Paper 2023/436
SQISignHD: New Dimensions in Cryptography
Abstract
We introduce SQISignHD, a new post-quantum digital signature scheme inspired by SQISign. SQISignHD exploits the recent algorithmic breakthrough underlying the attack on SIDH, which allows to efficiently represent isogenies of arbitrary degrees as components of a higher dimensional isogeny. SQISignHD overcomes the main drawbacks of SQISign. First, it scales well to high security levels, since the public parameters for SQISignHD are easy to generate: the characteristic of the underlying field needs only be of the form $2^{f}3^{f'}-1$. Second, the signing procedure is simpler and more efficient. Third, the scheme is easier to analyse, allowing for a much more compelling security reduction. Finally, the signature sizes are even more compact than (the already record-breaking) SQISign, with compressed signatures as small as 116 bytes for the post-quantum NIST-1 level of security. These advantages may come at the expense of the verification, which now requires the computation of an isogeny in dimension $4$, a task whose optimised cost is still uncertain, as it has been the focus of very little attention.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- Post-quantum cryptographyIsogeniesSQISignSIDHKani's lemma
- Contact author(s)
- pierrick dartois @ u-bordeaux fr
- History
- 2023-05-26: last of 3 revisions
- 2023-03-25: received
- See all versions
- Short URL
- https://ia.cr/2023/436
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/436, author = {Pierrick Dartois and Antonin Leroux and Damien Robert and Benjamin Wesolowski}, title = {SQISignHD: New Dimensions in Cryptography}, howpublished = {Cryptology ePrint Archive, Paper 2023/436}, year = {2023}, note = {\url{https://eprint.iacr.org/2023/436}}, url = {https://eprint.iacr.org/2023/436} }