01. June 2012

Counting digits in non-adjacent forms in conjunction with hyperelliptic curve cryptography

Abstract

One main operation in hyperelliptic curve cryptography is building multiples of a point on a hyperelliptic curve over a finite field. For a class of curves we can use a Frobenius-and-add method. In order to do that efficiently we need to understand digital expansions, where the base is an algebraic integer whose conjugates all have the same absolute value. The talk will be about the existence of ``good'' expansions (non-adjacent forms) and about the number of occurrences of digits in such expansions.