Digital signature scheme
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 formula_1, where formula_2 and formula_3 are elliptic curve groups of prime order formula_4, and a hash function formula_5 from the message space into formula_6. Signature are elements of formula_6, public keys are elements of formula_8, and the secret key is an integer in formula_9. 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 formula_3 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".
The key generation algorithm selects the private key by picking a random integer formula_11. The holder of the private key publishes the public key, formula_12, where formula_13 is a generator of formula_8.
Given the private key formula_15, and some message formula_16, we compute the signature by hashing the bitstring formula_16, as formula_18, and we output the signature formula_19.
Given a signature formula_20 for message formula_16 and public key formula_12, we verify that formula_23.
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 planned usage of BLS12-381 for BLS signatures is detailed in the June 2022 IETF internet draft.
References.
 ;templatestyles src="Reflist/styles.css" / ;