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Succinct Non-interactive Arguments of Knowledge from Supersingular Isogenies

A succinct non-interactive argument of knowledge (SNARK) enables a party to convince another of some statement (typically, knowledge of some information) by means of a short argument, while ensuring it is infeasible for an adversary to create a short argument of the opposite statement. We hereby describe a SNARK for CSI-FiSh signatures, whose security stems from hard problems involving supersingular isogenies. Although the scheme looks analogous to a SNARK for conventional Schnorr signatures, it is non-trivial in that, as we also show, a similar SNARK for another isogeny-based signature scheme (SQISign) is not viable. As a bonus, we also discuss how to drastically reduce the memory needed to implement the CSIDH framework required by CSI-FiSh signatures.