An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
A course in computational algebraic number theory
A course in computational algebraic number theory
Asymptotic semismoothness probabilities
Mathematics of Computation
Efficient algorithms for computing the Jacobi symbol
Journal of Symbolic Computation
A space efficient algorithm for group structure computation
Mathematics of Computation
On random walks for Pollard's Rho method
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
| Hi-index | 0.00 |
Various cryptosystems have been proposed whose security relies on the difficulty of factoring integers of the special form N = pq2. To factor integers of that form, Peralta and Okamoto introduced a variation of Lenstra's Elliptic Curve Method (ECM) of factorization, which is based on the fact that the Jacobi symbols (a/N) and (a/P) agree for all integers a coprime with q. We report on an implementation and extensive experiments with that variation, which have been conducted in order to determine the speed-up compared with ECM for numbers of general form.