20 search results - page 2 / 4 » The Tower Number Field Sieve |
ASIACRYPT
2007
Springer
13 years 9 months ago
2007
Springer
We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne nu...
MOC
2000
13 years 5 months ago
2000
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 ...
FQ
2003
Springer
13 years 10 months ago
2003
Springer
We construct a tower of function fields F0 ⊂ F1 ⊂ . . . over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] < ∞. We...
WAIFI
2010
Springer
13 years 10 months ago
2010
Springer
A cryptographic pairing evaluates as an element of a finite extension field, and the evaluation itself involves a considerable amount of extension field arithmetic. It is recogn...
ITCC
2005
IEEE
13 years 11 months ago
2005
IEEE
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 ...