Algorithmica
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A course in computational algebraic number theory
A course in computational algebraic number theory
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Computing Discrete Logarithms with the General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
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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 fields. The cubic sieve algorithm is asymptotically faster than the linear sieve algorithm. We discuss an efficient implementation of the cubic sieve algorithm incorporating two heuristic principles. We demonstrate through empirical performance measures that for a special class of primes the cubic sieve method runs about two to three times faster than the linear sieve method even in cases of small prime fields of size about 150 bits.