International Association for Cryptologic Research

International Association
for Cryptologic Research


New algorithms for the Deuring correspondence: Towards practical and secure SQISign signatures

Luca De Feo , IBM Research
Antonin Leroux , DGA, LIX, Ecole Polytechnique, Inria Saclay
Patrick Longa , Microsoft Research
Benjamin Wesolowski , Univ. Bordeaux, CNRS
DOI: 10.1007/978-3-031-30589-4_23 (login may be required)
Search ePrint
Search Google
Presentation: Slides
Conference: EUROCRYPT 2023
Abstract: 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 GF(p^2) 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.
  title={New algorithms for the Deuring correspondence: Towards practical and secure SQISign signatures},
  author={Luca De Feo and Antonin Leroux and Patrick Longa and Benjamin Wesolowski},