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In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods for computing discrete logarithms over prime fields. We demonstrate through empirical performance measures that for a special class of primes the cubic sieve method runs about two times faster than the linear sieve method even in cases of small prime fields of… (More)

It is of interest in cryptographic applications to obtain practical performance improvements for the discrete logarithm problem over prime fields Fp with p of size ≤ 500 bits. The linear sieve and the cubic sieve methods described in Coppersmith, Odlyzko and Schroeppel's paper [3] are two practical algorithms for computing discrete logarithms over prime… (More)