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- Thorsten Kleinjung, Kazumaro Aoki, +10 authors Paul Zimmermann
- IACR Cryptology ePrint Archive
- 2010

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.

- Thorsten Kleinjung
- Math. Comput.
- 2006

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present anâ€¦ (More)

We describe a Cell processor implementation of Pollardâ€™s rho method to solve discrete logarithms in groups of elliptic curves over prime fields. The implementation was used on a cluster ofâ€¦ (More)

Since 1999 specialized hardware architectures for factoring numbers of 1024 bit size with the General Number Field Sieve (GNFS) have attracted a lot of attention ([Ber], [ST]). Concerns about theâ€¦ (More)

Since the introduction of public key cryptography, the problem of factoring large composites has been of increased interest. The security of the most popular asymmetric cryptographic scheme RSAâ€¦ (More)

- Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra
- ANTS
- 2010

The negation map can be used to speed up the Pollard rho method to compute discrete logarithms in groups of elliptic curves over finite fields. It is well known that the random walks used by Pollardâ€¦ (More)

- Razvan Barbulescu, Pierrick Gaudry, Thorsten Kleinjung
- IACR Cryptology ePrint Archive
- 2015

The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n is a small integer larger than 1. The state-of-art algorithm is theâ€¦ (More)

- Robert Granger, Thorsten Kleinjung, Jens ZumbrÃ¤gel
- CRYPTO
- 2014

- Arjen K. Lenstra, James P. Hughes, Maxime Augier, Joppe W. Bos, Thorsten Kleinjung, Christophe Wachter
- IACR Cryptology ePrint Archive
- 2012

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 foundâ€¦ (More)

- Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra, Peter L. Montgomery
- IACR Cryptology ePrint Archive
- 2009

Meeting the requirements of NISTâ€™s new cryptographic standards means phasing out usage of 1024-bit RSA and 160-bit elliptic curve cryptography (ECC) by the end of the year 2010. This write-upâ€¦ (More)