Abstract

We propose a Las Vegas probabilistic algorithm to compute the zeta function of a genus- hyperelliptic curve defined over a finite field , with explicit real multiplication by an order in a totally real cubic field. Our main result states that this algorithm requires an expected number of bit-operations, where the constant in the depends on the ring and on the degrees of polynomials representing the endomorphism . As a proof-of-concept, we compute the zeta function of a curve defined over a 64-bit prime field, with explicit real multiplication by .

Keywords

Mathematical Subject Classification 2010

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