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Expander graphs based on GRH with an application to elliptic curve cryptography by David Jao; Stephen D. Miller; Ramarathnam Venkatesan is a Mathematics article available to read on EtoBox.

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Text. 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 nonnegligible 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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Author

David Jao; Stephen D. Miller; Ramarathnam Venkatesan

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)