Cryptology ePrint Archive: Report 2010/367

Starfish on Strike

Daniel J. Bernstein and Peter Birkner and Tanja Lange

Abstract: This paper improves the price-performance ratio of ECM, the elliptic-curve method of integer factorization. In particular, this paper constructs "a = -1" twisted Edwards curves having Q-torsion group Z/2 x Z/4, Z/8, or Z/6 and having a known non-torsion point; demonstrates that, compared to the curves used in previous ECM implementations, some of the new curves are more effective at finding small primes despite being faster; and precomputes particularly effective curves for several specific sizes of primes.

Category / Keywords: public-key cryptography /

Publication Info: LATINCRYPT 2010 (includes corrected bibliography)

Date: received 25 Jun 2010

Contact author: tanja at hyperelliptic org

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Version: 20100625:125227 (All versions of this report)

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