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» The Pseudosquares Prime Sieve
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MOC
2010
13 years 4 days 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
1992
Springer
138views Cryptology» more  CRYPTO 1992»
13 years 9 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
FPGA
2000
ACM
128views FPGA» more  FPGA 2000»
13 years 9 months ago
Factoring large numbers with programmable hardware
The fastest known algorithms for factoring large numbers share a core sieving technique. The sieving cores find numbers that are completely factored over a prime base set raised t...
Hea Joung Kim, William H. Mangione-Smith
EUROCRYPT
2006
Springer
13 years 9 months ago
The Function Field Sieve in the Medium Prime Case
In this paper, we study the application of the function field sieve algorithm for computing discrete logarithms over finite fields of the form Fqn when q is a medium-sized prime po...
Antoine Joux, Reynald Lercier
CRYPTO
2006
Springer
115views Cryptology» more  CRYPTO 2006»
13 years 9 months ago
The Number Field Sieve in the Medium Prime Case
Antoine Joux, Reynald Lercier, Nigel P. Smart, Fre...