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We describe a single-instruction multiple data (SIMD) implementation of the multiple polynomial quadratic sieve integer factoring algorithm. On a 16K MasPar massively parallel computer, the implementation can factor 100 digit integers in a few days. Its mo ...
Let d(n) denote Dirichlet's divisor function for positive integer numbers. This work is primarily concerned with the study of We are interested, in the error term where Ρ3 is a polynomial of degree 3 ; more precisely xΡ3(log x) is the residue of in s = 1. ...
D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an as ...
The number field sieve is an algorithm to factor integers of the form re−s for small positive r and s. The authors present a report on work in progress on this algorithm. They informally describe the algorithm, discuss several implementation related ...
We consider the following integer feasibility problem: Given positive integer numbers a0, a1,&mellip;,an with gcd(a1,&mellip;,an) = 1 and a = (a1,&mellip;,an), does there exist a ...
Shamir (1993) presented a family of cryptographic signature schemes based on birational permutations of the integers modulo a large integer N of unknown factorization. These schemes are attractive because of the low computational requirements, both ...
