A Key Sharing Scheme over GF(2⁵) to Use in ECC

Abstract

Since the introduction of public-key cryptography by Diffe and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffe and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers module a prime, this idea can be extended to arbitrary groups and in particular, to elliptic curve groups. The resulting public-key systems provide relatively small block size, high speed, and high security. In this paper, a vector space secrets sharing scheme is proposed in detail. Its security is based on the security of ECC. This scheme has the following characteristic: the precondition of (t,n)- threshold secret sharing scheme that all assignees purview must be same is generalized. A verifiable infrastructure is provided, which can be used to detect the cheaters from the dealers and assignees. The shared key distributed by dealer is encrypted based on ECC, which enhances the security. So this scheme is of less computation cost which is valuable in applications with limited memory, communications bandwidth or computing power.