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Arjen Lenstra

Related publications (73)

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This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

Computation of a 768-Bit Prime Field Discrete Logarithm

Arjen Lenstra, Thorsten Kleinjung

This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly disc ...

Springer International Publishing Ag2017

Efficient Ephemeral Elliptic Curve Cryptographic Keys

Arjen Lenstra, Andrea Miele

We show how any pair of authenticated users can on-the-fly agree on an elliptic curve group that is unique to their communication session, unpredictable to outside observers, and secure against known attacks. Our proposal is suitable for deployment on cons ...

Springer-Verlag Berlin2015

Cofactorization on Graphics Processing Units

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Andrea Miele

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-a ...

Springer-Verlag Berlin2014

Solving 112-bit prime ECDLP on game consoles using sloppy reduction

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Marcelo Kaihara

We describe a cell processor implementation of Pollard’s rho method to solve discrete logarithms in groups of elliptic curves over prime fields. The implementation was used on a cluster of PlayStation 3 game consoles to set a new record. We present in deta ...

2012

A heterogeneous computing environment to solve the 768-bit RSA challenge

Arjen Lenstra, Pénélope Leyland, Pascal Jermini, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Michela Thiémard, Heinz Stockinger

In December 2009 the 768-bit, 232-digit number RSA-768 was factored using the number field sieve. Overall, the computational challenge would take more than 1700 years on a single, standard core. In the article we present the heterogeneous computing approac ...

Springer Verlag2012

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We performed a sanity check of public keys collected on the web. Our main goal was to test the validity of the assumption that different random choices are made each time keys are generated. We found that the vast majority of public keys work as intended. ...

IACR2012

Efficient SIMD arithmetic modulo a Mersenne number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...

IEEE Computer Soc Press2011

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This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementa ...

IEEE2011

We develop a new methodology to assess cryptographic key strength using cloud computing, by calculating the true economic cost of (symmetric- or private-) key retrieval for the most common cryptographic primitives. Although the present paper gives the curr ...

2011