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MOC
2010
13 years 4 months ago
The number field sieve for integers of low weight
We define the weight of an integer N to be the smallest w such that N can be represented as w i=1 i2ci , with 1,..., w{1,-1}. Since arithmetic modulo a prime of low weight is parti...
Oliver Schirokauer
CRYPTO
2006
Springer
115views Cryptology» more  CRYPTO 2006»
14 years 1 months ago
The Number Field Sieve in the Medium Prime Case
Antoine Joux, Reynald Lercier, Nigel P. Smart, Fre...
CATS
1998
13 years 11 months ago
On Quadratic Polynomials for the Number Field Sieve
Brian Murphy, Richard P. Brent
CRYPTO
1992
Springer
138views Cryptology» more  CRYPTO 1992»
14 years 1 months ago
Designing and Detecting Trapdoors for Discrete Log Cryptosystems
Using a number field sieve, discrete logarithms modulo primes of special forms can be found faster than standard primes. This has raised concerns about trapdoors in discrete log cr...
Daniel M. Gordon
SACRYPT
2009
Springer
176views Cryptology» more  SACRYPT 2009»
14 years 4 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