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

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.