Reo Yoshida

Simple Algorithms for Computing a Sequence of 2-Isogenies

Recently, some cryptographic primitives have been described that are based on the supposed hardness of finding an isogeny between two (supersingular) elliptic curves. As a part of such a primitive, Charles et al. proposed an algorithm for computing sequences of 2-isogenies.However, their method involves several redundant computations. We construct simple algorithms without such redundancy, based on very compact descriptions of the 2-isogenies. For that, we use some observations on 2-torsion points.

AN ALGORITHM FOR COMPUTING A SEQUENCE OF RICHELOT ISOGENIES

We show that computation of a sequence of Richelot isogenies from specified supersingular Jacobians of genus-2 curves over Fp can be executed in Fp2 or Fp4. Based on this, we describe a practical algorithm for computing a Richelot isogeny sequence.