BLS digital signature

The BLS digital signature, named for Boneh, Lynn and Shacham, is a cryptographic signature scheme that lets a verifier check that a signer is authentic. It works with a bilinear pairing over elliptic curve groups of prime order and a hash function that maps messages into one of those groups. A signature is an element of the first group, a public key is an element of the second, and the secret key is an integer. Signing hashes the message to a group element and raises it to the secret key, and verification compares two pairing values. Because the scheme works in an elliptic curve group it gives shorter signatures than full domain hash signatures at a similar security level, which is why the outputs are often called short signatures. The scheme is deterministic, so a given key and message yield exactly one valid signature, and signatures made under many keys can be aggregated into one. It is provably secure in the random oracle model under the computational Diffie-Hellman assumption in a gap Diffie-Hellman group, and has been used by Chia, drand and the proof-of-stake Ethereum consensus layer.