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» A General Polynomial Sieve
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DCC
1999
IEEE
13 years 4 months ago
A General Polynomial Sieve
An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve...
Shuhong Gao, Jason Howell
ASIACRYPT
2003
Springer
13 years 10 months ago
Rotations and Translations of Number Field Sieve Polynomials
We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also...
Jason E. Gower
DM
2010
77views more  DM 2010»
13 years 4 months ago
Hall-Littlewood polynomials and fixed point enumeration
We resolve affirmatively some conjectures of Reiner, Stanton, and White [6] regarding enumeration of various classes of matrices which are invariant under certain cyclic row and co...
Brendon Rhoades
CATS
1998
13 years 6 months ago
On Quadratic Polynomials for the Number Field Sieve
Brian Murphy, Richard P. Brent
SACRYPT
2009
Springer
176views Cryptology» more  SACRYPT 2009»
13 years 11 months ago
Optimization Strategies for Hardware-Based Cofactorization
Abstract. We use the specific structure of the inputs to the cofactorization step in the general number field sieve (GNFS) in order to optimize the runtime for the cofactorizatio...
Daniel Loebenberger, Jens Putzka