New algorithms for the Deuring correspondence Towards practical and secure SQISign signatures
WESOLOWSKI, Benjamin
Centre National de la Recherche Scientifique [CNRS]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Leer menos
Centre National de la Recherche Scientifique [CNRS]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Idioma
en
Communication dans un congrès
Este ítem está publicado en
Eurocrypt 2023, 2023-04-23, Lyon.
Resumen en inglés
The Deuring correspondence defines a bijection between isogenies of supersingular elliptic curves and ideals of maximal orders in a quaternion algebra. We present a new algorithm to translate ideals of prime-power norm to ...Leer más >
The Deuring correspondence defines a bijection between isogenies of supersingular elliptic curves and ideals of maximal orders in a quaternion algebra. We present a new algorithm to translate ideals of prime-power norm to their corresponding isogenies — a central task of the effective Deuring correspondence. The new method improves upon the algorithm introduced in 2021 by De Feo, Kohel, Leroux, Petit and Wesolowski as a building-block of the SQISign signature scheme. SQISign is the most compact post-quantum signature scheme currently known, but is several orders of magnitude slower than competitors, the main bottleneck of the computation being the ideal-to-isogeny translation. We implement the new algorithm and apply it to SQISign, achieving a more than two-fold speedup in key generation and signing with a new choice of parameter. Moreover, after adapting the state-of-the-art Fp2 multiplication algorithms by Longa to implement SQISign’s underlying extension field arithmetic and adding various improvements, we push the total speedups to over three times for signing and four times for verification. In a second part of the article, we advance cryptanalysis by showing a very simple distinguisher against one of the assumptions used in SQISign. We present a way to impede the distinguisher through a few changes to the generic KLPT algorithm. We formulate a new assumption capturing these changes, and provide an analysis together with experimental evidence for its validity.< Leer menos
Palabras clave en inglés
Post-quantum cryptography
Isogenies
Group actions
Proyecto ANR
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Orígen
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