| Internet-Draft | draft-denhartog-pairing-curves-jose-cose | May 2021 |
| Den Hartog | Expires 2 December 2021 | [Page] |
This specification defines representations enabling the Standards for Pairing Frinedly Curves to be used for JSON Object Signing and Encryption (JOSE) and CBOR Object Signing and Encryption (COSE) messages.¶
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This specification defines algorithm encodings and representations enabling the Standard Pairing Frinedly Curves to be used for JSON Object Signing and Encryption (JOSE) [RFC7517] [RFC7517] and CBOR Object Signing and Encryption (COSE) [RFC8152] [RFC8152] messages. The elliptic curve and associated algorithm are registered in appropriate IANA JOSE and COSE registries.¶
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 RFC 2119 [RFC2119] RFC 8174 [RFC8174] when, and only when, they appear in all capitals, as shown here.¶
The pairing friendly elliptic curve "BN256" which uses the largest prime-order subgroup of E(GF(p)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values: o "kty": "OKP" o "crv": "Bn256G1" plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] format and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
It is represented in a COSE_Key [RFC8152] [RFC8152] using these values:¶
o "kty" (1): "OKP" (1) o "crv" (-1): "Bn256G1" (TBD - requested assignment 9)¶
plus "x" (-2) values to represent the curve point for the key. The "x" value MUST be encoded using [SEC1] [SEC1] point compression format.¶
The pairing friendly elliptic curve "BN256" which uses an r-order subgroup of E'(GF(p^2)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bn256G2"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
It is represented in a COSE_Key [RFC8152] [RFC8152] using these values:¶
o "kty" (1): "OKP" (1) o "crv" (-1): "Bn256G2" (TBD - requested assignment 10)¶
plus "x" (-2) values to represent the curve point for the key. The "x" value MUST be encoded using [SEC1] [SEC1] point compression format.¶
The pairing friendly elliptic curve "BN462" which uses the largest prime-order subgroup of E(GF(p)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bn462G1"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
It is represented in a COSE_Key [RFC8152] [RFC8152] using these values:¶
o "kty" (1): "OKP" (1) o "crv" (-1): "Bn462G1" (TBD - requested assignment 11)¶
plus "x" (-2) values to represent the curve point for the key.¶
The pairing friendly elliptic curve "BN462" which uses an r-order subgroup of E'(GF(p^2)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bn462G2"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
The pairing friendly elliptic curve "BLS12-381" which uses the largest prime-order subgroup of E(GF(p)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bls12381G1"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using the Z-Cash serialization defined in [DPFC09] [DPFC09] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
It is represented in a COSE_Key [RFC8152] [RFC8152] using these values:¶
o "kty" (1): "OKP" (1) o "crv" (-1): "Bls12381G1" (TBD - requested assignment 13)¶
plus "x" (-2) values to represent the curve point for the key.¶
The pairing friendly elliptic curve "BLS12-381" which uses an r-order subgroup of E'(GF(p^2)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bls12381G2"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using the Z-Cash serialization defined in [DPFC09] [DPFC09] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
The pairing friendly elliptic curve "BLS48-581" which uses the largest prime-order subgroup of E(GF(p)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bls48581G1"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
It is represented in a COSE_Key [RFC8152] [RFC8152] using these values:¶
o "kty" (1): "OKP" (1) o "crv" (-1): "Bls48581G1" (TBD - requested assignment 15)¶
plus "x" (-2) values to represent the curve point for the key.¶
The pairing friendly elliptic curve "BLS48-581" which uses the largest prime-order subgroup of E'(GF(p^8)) is represented in a JSON Web Key (JWK) [RFC7517] [RFC7517] using these values:¶
o "kty": "OKP" o "crv": "Bls48581G2"¶
plus "x" value to represent the curve point for the public key. The "x" value MUST be encoded using [SEC1] [SEC1] and MUST be base64url encoded without padding as defined in [RFC7515] [RFC7515] Appendix C.¶
This section registers the following value in the IANA "JSON Web Key Elliptic Curve" registry [IANA.JOSE.Curves].¶
