Discrete Logarithm Based Cryptosystems in Quadratic Function Fields of Characteristic 2

We present a key exchange scheme similar to that of Diie and Hellman using the infrastructure of quadratic function elds of even characteristic. This is a modiication of the results of Scheidler, Stein and Williams who used quadratic function elds of odd characteristic. We also extend these results to give a digital signature scheme similar to that of ElGamal. These schemes are possible in this structure even though it is not a group. Finally we examine the security of such systems, and give a possible attack based on Pohlig and Hellman's attack on discrete logarithms in nite groups.