Cryptography in Real Quadratic Congruence Function Fields
نویسنده
چکیده
The Diffie-Hellman key exchange protocol as well as the ElGamal signature scheme are based on exponentiation modulo p for some prime p. Thus the security of these schemes is strongly tied to the difficulty of computing discrete logarithms in the finite field Fp. The Diffie-Hellman protocol has been generalized to other finite groups arising in number theory, and even to the sets of reduced principal ideals of both a real quadratic number field and a real quadratic congruence function field (neither one of which is a group!). In this paper, we show how the ideas underlying the recent implementation of this protocol in real quadratic congruence function fields can be extended to realize an ElGamal-like signature scheme in these fields.
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