Concept

Crible quadratique

Publications associées (42)

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This thesis studies the implications of using public key cryptographic primitives that are based in, or map to, the multiplicative group of finite fields with small extension degree. A central observation is that the multiplicative group of extension field ...

PhD dissertation, University of Bristol, UK, February 20062006

Multiparametric Linear Complementarity Problems

Colin Neil Jones

The linear complementarity problem (LCP) is a general problem that unifies linear and quadratic programs and bimatrix games. In this paper, we present an efficient algorithm for the solution to multiparametric linear complementarity problems (pLCPs) that a ...

IEEE2006

In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields

\mathbb{F}_{3^n}

. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...

Springer Berlin Heidelberg2004

We present conditions that allow consistent exponential-polynomial forward curve models with two exponential terms to have more than one nontrivial factor. This result leads to seven- and nine-parameter extensions of the Svensson model, for which the consi ...

2004

Factoring estimates for a 1024-bit RSA modulus

Arjen Lenstra, Pénélope Leyland

We estimate the yield of the number field sieve factoring algorithm when applied to the 1024-bit composite integer RSA-1024 and the parameters as proposed in the draft version [17] of the TWIRL hardware factoring device [18]. We present the details behind ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2003

Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic

Robert Granger

We give estimates for the running-time of the function field sieve (FFS) to compute discrete logarithms in

\mathbb{F}_{p^n}^{\times}

for small

p

. Specifically, we obtain sharp probability estimates that allow us to select optimal parameters in cases of ...

Springer Berlin Heidelberg2003

Analysis of Bernstein's factorization circuit

Arjen Lenstra

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

Analysis and optimization of the TWINKLE factoring device

Arjen Lenstra

We describe an enhanced version of the TWINKLE factoring device and analyse to what extent it can be expected to speed up the sieving step of the quadratic Sieve and number field Sieve factoring algorithms. The bottom line of our analysis is that the TWINK ...

2000

Factorization of a 512 bit RSA modulus

Arjen Lenstra, Pénélope Leyland

This paper reports on the factorization of the 512 bit number RSA-155 by the number field Sieve factoring method (NFS) and discusses the implications for RSA ...