o Curve Name: Bn256G1 o Curve Description: 256 bit Barreto-Naehrig pairing friendly curve using the largest prime-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Prohibited o Change Controller: IESG o Specification Document(s): Section 2.1 of [[ this specification ]]¶
o Curve Name: Bn256G2 o Curve Description: 256 bit Barreto-Naehrig pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Prohibited o Change Controller: IESG o Specification Document(s): Section 2.3 of [[ this specification ]]¶
o Curve Name: Bn462G1 o Curve Description: 462 bit Barreto-Naehrig pairing friendly curve using the largest prime-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 2.5 of [[ this specification ]]¶
o Curve Name: Bn462G2 o Curve Description: 462 bit Barreto-Naehrig pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 2.7 of [[ this specification ]]¶
o Curve Name: Bls12381G1 o Curve Description: 381 bit with an embedding degree of 12 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.1 of [[ this specification ]]¶
o Curve Name: Bls12381G2 o Curve Description: 381 bit with an embedding degree of 12 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.3 of [[ this specification ]]¶
o Curve Name: Bls48581G1 o Curve Description: 581 bit with an embedding degree of 48 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.5 of [[ this specification ]]¶
o Curve Name: Bls48581G1 o Curve Description: 581 bit with an embedding degree of 48 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E'(GF(p^8)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.7 of [[ this specification ]]¶
This section registers the following value in the IANA "JSON Web Key Elliptic Curve" registry [IANA.JOSE.Curves].¶
o Curve Name: Bn256G1 o Value: TBD (requested assignment 9) o Key Type: OKP o Curve Description: 256 bit Barreto-Naehrig pairing friendly curve using the largest prime-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Prohibited o Change Controller: IESG o Specification Document(s): Section 2.2 of [[ this specification ]] o Recommended: No (Prohibited)¶
o Curve Name: Bn256G2 o Value: TBD (requested assignment 10) o Key Type: OKP o Curve Description: 256 bit Barreto-Naehrig pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Prohibited o Change Controller: IESG o Specification Document(s): Section 2.4 of [[ this specification ]] o Recommended: No (Prohibited)¶
o Curve Name: Bn462G1 o Value: TBD (requested assignment 11) o Key Type: OKP o Curve Description: 462 bit Barreto-Naehrig pairing friendly curve using the largest prime-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 2.6 of [[ this specification ]] o Recommended: No¶
o Curve Name: Bn462G2 o Value: TBD (requested assignment 12) o Key Type: OKP o Curve Description: 462 bit Barreto-Naehrig pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 2.8 of [[ this specification ]] o Recommended: No¶
o Curve Name: Bls12381G1 o Value: TBD (requested assignment 13) o Key Type: OKP o Curve Description: 381 bit with an embedding degree of 12 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.2 of [[ this specification ]] o Recommended: Yes¶
o Curve Name: Bls12381G2 o Value: TBD (requested assignment 14) o Key Type: OKP o Curve Description: 381 bit with an embedding degree of 12 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E'(GF(p^2)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.4 of [[ this specification ]] o Recommended: Yes¶
o Curve Name: Bls48581G1 o Value: TBD (requested assignment 15) o Key Type: OKP o Curve Description: 581 bit with an embedding degree of 48 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E(GF(p)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.6 of [[ this specification ]] o Recommended: No¶
o Curve Name: Bls48581G1 o Value: TBD (requested assignment 16) o Key Type: OKP o Curve Description: 581 bit with an embedding degree of 48 Barreto-Lynn-Scott pairing friendly curve using an r-order subgroup of E'(GF(p^8)) o JOSE Implementation Requirements: Optional o Change Controller: IESG o Specification Document(s): Section 3.8 of [[ this specification ]] o Recommended: No¶
See [DPFC09] [DPFC09] for additional details about security considerations of the curves used. Implementers should also consider section 9 of [RFC7517] [RFC7517] when implementing this work.¶
To be added.¶
The authors of this draft would like to acknowledge the following individuals for the significant contribution of ideas and time spent reviewing this document:¶