Ali Saeidi Rashkolia - Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

In this paper, we proposed a new verifiable multi-use, multi-secret sharing scheme based on the oneway hash function in which automata and column vector spaces over GF(q) are applied, moreover this scheme is secure and renewable with the following properties: (۱) Each participant has to keep only one secret share (shadow) to share a secret, (۲) Operations like modular multiplication, exponentiation and discrete logarithm are not used, (۳) The secret space has the same size as the shadow space, (۴) There is no limitation for the number of secrets, (۵) Both the combiner and the participants can check the correctness of the information exchanged among themselves.

Finite automaton, Secret sharing, Weakly invertible, Weak inverse, Hash function