arXiv subjects

Natalia Mosina

Publications and source records attributed to Natalia Mosina.

2 recordsLinked to original sources

arXiv2010

Strong law of large numbers on graphs and groups

We consider (graph-)group-valued random element $ξ$, discuss the properties of a mean-set $\ME(ξ)$, and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's inequality for $ξ$ and Chernoff-like asymptotic bounds. In addition, we prove several results about configurations of mean-sets in graphs and discuss computational problems together with methods of computing mean-sets in practice and propose an algorithm for such computation.

math.PR↗

arXiv2010

Mean-Set Attack: Cryptanalysis of Sibert et al. Authentication Protocol

We analyze the Sibert et al. group-based (Feige-Fiat-Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge. In addition, we provide experimental evidence that our approach is practical and can succeed even for groups with no efficiently computable length function such as braid groups. The novelty of this work is that we are not attacking the protocol by trying to solve an underlying complex algebraic problem, namely, the conjugacy search problem, but use a probabilistic approach, instead.

math.GR↗