Mathematical Methods of Cryptography

Mental poker protocol based on the problem of finding isogenies between elliptic curves

I. D. Ioganson^abc, V. V. Davydov^abc, Zh.-M. N. Dakuo^abc, A. F. Khutsaeva<sup>ac

a</sup> ITMO University, Saint Petersburg, Russia
^b QApp, Moscow, Russia
^c Saint-Petersburg State University of Aerospace Instrumentation, Saint Petersburg, Russia

Abstract: In the paper, a novel isogeny-based protocol for mental poker game is presented. This protocol allows multiple users to create and shuffle a deck of cards, and then issue a card to a specific user. Two versions of the protocol are developed: one without validation, which protects only against passive adversaries, and one with validation, which also allows detecting active interference with the protocol using zero-knowledge proof protocols. To validate the resulting solution, a C program was developed that implements the described protocol. This demonstrates the practical applicability of the proposed solution while ensuring protection against quantum attacks.

Keywords: mental poker protocol, elliptic curves, isogenies, post-quantum cryptography.

UDC: 003.26

DOI: 10.17223/20710410/69/5