BLS digital signature

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A BLS digital signature, also known as Boneh–Lynn–Shacham[1] (BLS), is a cryptographic signature scheme which allows a user to verify that a signer is authentic.

The scheme uses a bilinear pairing for verification, and signatures are elements of an elliptic curve group. 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 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.[2] 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.[1]

Pairing functions[edit]

A gap group is a group in which the computational Diffie–Hellman problem is intractable but the decisional Diffie–Hellman problem can be efficiently solved. Non-degenerate, efficiently computable, bilinear pairings permit such groups.

Let be a non-degenerate, efficiently computable, bilinear pairing where , are groups of prime order, . Let be a generator of . Consider an instance of the CDH problem, ,, . Intuitively, the pairing function does not help us compute , the solution to the CDH problem. It is conjectured that this instance of the CDH problem is intractable. Given , we may check to see if without knowledge of , , and , by testing whether holds.

By using the bilinear property times, we see that if , then, since is a prime order group, .

BLS signature scheme[edit]

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

Key generation

The key generation algorithm selects a random integer such as . The private key is . The holder of the private key publishes the public key, .


Given the private key , and some message , we compute the signature by hashing the bitstring , as . We output the signature .


Given a signature and a public key , we verify that .


  • Simple Threshold Signatures[3][better source needed]
  • Signature Aggregation: Multiple signatures generated under multiple public keys for multiple messages can be aggregated into a single signature.[4]
  • 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).[citation needed]



BLS12-381 is part of a family of elliptic curves named after Barreto, Lynn, and Scott[5] (a different BLS trio, except for the L). 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]


  • To include BLS12-381 in IETF internet encryption standards.[7]
  • Chia network has used BLS12-381 signatures.[7][8][9]
  • By 2020, BLS12-381 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.[2] 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.[7][10]
  • Dfinity(developers of the "Internet Computer" cryptocurrency) BLS12-381 implementation.[7]
  • Algorand cryptocurrency uses BLS12-381.[7]
  • Skale cryptocurrency uses BLS12-381.[6]

See also[edit]


  1. ^ a b c Dan Boneh; Ben Lynn & Hovav Shacham (2004). "Short Signatures from the Weil Pairing". Journal of Cryptology. 17 (4): 297–319. CiteSeerX doi:10.1007/s00145-004-0314-9. S2CID 206885645.
  2. ^ a b "Ethereum 2.0 Phase 0 -- The Beacon Chain : BLS Signatures". GitHub. 28 July 2020. Retrieved 4 September 2020.
  3. ^ Craige, Jake (11 March 2020). "Threshold BLS Signatures". Retrieved 8 August 2022.
  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. ^ 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
  6. ^ a b "BLS12-381 For The Rest Of Us". HackMD. Retrieved 2024-02-11.
  7. ^ a b c d e Boneh, Dan; Gorbunov, Sergey; Wahby, Riad S.; Wee, Hoeteck; Wood, Christopher A.; Zhang, Zhenfei (2022-06-16). BLS Signatures (Report). Internet Engineering Task Force.
  8. ^ "5. BLS Signatures | Chia Documentation". Retrieved 2023-06-07.
  9. ^ BLS signatures
  10. ^ Drake, Justin (5 December 2019). "Pragmatic signature aggregation with BLS". Eth research. Retrieved 8 January 2021.

External links[edit]