Paper 2019/950

Another look at some isogeny hardness assumptions

Simon-Philipp Merz, Romy Minko, and Christophe Petit

Abstract

The security proofs for isogeny-based undeniable signature schemes have been based primarily on the assumptions that the One-Sided Modified SSCDH problem and the One-More SSCDH problem are intractable. We challenge the validity of these assumptions, showing that both the decisional and computational variants of these problems can be solved in polynomial time. We further demonstrate an attack, applicable to two undeniable signature schemes, one of which was proposed at PQCrypto 2014. The attack allows to forge signatures in $2^{4\lambda/5}$ steps on a classical computer. This is an improvement over the expected classical security of $2^{\lambda}$, where $\lambda$ denotes the chosen security parameter.