A fast (3, n)-threshold secret sharing scheme using Exclusive-OR operations
In Shamir's (k,n)-threshold secret sharing scheme [11, 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 >= 3 and n is arbitrary. This paper proposes a new fast (3, n)-threshold scheme by 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 evaluate the efficiency of the scheme, and show that it is more efficient than Shamir's in terms of computational cost. Moreover, we suggest a fast (k, n)-threshold scheme can be constructed in a similar way by increasing the sets of random numbers constructing pieces of shares.
secret sharing schemes ideal secret sharing schemes random number xor entropy