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Arjen Lenstra

Publications associées (73)

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Selective forgery of RSA signatures with fixed-pattern padding

Arjen Lenstra

We present a practical selective forgery attack against RSA signatures with fixed-pattern padding shorter than two thirds of the modulus length. Our result extends the practical existential forgery of such RSA signatures (Brier et al., 2001). For an n-bit ...

2002

Efficient subgroup exponentiation in quadratic and sixth degree extensions

Arjen Lenstra, Martijn Stam

This paper describes several speedups for computation in the order p + 1 subgroup of F*(p2) and the order p2 - p + 1 subgroup of F*(p6). These results are in a way complementary to LUC and XTR, where computations in these g ...

2002

On the security of Lenstra's variant of DSA without long inversions

Arjen Lenstra

We use bounds of exponential sums to show that, for a wide class of parameters, the modification of the digital signature algorithm (DSA) scheme proposed by A.K. Lenstra (see Proc. Asiacrypt'96, Lect. Notes in Comp. Sci., vol.1163, p.57-64, 1996) is as sec ...

2001

Fast irreducibility and subgroup membership testing in XTR

Arjen Lenstra

We describe a new general method to perform part of the setup stage of the XTR system introduced at Crypto 2000 (see Lenstra, A.K. and Verheul, E.R., Proc. Crypto 2000, Lect. Notes in Comp. Science, vol.1880, p.1-19, 2000), namely finding the trace of a ge ...

2001

Selecting cryptographic key sizes

Arjen Lenstra

In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based ...

Springer Verlag2001

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

Market split and basis reduction: towards a solution of the Cornuejols-Dawande instances

Arjen Lenstra

Previously, G. Cornuejols and M. Dawande (1998) proposed a set of 0-1 linear programming instances that proved to be very hard to solve by traditional methods, and in particular by linear programming based branch-and-bound. They offered these market split ...

2000

Solving a system of linear diophantine equations with lower and upper bounds on the variables

Arjen Lenstra

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector satisfying the system of diophantine equations, and a set o ...

INFORMS2000

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 ...

2000

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