IMI/Publicaţii/CSJM/Ediţii/CSJM v.23, n.3 (69), 2015/

Probability on groups and an application to cryptography

Authors: Sidoine Djimnaibeye, Daniel Tieudjo, Norbert Youmbi
Keywords: Braid group, Authentication protocol, Probability on groups, Mean-set attack, CRAG


In her thesis, Mosina introduced the concept of {\it mean-set of random (graph-) group-variables} and generalized Strong Law of Large Numbers (SLLN) to (graphs) groups, which she used for cryptanalysis of authentication schemes. This attack called the {\it mean-set attack} is presented here. It allows to break the Sibert authentication scheme on braid groups without solving the underlined difficult problem. We propose an amelioration to this attack and its implementation on the platform CRAG. We carry some experiments and we present the results. These results are discussed and they confirm those obtained by Mosina and Ushakov with a considerable gain of time.

Sidoine Djimnaibeye, Daniel Tieudjo
Department of Mathematics and computer science
The University of Ngaoundere
P.O. Box 454 Ngaoundere - Cameroon
E-mail: ,

Norbert Youmbi
School of Science, Department of Mathematics
Saint Francis University
117 Evergreen Dr, Loretto PA, 15940 USA

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