Barreto-Lynn-Scott Elliptic Curve Key Representations for JOSE and COSE
Internet-Draft draft-ietf-cose-bls-key-representations-00
Tobias Looker
Mattr
tobias.looker@mattr.global
Michael B. Jones
Microsoft
mbj@microsoft.com
https://self-issued.info/
Internet
COSE
COSE
JOSE
This specification defines how to represent cryptographic keys for the pairing-friendly elliptic curves known as Barreto-Lynn-Scott (BLS), for use with the key representation formats of JSON Web Key (JWK) and COSE (COSE_Key).

Discussion Venues
Source for this draft and an issue tracker can be found at https://github.com/tplooker/draft-ietf-cose-bls-key-representations.
Introduction
This specification defines how to represent cryptographic keys for the pairing-friendly elliptic curves known as Barreto-Lynn-Scott [BLS], for use with the key representation formats of JSON Web Key (JWK) and COSE_Key. This specification registers the elliptic curves in appropriate IANA JOSE and COSE registries.
There are a variety of applications for pairing based cryptography including schemes already published as RFCs, such as Identity-Based Cryptography [RFC5091] Sakai-Kasahara Key Encryption (SAKKE) [RFC6508], and Identity-Based Authenticated Key Exchange (IBAKE) [RFC6539]. SAKKE is applied to Multimedia Internet KEYing (MIKEY) [RFC6509].
This branch of cryptography has also been used to develop privacy-preserving cryptographic hardware attestations schemes, including the Elliptic Curve Direct Anonymous Attestation (ECDAA) in the Trusted Platform Modules [TPM] specified by the Trusted Computing Group. Further work on similar schemes has also occurred at the FIDO Alliance [ECDAA]. Similarly, Intel released [EPID] which provides a solution to remote hardware attestation for Intel Software Guard Extension (SGX) enabled environments.
More recently, applications of pairing based cryptography using the Barreto-Lynn-Scott curves include the standardization effort for BLS Signatures [id.draft.bls-signature-04], which are used extensively in multiple blockchain projects due to their unique signature aggregation properties, including [Ethereum] [DFINITY] [Algorand]. Additionally, efforts are under way to standardize the general purpose short group signature scheme of BBS Signatures [BBS], which features novel properties such as multi-message signing and selective disclosure alongside zero knowledge proving. It is intended that this draft will help with these efforts by standardizing the associated cryptographic key representation in the popular formats of JWK and COSE_Key.
Other relevant work to this draft includes [JWP] which is extending the JOSE family of specifications to provide support for representing a variety of new proof based cryptographic schemes such as [BBS] which as referred to above uses the Barreto-Lynn-Scott curves.
There are multiple different pairing-friendly curves in active use; however, this draft focuses on a definition for the Barreto-Lynn-Scott curves due to them being the most "widely used" and "efficient" whilst achieving 128-bit and 256-bit security (BLS12-381 and BLS48-581 respectively).
More extensive discussion on the broader application of pairing based cryptography and the assessment of various elliptic curves (including the BLS family) can be found in [id.draft.pairing-friendly-curves-10].
Conventions and Definitions
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 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.
Representation Definition
The following definitions apply to the pairing-friendly elliptic curves known as the Barreto-Lynn-Scott (BLS) curves.
JSON Web Key Representation
When expressing a cryptographic key for these curves in JSON Web Key (JWK) form, the following rules apply:
- The parameter "kty" MUST be present and set to "OKP".
- The parameter "crv" MUST be present and value MUST be one defined in Section 2.1.3.
- The parameter "x" MUST be present whose value represents the curve point for the public key. This value MUST be encoded using the serialization defined in [id.draft.pairing-friendly-curves-10] Appendix C and MUST be base64url encoded without padding as defined in [RFC7515] Appendix C.
- The parameter "d" MUST be present for private key representations whose value MUST contain the little-endian representation of the private key base64url encoded without padding as defined in [RFC7515] Appendix C. This parameter MUST NOT be present for public keys.
COSE_Key Representation
When expressing a cryptographic key for these curves in COSE_Key form, the following rules apply:
- The parameter "kty" (1) MUST be present and set to "OKP" (1).
- The parameter "crv" (-1) MUST be present and value MUST be one defined in Section 2.1.3.
- The parameter "x" (-2) MUST be present whose value represents the curve point for the public key. This value MUST be encoded using the serialization defined in [id.draft.pairing-friendly-curves-10] Appendix C.
- The parameter "d" (-4) MUST be present for private key representations whose value MUST contain the little-endian representation of the private key. This parameter MUST NOT be present for public keys.
Curve Parameter Registration
JWK "crv" value | COSE_Key "crv" value | Description
Bls12381G1 | TBD (13 requested) | A cryptographic key on the Barreto-Lynn-Scott (BLS) curve featuring an embedding degree 12 with 381-bit p in the subgroup of G1 defined as E(GF(p)) of order r
Bls12381G2 | TBD (14 requested) | A cryptographic key on the Barreto-Lynn-Scott (BLS) curve featuring an embedding degree 12 with 381-bit p in the subgroup of G1 defined as E(GF(p^2)) of order r
Bls48581G1 | TBD (15 requested) | A cryptographic key on the Barreto-Lynn-Scott (BLS) curve featuring an embedding degree 48 with 581-bit p in the subgroup of G1 defined as E(GF(p)) of order r
Bls48581G2 | TBD (16 requested) | A cryptographic key on the Barreto-Lynn-Scott (BLS) curve featuring an embedding degree 48 with 581-bit p in the subgroup of G1 defined as E(GF(p^8)) of order r
Security Considerations
See [id.draft.pairing-friendly-curves-10] for additional details on security considerations for the curves used. Implementers should also consider the general guidance provided in Section 9 of [RFC7517] and Section 17 of [RFC8152] when using this specification.
Furthermore, because this specification only defines the cryptographic key representations and not the usage of these keys with specific algorithms, implementers should be aware to follow any guidance that may be provided around appropriate usage of the keys and or additional steps that may be required to validate the keys within the context of particular algorithms.
IANA Considerations
JSON Web Key (JWK) Elliptic Curve Registrations
This section registers the following values in the IANA "JSON Web Key Elliptic Curve" registry [IANA.JOSE.Curves].
Bls12381G1
- Curve Name: Bls12381G1
- Curve Description: 381 bit with an embedding degree of 12 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E(GF(p))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.1
Bls12381G2
- Curve Name: Bls12381G2
- Curve Description: 381 bit with an embedding degree of 12 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E'(GF(p^2))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.1
Bls48581G1
- Curve Name: Bls48581G1
- Curve Description: 581 bit with an embedding degree of 48 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E(GF(p))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.1
Bls48581G2
- Curve Name: Bls48581G2
- Curve Description: 581 bit with an embedding degree of 48 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E'(GF(p^8))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.1
COSE Elliptic Curve Registrations
This section registers the following value in the IANA "COSE Elliptic Curves" registry [IANA.COSE.Curves].
Bls12381G1
- Curve Name: Bls12381G1
- Value: TBD (13 requested)
- Key Type: OKP
- Curve Description: 381 bit with an embedding degree of 12 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E(GF(p))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.2
- Recommended: Yes
Bls12381G2
- Curve Name: Bls12381G2
- Value: TBD (14 requested)
- Key Type: OKP
- Curve Description: 381 bit with an embedding degree of 12 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E'(GF(p^2))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.2
- Recommended: Yes
Bls48581G1
- Curve Name: Bls48581G1
- Value: TBD (15 requested)
- Key Type: OKP
- Curve Description: 581 bit with an embedding degree of 48 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E(GF(p))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.2
- Recommended: Yes
Bls48581G2
- Curve Name: Bls48581G2
- Value: TBD (16 requested)
- Key Type: OKP
- Curve Description: 581 bit with an embedding degree of 48 Barreto- Lynn-Scott pairing-friendly curve using the r-order subgroup of E'(GF(p^8))
- JOSE Implementation Requirements: Optional
- Change Controller: IESG
- Specification Document(s): Section 2.1.2
- Recommended: Yes
Normative References
[BLS]

