BLS digital signature explained

A BLS digital signature, also known as Boneh - Lynn - Shacham (BLS), is a cryptographic signature scheme which allows a user to verify that a signer is authentic.

e: G _{1 x} G _{2\to} G _{T} , where G _{1,} G _{2,} and G _{T} are elliptic curve groups of prime order q , and a hash function H from the message space into G _{1} . Signature are elements of G _{1} , public keys are elements of G _{2} , and the secret key is an integer in [ 0 ,q -1 ] . Working in an elliptic curve group provides some defense against index calculus attacks (with the caveat that such attacks are still possible in the target group G _{T} of the pairing), allowing shorter signatures than FDH signatures for a similar level of security.

Signatures produced by the BLS signature scheme are often referred to as short signatures, BLS short signatures, or simply BLS signatures. The signature scheme is provably secure (the scheme is existentially unforgeable under adaptive chosen-message attacks) in the random oracle model assuming the intractability of the computational Diffie–Hellman problem in a gap Diffie–Hellman group.

BLS signature scheme

A signature scheme consists of three functions: generate, sign, and verify.^[1]

Key generationThe key generation algorithm selects the private key by picking a random integer

x\in [ 0 ,q -1 ] . The holder of the private key publishes the public key, g ^{x} _{2} , where g _{2} is a generator of G _{2} .

SigningGiven the private key

x , and some message m , we compute the signature by hashing the bitstring m , as h = H(m) , and we output the signature \sigma = h ^{x} .

VerificationGiven a signature

\sigma for message m and public key g ^{x} _{2} , we verify that e(\sigma, g _{2} ) = e(H(m), g ^{x)} _{2} .

Properties

• Unique and deterministic: for a given key and message, there is only one valid signature (like RSA PKCS1 v1.5, EdDSA and unlike RSA PSS, DSA, ECDSA and Schnorr).^[2]
• Signature Aggregation: Multiple signatures generated under multiple public keys for multiple messages can be aggregated into a single signature.^[3]
• Simple Threshold Signatures^[4] and multisignatures.^[5]

Curves

BLS12-381

BLS12-381 is part of a family of elliptic curves named after Barreto, Lynn, and Scott (a different BLS trio, except for the L). It was designed by Sean Bowe in early 2017 as the foundation for an upgrade to the Zcash protocol. It is both pairing-friendly, making it efficient for digital signatures, and effective for constructing zkSnarks.^[6] The usage of BLS12-381 for BLS signatures is detailed in the IETF internet draft.^[7]

Implementations

• Chia network has used BLS signatures.^{[8] [9]}
• By 2020, BLS signatures were used extensively in version 2 (Eth2) of the Ethereum blockchain, as specified in the IETF draft BLS signature specification—for cryptographically assuring that a specific Eth2 validator has actually verified a particular transaction.^[10] The use of BLS signatures in Ethereum is considered a solution to the verification bottleneck only for the medium term, as BLS signatures are not quantum secure. Over the longer term—say, 2025–2030—STARK aggregation is expected to be a drop-in replacement for BLS aggregation.^[11]
• Dfinity (developers of the "Internet Computer" cryptocurrency) uses a BLS implementation.^[12]
• Skale cryptocurrency uses BLS signature algorithm.^[13]
• drand uses the BLS12-381 curve as a threshold scheme.^[14]

See also

• Pairing-based cryptography

External links

• Summary description of the Algorand draft standard effort
• Ben Lynn's PBC Library
• Chia Network's BLS signatures implementation (C++)

Notes and References

1. Dan Boneh . Dan Boneh . Ben Lynn . Ben Lynn . Hovav Shacham . Hovav Shacham . amp . Short Signatures from the Weil Pairing . Journal of Cryptology . 17 . 4 . 2004 . 297–319 . 10.1007/s00145-004-0314-9 . 10.1.1.589.9141 . 206885645 .
2. Web site: Shacham . Hovav . New Paradigms in Signature Schemes . 2024-06-07 . www.semanticscholar.org . 18.
3. D. Boneh, C. Gentry, H. Shacham, and B. Lynn Aggregate and Verifiably Encrypted Signatures from Bilinear Maps, proceedings of Eurocrypt 2003, LNCS 2656, pp. 416-432, 2003
4. Web site: Threshold BLS Signatures . jcraige.com . Craige. Jake . 11 March 2020 . 8 August 2022.
5. Boldyreva . Alexandra . 2002 . Desmedt . Yvo G. . Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme . Public Key Cryptography — PKC 2003 . en . Berlin, Heidelberg . Springer . 31–46 . 10.1007/3-540-36288-6_3 . 978-3-540-36288-3.
6. Web site: BLS12-381 For The Rest Of Us . 2024-02-11 . HackMD . en.
7. BLS Signatures . Boneh . Dan . Gorbunov . Sergey . 2022-06-16 . Internet Engineering Task Force . draft-irtf-cfrg-bls-signature-05 . Wahby . Riad S. . Wee . Hoeteck . Wood . Christopher A. . Zhang . Zhenfei.
8. Web site: 5. BLS Signatures Chia Documentation . 2023-06-07 . docs.chia.net . en.
9. https://github.com/Chia-Network/bls-signatures BLS signatures
10. Web site: Ethereum 2.0 Phase 0 -- The Beacon Chain : BLS Signatures . . 28 July 2020 . 4 September 2020 .
11. Web site: Pragmatic signature aggregation with BLS . Drake. Justin . Eth research . ethresear.ch/ . 5 December 2019 . 8 January 2021 .
12. Web site: Chain-key signatures Internet Computer . 2024-08-16 . internetcomputer.org . en.
13. Web site: SKALE Documentation :: SKALE Network Documentation . 2024-08-16 . docs.skale.network.
14. Web site: 2.1 Cryptography . drand . 2024-11-18.