Bipartite Threshold Multi-Secret Sharing Scheme Based on Hypersphere

Abstract

To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite ( n 1 + n 2 , m 1 + m 2 ) -threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Z p to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.