Publications by Arjen Lenstra | EPFL Graph Search

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arjen Lenstra, Robert Granger, Thorsten Kleinjung, Benjamin Pierre Charles Wesolowski

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

STEP-Archival: Storage Integrity and Tamper Resistance Using Data Entanglement

Arjen Lenstra, Maxime Augier

2018

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

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

Arjen Lenstra, Pénélope Leyland, Thorsten Kleinjung, Pascal Jermini, Dag Arne Osvik, Joppe Willem Bos, 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

Chosen-prefix collisions for MD5 and applications

Arjen Lenstra

Springer Verlag2012

Arjen Lenstra

Graph Chatbot

L Notation

Birthday Paradox

Integer Factoring

Computation Of A 30750-Bit Binary Field Discrete Logarithm

STEP-Archival: Storage Integrity and Tamper Resistance Using Data Entanglement

Computation of a 768-Bit Prime Field Discrete Logarithm

Efficient Ephemeral Elliptic Curve Cryptographic Keys

Cofactorization on Graphics Processing Units

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

Chosen-prefix collisions for MD5 and applications

Computation of a 768-Bit Prime Field Discrete Logarithm

L Notation

Integer Factoring

Birthday Paradox

Computation Of A 30750-Bit Binary Field Discrete Logarithm

STEP-Archival: Storage Integrity and Tamper Resistance Using Data Entanglement

Chosen-prefix collisions for MD5 and applications

Cofactorization on Graphics Processing Units

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

Efficient Ephemeral Elliptic Curve Cryptographic Keys