Efficient signature generation by smart cards

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 _p 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 in _p such that the order of 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.European patent application 89103290.6 from February 24, 1989. U.S. patent number 4995082 of February 19, 1991.