Catégorie

Théorie algébrique des nombres

Publications associées (38)

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Raptor codes

Mohammad Amin Shokrollahi

This paper exhibits a class of universal Raptor codes: for a given integer k, and any real /spl epsiv/>0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1 + /spl epsiv/) is sufficient t ...

2004

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 ...

2002

Integer factoring

Arjen Lenstra

Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ...

2000

Normal bases in finite fields via general Gauss periods

Mohammad Amin Shokrollahi

Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive

r

th root of unity, one obtains under certain conditions a normal basis for

mathbb F_q^n

over

F_q

, where

r

is a prime and ...

1999

Factoring integers using SIMD sieves

Arjen Lenstra

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 ...

1994

Attacks on the birational permutation signature schemes

Serge Vaudenay, Jacques Stern

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 ...

1993

The number field sieve

Arjen Lenstra

The number field sieve is an algorithm to factor integers of the form

r^e-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 ...

Springer Berlin Heidelberg1993

Finite parts of the spectrum of a Riemann surface

Gilles André Courtois

Let S and

S'

be compact Riemann surfaces of the same genus g (g

ge 2)

endowed with the Poincaré metric of constant negative curvature -1. par The authors show that for every

epsilon >0

, there exists an integer

m=m(g,epsilon)

with the property: Assum ...

1990

Normal bases in finite fields via general Gauss periods

Mohammad Amin Shokrollahi

Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive

r

th root of unity, one obtains under certain conditions a normal basis for

mathbb F_q^n

over

F_q

, where

r

is a prime and ...

1999

The number field sieve

Arjen Lenstra

The number field sieve is an algorithm to factor integers of the form

r^e-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 ...

Springer Berlin Heidelberg1993

Finite parts of the spectrum of a Riemann surface

Gilles André Courtois

Let S and

S'

be compact Riemann surfaces of the same genus g (g

ge 2)

endowed with the Poincaré metric of constant negative curvature -1. par The authors show that for every

epsilon >0

, there exists an integer

m=m(g,epsilon)

with the property: Assum ...

1990