Paper 2024/1569
The Supersingular Isogeny Path and Endomorphism Ring Problems: Unconditional Reductions
, Pennsylvania State UniversityAbstract
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). Consequently, given Shor’s quantum algorithm for factorisation, our results yield unconditional quantum polynomial reductions between the isogeny path and EndRing problems. Recently these reductions have become foundational for the security of isogeny-based cryptography
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Contact author(s)
- mmm8895 @ psu edu
- History
- 2024-10-06: last of 2 revisions
- 2024-10-05: received
- See all versions
- Short URL
- https://ia.cr/2024/1569
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1569,
author = {Maher Mamah},
title = {The Supersingular Isogeny Path and Endomorphism Ring Problems: Unconditional Reductions},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1569},
year = {2024},
url = {https://eprint.iacr.org/2024/1569}
}
