22.5 Signatures

22.5.1 BLS Signatures

Alice wants to sign a document m. In earlier chapters, we have seen how to do this with RSA and ElGamal signatures. The BLS method, due to Boneh, Lynn, and Schacham, uses pairings.

We use a supersingular elliptic curve E0 and point P0,  as in Section 22.1. To set up the signature scheme, we’ll need a public hash function H that maps arbitrary length binary strings to multiples of P0. A little care is needed in defining H,  since no one should be able, given a binary string b,  to find k with H(b)=kP0. See Exercise 7.

To set up the system, Alice chooses, once and for all, a secret integer a and computes KAlice=aP0,  which is made public.

Alice’s signature for the message m is S=aH(m),  which is a point on ...

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