[Resource Topic] 2024/1569: The Supersingular Isogeny Path and Endomorphism Ring Problems: Unconditional Reductions

Welcome to the resource topic for 2024/1569

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

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .