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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.
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Submitted on : Monday, July 8, 2019 - 5:12:08 PM
Last modification on : Saturday, June 25, 2022 - 9:12:45 PM

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E. Volte, J. Patarin, V. Nachef. Zero knowledge with Rubik's cubes and non-abelian groups. 12th International Conference on Cryptology and Network Security, CANS 2013, Nov 2013, Paraty, Brazil. pp.74-91, ⟨10.1007/978-3-319-02937-5_5⟩. ⟨hal-02177218⟩



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