Cryptology ePrint Archive: Report 2021/1617

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.

Category / Keywords: public-key cryptography / Hyperelliptic Curves, Squared Kummer Surfaces, Richelot Isogenies, Squared Pairings, Verifiable Delay Function, Delay Encryption

Date: received 12 Dec 2021

Contact author: isszhfg at mail sysu edu cn

Available format(s): PDF | BibTeX Citation

Version: 20211214:093929 (All versions of this report)

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