A (t,n) multi-secret sharing scheme

摘要

In the (t,n) multi-secret sharing scheme, there are n participants in the system. At least t or more participants can easily pool their secrets shadows and reconstruct p secrets at the same time. Chien et al. [IEICE Trans. Fundamentals E83-A (2000) 2762] used (n+p−t+1) public values, (2(n+p)−t)×(n+p) storages, and solved (n+p−t) simultaneous equations to share p secrets. In this article, we shall propose an alternative (t,n) multi-secret sharing based on Shamir’s secret sharing. We shall use (n+p−t+1) or (n+1) public values, 2(t−1) or 2(p−1) storages, and employ the Lagrange interpolation polynomial to share p secrets. Our scheme will have exactly the same power as Chien et al.’s scheme.