Probability on groups and an application to cryptography

Abstract

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.

Keywords

• Braid group
• Authentication protocol
• Probability on groups
• Mean-set attack
• CRAG