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...
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 ...
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...
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...
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 ...