Samenvatting
In this paper, we introduce a polynomial-time algorithm to compute a connecting O-ideal between two supersingular elliptic curves over Fp with common Fp-endomorphism ring O, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph.
Originele taal-2 | Engels |
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Titel | Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |
Redacteuren | Anne Canteaut, Yuval Ishai |
Uitgeverij | Springer |
Pagina's | 523-548 |
Aantal pagina's | 26 |
ISBN van geprinte versie | 9783030457235 |
DOI's | |
Status | Gepubliceerd - 2020 |
Evenement | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Kroatië Duur: 10 mei 2020 → 14 mei 2020 |
Publicatie series
Naam | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12106 LNCS |
ISSN van geprinte versie | 0302-9743 |
ISSN van elektronische versie | 1611-3349 |
Congres
Congres | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 |
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Land/Regio | Kroatië |
Stad | Zagreb |
Periode | 10/05/20 → 14/05/20 |
Bibliografische nota
Publisher Copyright:© International Association for Cryptologic Research 2020.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.