Zero Knowledge with  Rubik's Cubes and Non-Abelian Groups

Emmanuel VOLTE; Jacques PATARIN; Valérie NACHEF

Paper 2012/174

Zero Knowledge with Rubik's Cubes and Non-Abelian Groups

Emmanuel VOLTE, Jacques PATARIN, and Valérie NACHEF

Abstract

The factorization problem in non-abelian groups is still an open and a difficult problem. The Rubik's cube is a famous group that illustrates the hardness of the problem. 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.

Note: The scheme has been simplified, there are more references to other existing papers, and the scheme has been extended to non-abelian groups.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: zero-knowledge Rubik's cube authentication symmetric group cryptographic protocol factorization
Contact author(s): emmanuel volte @ u-cergy fr
valerie nachef @ u-cergy fr
History: 2012-12-09: revised; 2012-04-11: received; See all versions
Short URL: https://ia.cr/2012/174
License: CC BY

BibTeX

@misc{cryptoeprint:2012/174,
      author = {Emmanuel VOLTE and Jacques PATARIN and Valérie NACHEF},
      title = {Zero Knowledge with  Rubik's Cubes and Non-Abelian Groups},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/174},
      year = {2012},
      url = {https://eprint.iacr.org/2012/174}
}