Pairing Friendly Curves representations in JOSE and COSE
Mattr
kyle.denhartog@mattr.global
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.
This specification defines algorithm encodings and representations enabling the Standard Pairing Frinedly Curves to be used for
JSON Object Signing and Encryption (JOSE) [RFC7517] and CBOR Object Signing and Encryption (COSE) [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
RFC
8174 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] 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] format and MUST be base64url encoded without padding as defined in
[RFC7515] Appendix C.
It is represented in a COSE_Key [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] 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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [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] 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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [RFC8152] using these values:
o "kty" (1): "OKP" (1)
o "crv" (-1): "Bn462G2" (TBD - requested assignment 12)
plus "x" (-2) values to represent the curve point for the key.
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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [RFC8152] using these values:
o "kty" (1): "OKP" (1)
o "crv" (-1): "Bls12381G2" (TBD - requested assignment 14)
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)) is represented in a JSON Web Key (JWK) [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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [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] 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] and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
It is represented in a COSE_Key [RFC8152] using these values:
o "kty" (1): "OKP" (1)
o "crv" (-1): "Bls48581G1" (TBD - requested assignment 16)
plus "x" (-2) values to represent the curve point for the key.
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] for additional details about security considerations of the curves used. Implementers should also consider section 9 of
[RFC7517] when implementing this work.
The authors of this draft would like to acknowledge the
following individuals for the significant contribution of ideas and
time spent reviewing this document:
Pairing-Friendly Curves
IRTF CFRG
SEC 1: Elliptic Curve Cryptography
Standards for Efficient Cryptography Group (SECG)