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Published in:
2009 | OriginalPaper | Chapter
Elliptic Twin Prime Conjecture
Authors : John B. Friedlander, Igor E. Shparlinski
Published in: Coding and Cryptology
Publisher: Springer Berlin Heidelberg
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Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime. In a work in progress theoretical extimates are obtained wherein the number of such points on both curves has a prescribed arithmetic structure.