Titlebook: Algorithmic Number Theory; 6th International Sy Duncan Buell Conference proceedings 2004 Springer-Verlag Berlin Heidelberg 2004 Farey seque

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Elliptic Curves of Large Rank and Small Conductorng from 1.0136 (for .=6) to over 100 (for .=10 and .=11). We describe our search methods, and tabulate, for each .=5,6,...,11, the five curves of lowest conductor, and (except for .=11) also the five of lowest absolute discriminant, that we found.

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Function Field Sieve in Characteristic Three identity based encryption systems using supersingular elliptic curves, we pay special attention to the case where . is composite. This allows us to represent the function field over different base fields. Practical experiments appear to show that a function field over . gives the best results.

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https://doi.org/10.1007/978-3-540-73139-9PP. As a consequence, we show that . for an ideal in . is in SPP. Furthermore, assuming the GRH, the class number of ., and a presentation for the class group of . can also be computed in SPP. A corollary of our result is that solving PELL’S EQUATION, recently shown by Hallgren [12] to have a quantu

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