Abstract
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. © 2009 Springer Berlin Heidelberg.
Cite
CITATION STYLE
Friedlander, J. B., & Shparlinski, I. E. (2009). Elliptic twin prime conjecture. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5557 LNCS, pp. 77–81). https://doi.org/10.1007/978-3-642-01877-0_8
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