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Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive rth root of unity, one obtains under certain conditions a normal basis for mathbbFqn over Fq, where r is a prime and ...
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 ...
Nowadays, the use of micro- or nano-patterned surfaces is well established in wide fields of science and in numerous applications in the industry. Periodic surface-relief profiles with dimensions in the wavelength range of the light can act as diffractive ...
Institut de Microtechnique, Université de Neuchâtel2007
The Gröbner walk is an algorithm for conversion between Gröbner bases for different term orders. It is based on the polyhedral geometry of the Gröbner fan and involves tracking a line between cones representing the initial and target term order. An importa ...
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 ...
We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accoun ...
Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ...
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 ...
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 ...
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. ...
