI5YW1VQXdrNWpVYTF0UUtrdHlMMm51bTRrL1poOEcrWXF6QklDMjhvQ2JU\ VzhJTU93OGJSTEc4WnZ2N1dsUDk3cTgvVFJlYzVPQ3I4N1dHMTJ5K0J6ckxIZlg4TTBX\ ZnVvWkh6cFI4U2VaWXNtWit0dk5EWi9OUjV5R0VWQ24xR21tQU1QcmI0R05XTDFJWkp2\ VGovR0dtT1Y2L3U3NGNlSHlGQXdvdi8yaE5LWkRwYmJiS09KeXpWallQWjBHa1VYRlZW\ Tng0c0tPTTVKRkpUeFdCSTEvQ3JCcGVRWlp5NnBIYjZkOWlXbmRKN0VDek5zVDVqMWFv\ NUpCS2t1Z2d5ZDduTTk4OEZRVDVpWnJzYytkby9HNmRsVHZ5NXYrUzZYRkhYSWV4YzJV\ dEhnY2lzTmhGYmRicDRhSXNSNU9ielppRzQyS1JVMTFrZUJEbW1VeFdOMkV0MXpMKzlP\ b3hzeTJDczNMVUhBYkVKRmREWmZSVmR5TnhSZFV1YklkODNyY0pMTmN2aGxidnZCWjll\ K2VSZXNyeS90WmNGYVBWVHZWZkRrWkJmMGF5b2pSbm50WUhEVTR5c0xHUUxZSXczdlhC\ aERHbzVKdGdWY3ZJT21TTHJKbENlVUNCOWJpQkhwYjZxSlZQSzRodURncVlWYUtISDJJ\ S3VTZkRPSFg1R0FhcmVLaGlBWnBHelZYVS9GMlIybjQzK2MxOURCWTF1WWZaU0pQdkt1\ Zk8vWFY4YXFsazh0ZVVraWprWkpiUW1maEVnLzRieDFpVDlKdGMwMlFQN2x2bThnRnpj\ L3l5U2RmaGsxUE8yWXdSNWdHdVh6bHh4TWJLalpaZnRqempaVzQ4aFZpdVhRekRIdjA4\ UlBBc0dPTkM0RTE5aWdkWUoxNGJpaHJncDlVRmJMRXJiMlFES3Y0SllLa25PVHM3L2p1\ cVQwNndEakpOSGc1empQVlFNUW9lbEJ3L2xGdnozZDl2MHJqYTUzeFUrTUhTZGs2WVRx\ c2JHd1F5RGlnVktZaVYyRnYyV3RKbVdvVE1WeDdMUHc3VFlVWFl2Rk5od1U5WHVvUTlJ\ MmZocHo3a0xCWHlLSDByVEt5bytzaVh6SGZyN3BTNFFoUEdPUjUvS0l0d1Y0UTBXaVhh\ bm1TUE0ySTZZdWJIT3lyd0tnRGlnbWhpc2lRY0JJb3JYcXVoVXVpZllDZjdPWEFTRGxj\ M0U4UERmOW8zdkpCWm9MT0tFREg1cEo0YW90NnB2cmtIaEx3dnIwWVNORVdnM1RWOHVV\ NmcySHFBNThzL1BCNFR1RnhUOWVzRUFIZFpRK0U1RE9DWk1yQjk4Y2ZXTDNjN3JtdTZR\ SkVUdkxxclhLTWdoMEJrSzBhZ2pVbU5ramtBbVJBNUdhcG5EK2VYRXNwL3pOcWhZZExm\ bGRFWCtvWWZ1ODJzVGFpZzc1alpYam4zd09BeUpFVEN2T21YY21UZlRVUUJxQ0JhaHNC\ RlZCZlpPdExqQS84ZjFqUWhlSitUMjJ2RlY2R3VPTFZXMXQrSnMyVjgrWVh3V01uVFZP\ ZVRsbXRqeE05VWZLME5laU10YlU5dlhqTkFBU0xpTXNBK2Faa1ZVa3NkM1FNZVNhTmdj\ ZXR6QzhvZ2FZczc5aVZvNTN2RmxzY0NZaXo2alB4OG9PcGxHY0ZIUGIwald6V01FMWJL\ a2hiNlc2eklRS0JZNkNzcHhHcmhOSHhZdWFsY1ZjQWI4M2s1alRwM0Y5YnVGbjkyazRG\ enFIcnJIVFV1ZGVvMmhUUCtuOHVPVm1DbzRlVWcvbkpDQ2hyTVNoNnQzczZScHpIY1A5\ VmJBYlFxdERJc3lGb2RYZnQvK25tdUhxNVh5ejZJY1ByNjFhNjhtQVBoYXF5RkdmakFu\ VGNJSlhzakFvUmIzN0xhdXJYU0h2QWNLcHJxNElQZmZRdGNKYlVzWHRKbXhVbklJL1N0\ VGxMdDlrUkwrejJyUitFV210QldSYmdMbVE1VG4wVWk2eDhGTk5nVTA1eUpFL29YMmdJ\ VEMwL2xLVCtEakh1eTNLcHRiYmVYaHpLWGhOclRteEdRbmhkT3ZpSVIvRS9zczNzTlZV\ WWIzUzBMQWk1anRrOGtGSEhnZUlJUlhKY3NST0Y2OVJjdERzZXNLckFQajFOU2E5SjRT\ MWhKSzU4bEhndmV6MFA0Q0g3bkdOUGE5RER2eVRtUmRzZVVYNkJhMEMvdzFobFFSendM\ R0JNTXNSMlkzZ0NzMjlrMERsVG1wWkhnNDdKMnZTK1hEMS9WVGZYMGE3YnEwQitlc2Z1\ ektValRhMjdITHVkZEorVG5XdDZvVTBsOFVaZ3Z3R0I4anlYT3ZIcElwODZJREhiNHFo\ OTRqUmQxY3hNWVFwUkorZ1IwR210TmpZTFNKSlgzc1l3bFh0dEJ1cnRlZWRtdmwvNzI2\ amZoaDFKSjUxNXkyOVdiU2xUY2oyMFNEb3V0OStNVlB0MldGVnNuOVIva1ZJRlY1bnVN\ cjJRUG50dHFzNkVITXppdFY5NUcvVEJ4cWgwcXBKT0ZXM3BYNExaYnl0QkhtODBNcVlw\ Q3N5aXhMaUVnRGlCaXBNd1BvaHZFZmRqeWY", "use": "sig" }

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