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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.

The scheme uses a bilinear pairing ${\displaystyle e:G_{1}\times G_{2}\to G_{T}}$, where ${\displaystyle G_{1},G_{2},}$ and ${\displaystyle G_{T}}$ are elliptic curve groups of prime order ${\displaystyle q}$, and a hash function ${\displaystyle H}$ from the message space into ${\displaystyle G_{1}}$. Signature are elements of ${\displaystyle G_{1}}$, public keys are elements of ${\displaystyle G_{2}}$, and the secret key is an integer in ${\displaystyle }$. 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 ${\displaystyle G_{T}}$ 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.

Key generation

The key generation algorithm selects the private key by picking a random integer ${\displaystyle x\in }$. The holder of the private key publishes the public key, ${\displaystyle g_{2}^{x}}$, where ${\displaystyle g_{2}}$ is a generator of ${\displaystyle G_{2}}$.

Signing

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

Verification

Given a signature ${\displaystyle \sigma }$ for message ${\displaystyle m}$ and public key ${\displaystyle g_{2}^{x}}$, we verify that ${\displaystyle e(\sigma ,g_{2})=e(H(m),g_{2}^{x})}$.

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).
• Signature Aggregation: Multiple signatures generated under multiple public keys for multiple messages can be aggregated into a single signature.
• Simple Threshold Signatures and multisignatures.

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. The usage of BLS12-381 for BLS signatures is detailed in the IETF internet draft.

Implementations

• Chia network has used BLS signatures.
• 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. 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.
• Dfinity (developers of the "Internet Computer" cryptocurrency) uses a BLS implementation.
• Skale cryptocurrency uses BLS signature algorithm.
• drand uses the BLS12-381 curve as a threshold scheme.

See also

• Pairing-based cryptography

References

1. ^ Dan Boneh; Ben Lynn & Hovav Shacham (2004). "Short Signatures from the Weil Pairing". Journal of Cryptology. 17 (4): 297–319. CiteSeerX 10.1.1.589.9141. doi:10.1007/s00145-004-0314-9. S2CID 206885645.
2. ^ "Ethereum 2.0 Phase 0 -- The Beacon Chain : BLS Signatures". GitHub. 28 July 2020. Retrieved 4 September 2020.
3. Shacham, Hovav. "New Paradigms in Signature Schemes" (PDF). www.semanticscholar.org. p. 18. Retrieved 2024-06-07.
4. 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
5. Craige, Jake (11 March 2020). "Threshold BLS Signatures". jcraige.com. Retrieved 8 August 2022.
6. Boldyreva, Alexandra (2002). Desmedt, Yvo G. (ed.). "Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme". Public Key Cryptography — PKC 2003. Berlin, Heidelberg: Springer: 31–46. doi:10.1007/3-540-36288-6_3. ISBN 978-3-540-36288-3.
7. Barreto, Paulo S. L. M.; Lynn, Ben; Scott, Michael (2003), "Constructing Elliptic Curves with Prescribed Embedding Degrees", Security in Communication Networks, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 257–267, ISBN 978-3-540-00420-2, retrieved 2024-02-11
8. "BLS12-381 For The Rest Of Us". HackMD. Retrieved 2024-02-11.
9. ^ Boneh, Dan; Gorbunov, Sergey; Wahby, Riad S.; Wee, Hoeteck; Wood, Christopher A.; Zhang, Zhenfei (2022-06-16). BLS Signatures (Report). Internet Engineering Task Force.
10. "5. BLS Signatures | Chia Documentation". docs.chia.net. Retrieved 2023-06-07.
11. BLS signatures
12. Drake, Justin (5 December 2019). "Pragmatic signature aggregation with BLS". ethresear.ch/. Eth research. Retrieved 8 January 2021.
13. "Chain-key signatures | Internet Computer". internetcomputer.org. Retrieved 2024-08-16.
14. "SKALE Documentation :: SKALE Network Documentation". docs.skale.network. Retrieved 2024-08-16.
15. "2.1 Cryptography". drand. Retrieved 2024-11-18.

External links

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

• Digital signature schemes
• Pairing-based cryptography