Paper 2021/984
On the Use of the Legendre Symbol in Symmetric Cipher Design
Alan Szepieniec
Abstract
This paper proposes the use of Legendre symbols as component gates in the design of ciphers tailored for use in cryptographic proof systems. Legendre symbols correspond to high-degree maps, but can be evaluated much faster. As a result, a cipher that uses Legendre symbols can offer the same security as one that uses high-degree maps but without incurring the penalty of a comparatively slow evaluation time. After discussing the design considerations induced by the use of Legendre symbol gates, we present a concrete design that follows this strategy, along with an elaborate security analysis thereof. This cipher is called Grendel.
Note: add root finding attack to security analysis
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- arithmetization-orientedhash functionszero knowledge
- Contact author(s)
- alan szepieniec @ gmail com
- History
- 2021-11-29: revised
- 2021-07-23: received
- See all versions
- Short URL
- https://ia.cr/2021/984
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/984,
author = {Alan Szepieniec},
title = {On the Use of the Legendre Symbol in Symmetric Cipher Design},
howpublished = {Cryptology ePrint Archive, Paper 2021/984},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/984}},
url = {https://eprint.iacr.org/2021/984}
}
