Multi-committer threshold commitment scheme from lattice

Abstract

A multi-committer threshold commitment scheme is proposed based on the intractability assumption of Learning with errors problem. A group of committers consult a secret and divide it into several share pieces. Each member possesses a share piece. When de-committing, if a committer doesn't want to admit or reveal the secret, he may refuse to open his piece, or even he may send an improper piece purposely when corrupted by a malicious adversary. If a majority of the committers agree to contribute their correct pieces, the receiver will accept the secret. The core idea is threshold secret share. This scheme satisfies the necessary properties, such as binding, hiding, non-malleability, and adaptive corruption chosen-plaintext security against malicious adversary. The commitment expansion factor is as small as O(log 2 q) so as to communicate efficiently. © 2012 Springer-Verlag.