Efficient signature generation by smart cards

Abstract

We present a new public-key signature scheme and a corresponding authentication scheme that are based on discrete logarithms in a subgroup of units in ℤp where p is a sufficiently large prime, e.g., p ≥ 2512. A key idea is to use for the base of the discrete logarithm an integer α in ℤp such that the order of α is a sufficiently large prime q, e.g., q ≥ 2140. In this way we improve the ElGamal signature scheme in the speed of the procedures for the generation and the verification of signatures and also in the bit length of signatures. We present an efficient algorithm that preprocesses the exponentiation of a random residue modulo p. © 1991 Springer-Verlag New York Inc.