Expander graphs based on GRH with an application to elliptic curve cryptography

Details Expander graphs based on GRH with an application to elliptic curve cryptography Expander graphs based on GRH with an application to elliptic curve cryptography

2008-11-05

arxiv.org/abs/0811.0647v2

Mathematics

Number Theory

24 pages, to appear in the Journal of Number Theory

Scientific paper

We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)* with respect to small prime generators is an expander. As another application, we show that the graph of small prime degree isogenies between ordinary elliptic curves achieves non-negligible eigenvalue separation, and explain the relationship between the expansion properties of these graphs and the security of the elliptic curve discrete logarithm problem.

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