Zero knowledge with Rubik's cubes and non-abelian groups

Abstract

The factorization problem in non-abelian groups is still an open and a difficult problem [12]. The hardness of the problem is illustrated by the moves of the Rubik's cube.We will define a public key identification scheme based on this problem, in the case of the Rubik's cube, when the number of moves is fixed to a given value. Our scheme consists of an interactive protocol which is zero-knowledge argument of knowledge under the assumption of the existence of a commitment scheme. We will see that our scheme works with any non-abelian groups with a set of authorized moves that has a specific property. Then we will generalize the scheme for larger Rubik's cubes and for any groups. © Springer International Publishing 2013.