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 diiculty of solving the discrete logarithm problem (8], 9], 14], etc.). In 10] and 18] it was described how to apply the number eld sieve algorithm to the discrete logarithm problem in prime elds. This resulted in the asymptotically fastest known discrete log algorithm for nite elds of p elements. Very little is known about the behaviour of this algorithm in practice. In this report we write about our practical experience with our implementation of their algorithm whose rst version was completed in October 1994 at the Department of Computer Science at the Universitt at des Saarlandes.