BLS digital signature

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 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 $$G_T$$ 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.

The key generation algorithm selects a random integer $$x$$ such as $$0 < x < r$$. The private key is $$x$$. The holder of the private key publishes the public key, $$g^x$$.
 * Key generation

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

Given a signature $$\sigma$$ and a public key $$g^x$$, we verify that $$e(\sigma, g )=e(H(m), g^x)$$.
 * Verification

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.

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). 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.

Implementations

 * To include BLS12-381 in IETF internet encryption standards.
 * Chia network has used BLS12-381 signatures.
 * 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.  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) BLS12-381 implementation.
 * Algorand cryptocurrency uses BLS12-381.
 * Skale cryptocurrency uses BLS12-381.