Starfish on strike

D.J. Bernstein, P. Birkner, T. Lange

Research output: Book/ReportReportAcademic


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.
Original languageEnglish
Number of pages17
Publication statusPublished - 2010

Publication series

NameCryptology ePrint Archive


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