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Title:
The Supersingular Isogeny Path and Endomorphism Ring Problems: Unconditional Reductions
Authors: Maher Mamah
Abstract:In this paper we study several computational problems related to current post-quantum cryptosystems based on isogenies between supersingular elliptic curves. In particular we prove that the supersingular isogeny path and endomorphism ring problems are unconditionally equivalent under polynomial time reductions. We show that access to a factoring oracle is sufficient to solve the Quaternion path problem of KLPT and prove that these problems are equivalent, where previous results either assumed heuristics or the generalised Riemann Hypothesis (GRH). Recently these reductions have become foundational for the security of isogeny-based cryptography
ePrint: https://eprint.iacr.org/2024/1569
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