A Novel (t, n) Secret Sharing Scheme Based upon Euler's Theorem.

The (t, n) secret sharing scheme is used to protect the privacy of information by distribution. More specifically, a dealer splits a secret into n shares and distributes them privately to n participants, in such a way that any t or more participants can reconstruct the secret, but no group of fewer than t participants who cooperate can determine it. Many schemes in literature are based on the polynomial interpolation or the Chinese remainder theorem. In this paper, we propose a new solution to the system of congruences different from Chinese remainder theorem and propose a new scheme for (t, n) secret sharing; its secret reconstruction is based upon Euler's theorem. Furthermore, our generalized conclusion allows the dealer to refresh the shared secret without changing the original share of the participants.