### Richelot Isogenies, Pairings on Squared Kummer Surfaces and Applications

Chao Chen and Fangguo Zhang

##### Abstract

Isogeny-based cryptosystem from elliptic curves has been well studied for several years, but there are fewer works about isogenies on hyperelliptic curves to this date. In this work, we make the first step to explore isogenies and pairings on generic squared Kummer surfaces, which is believed to be a better type of Kummer surfaces. The core of our work is the Richelot isogeny having two kernels together with each dual onto the squared Kummer surfaces, then a chain of Richelot isogenies is constructed simply. Besides, with the coordinate system on the Kummer surface, we modify the squared pairings, so as to propose a self-contained pairing named squared symmetric pairing, which can be evaluated with arithmetic on the same squared Kummer surface. In the end, as applications, we present a Verifiable Delay Function and a Delay Encryption on squared Kummer surfaces.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Hyperelliptic CurvesSquared Kummer SurfacesRichelot IsogeniesSquared PairingsVerifiable Delay FunctionDelay Encryption
Contact author(s)
isszhfg @ mail sysu edu cn
History
Short URL
https://ia.cr/2021/1617

CC BY

BibTeX

@misc{cryptoeprint:2021/1617,
author = {Chao Chen and Fangguo Zhang},
title = {Richelot Isogenies, Pairings on Squared Kummer Surfaces and Applications},
howpublished = {Cryptology ePrint Archive, Paper 2021/1617},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/1617}},
url = {https://eprint.iacr.org/2021/1617}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.