@inproceedings{95aa6d15e2a348eb947b56748a62a100,
title = "Isogeny Problems with Level Structure",
abstract = "Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the behavior of the isogeny on a large enough subgroup, the problem can become easy, as recent cryptanalyses on SIDH have shown. Between the restriction of the isogeny to a full N-torsion subgroup and no “torsion information” at all lies a spectrum of interesting intermediate problems, raising the question of how easy or hard each of them is. Here we explore modular isogeny problems where the torsion information is masked by the action of a group of 2×2 matrices. We give reductions between these problems, classify them by their difficulty, and link them to security assumptions found in the literature.",
keywords = "Isogenies, Post-quantum, Security reductions",
author = "\{De Feo\}, Luca and Fouotsa, \{Tako Boris\} and Lorenz Panny",
note = "Publisher Copyright: {\textcopyright} International Association for Cryptologic Research 2024.; 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024 ; Conference date: 26-05-2024 Through 30-05-2024",
year = "2024",
doi = "10.1007/978-3-031-58754-2\_7",
language = "English",
isbn = "9783031587535",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "181--204",
editor = "Marc Joye and Gregor Leander",
booktitle = "Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings",
}