An Implementation of the General Number Field Sieve to Compute Discrete Logarithms mod p

There are many cryptographic protocols the security of which depends on the difficulty of solving the discrete logarithm problem ([8], [9], [14], etc.). In [10] and [18] it was described how to apply the number field sieve algorithm to the discrete logarithm problem in prime fields. This resulted in the asymptotically fastest known discrete log algorithm for finite fields of p elements. Very little is known about the behaviour of this algorithm in practice. In this report we write about our practical ex- perience with our implementation of their algorithm whose first version was completed in October 1994 at the Department of Computer Science at the Universität des Saarlandes.