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The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps o...
Given two integers N1=p1q1 and N2=p2q2 with α-bit primes q1,q2, suppose that the t least significant bits of p1 and p2 are equal. May and Ritzenhofen (PKC 2009) developed a factoring algorithm for N1,...
This note presents a deterministic integer factorization algorithm based on a system of polynomials equations. This technique exploits a new idea in the construction of irreducible polynomials with p...
The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete lo...
The purpose of this paper is to calculate the running time of dense boolean matrix operations, as used in stream cipher cryptanalysis and integer factorization. Several variations of Gaussian Elimin...

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