On a fast (k,n)-threshold secret sharing scheme

In Shamir's (k, n)-threshold secret sharing scheme (threshold scheme) [1], a heavy computational cost is required to make n shares and recover the secret from k shares. As a solution to this problem, several fast threshold schemes have been proposed. However, there is no fast ideal (k, n)-threshold scheme, where k and n are arbitrary. This paper proposes a new fast (k, n)-threshold scheme which uses just EXCLUSIVE-OR(XOR) operations to make n shares and recover the secret from k shares. We prove that every combination of k or more participants can recover the secret, but every group of less than k participants cannot obtain any information about the secret in the proposed scheme. Moreover, the proposed scheme is an ideal secret sharing scheme similar to Shamir's scheme, in which every bit-size of shares equals that of the secret. We also evaluate the efficiency of the scheme, and show that our scheme realizes operations that are much faster than Shamir's.