A Fast (4, n)-Threshold Secret Sharing Scheme Using Exclusive-OR Operations, and Its Extension to (k, n) -Threshold Schemes

摘要

In Shamir's (k, n)-threshold secret sharing scheme, a heavy computational cost is required to recover the secret from k shares. As a solution to this problem, several fast threshold schemes are proposed. However, there is no fast ideal (k, n)-threshold scheme, where k≥4 and n is arbitrary. This paper proposes a new fast (4, n)-threshold scheme using just EXCLUSIVE-OR (XOR) operations to make shares and recover the secret, which is an ideal secret sharing scheme similar to Shamir's scheme. Furthermore, we extend and generalize the (4, n)-threshold scheme to a new fast (k, n) -threshold scheme using XOR operations with arbitrary k and n, which is also an ideal secret sharing scheme.