Constructing Elliptic Curves with Prescribed Embedding Degrees
Paulo S. L. M. Barreto
Ben Lynn
Michael Scott
2003
[IANA.COSE.Curves]

COSE Elliptic Curves
IANA
[IANA.JOSE.Curves]

JOSE Elliptic Curves
IANA
[id.draft.bls-signature-04]

BLS Signature
IETF CFRG
[id.draft.pairing-friendly-curves-10]

Pairing-Friendly Curves
IETF CFRG
Informative References
[BBS]

The BBS Signature Scheme
Decentralized Identity Foundation
[ECDAA]

ECDAA Algorithm
FIDO Alliance
2018
[EPID]

Intel (R) SGX: Intel (R) EPID Provisioning and Attestation Services
Intel Corporation
[JWP]

JSON Web Proof
Jeremie Miller
Michael B. Jones
[TPM]

Trusted Platform Module
Trusted Computing Group
[RFC5091]
[RFC6508]
[RFC6539]
[RFC6509]
[RFC2119]
[RFC8174]
[RFC7515]
[RFC7517]
[RFC8152]
Acknowledgments
The authors would like to acknowledge the work of Kyle Den Hartog, which was used as the foundation for this draft.
Document History
-00
- Created draft-ietf-cose-bls-key-representations-00 from draft-looker-cose-bls-key-representations-00 following working group adoption.