Paper 2022/234
New algorithms for the Deuring correspondence: SQISign twice as fast
Luca De Feo and Antonin Leroux and Benjamin Wesolowski
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 twofold speed-up in key generation and signing. Verification time is not directly impacted by the change, however we also achieve a twofold speed-up through various other improvements. 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.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Isogeny-based cryptographyDeuring correspondence
- Contact author(s)
- antonin leroux @ polytechnique org,luca @ defeo lu,benjamin wesolowski @ math u-bordeaux fr
- History
- 2023-04-06: last of 3 revisions
- 2022-02-25: received
- See all versions
- Short URL
- https://ia.cr/2022/234
- License
-
CC BY