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Function Field Sieve in Characteristic Three

Robert Granger, Andrew Holt, Dan Page, Nigel Smart, Fre Vercauteren, Function Field Sieve in Characteristic Three. Algorithmic Number Theory, 6th International Symposium, ANTS-VI. ISBN 3-540-22156-5, pp. 223–234. June 2004. PDF, 198 Kbytes.


In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields $\F_{3^n}$. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special attention to the case where $n$ is composite. This allows us to represent the function field over different base fields. Practical experiments appear to show that a function field over $\F_3$ gives the best results.

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