Thorsten Kleinjung

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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, 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

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

ECC2K-130 on Cell CPUs

Joppe Willem Bos, Thorsten Kleinjung

This paper describes an implementation of Pollard's rho algorithm to compute the elliptic curve discrete logarithm for the Synergistic Processor Elements of the Cell Broadband Engine Architecture. Our implementation targets the elliptic curve discrete loga ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

Factorization of a 768-Bit RSA Modulus

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Patric Zimmermann

This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA. ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

A kilobit special number field sieve factorization

Arjen Lenstra, Thorsten Kleinjung, Dag Arne Osvik

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 -1. Although this factorization is orders of magnitude ...

2007

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Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

A kilobit special number field sieve factorization

Arjen Lenstra, Thorsten Kleinjung, Dag Arne Osvik

2007