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» The Number Field Sieve
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ASIACRYPT
2003
Springer
13 years 11 months ago
On Class Group Computations Using the Number Field Sieve
The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a varian...
Mark L. Bauer, Safuat Hamdy
MOC
2000
78views more  MOC 2000»
13 years 5 months ago
Using number fields to compute logarithms in finite fields
We describe an adaptation of the number field sieve to the problem of computing logarithms in a finite field. We conjecture that the running time of the algorithm, when restricted ...
Oliver Schirokauer
ITCC
2005
IEEE
13 years 11 months ago
Improved Routing-Based Linear Algebra for the Number Field Sieve
Recently, efficient custom-hardware designs were proposed for the linear algebra step of the Number Field Sieve integer factoring algorithm. These designs make use of a heuristic ...
Willi Geiselmann, Hubert Köpfer, Rainer Stein...
MOC
2010
13 years 16 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