[BOOK][B] Non-commutative cryptography and complexity of group-theoretic problems

AG Myasnikov, V Shpilrain, A Ushakov - 2011 - books.google.com
Myasnikov (City College of New York) et al. apply the complexity of non-commutative groups
to public key cryptography, assess the generic-case performance of various algorithms, and …

[BOOK][B] Group-based cryptography

A Myasnikov, V Shpilrain, A Ushakov - 2008 - books.google.com
This book is about relations between three di? erent areas of mathematics and
theoreticalcomputer science: combinatorialgroup theory, cryptography, and c-plexity theory …

Cryptanalysis of Stickel's key exchange scheme

V Shpilrain - International computer science symposium in Russia, 2008 - Springer
We offer cryptanalysis of a key exchange scheme due to Stickel [11], which was inspired by
the well-known Diffie-Hellman protocol. We show that Stickel's choice of platform (the group …

Braid group cryptography

D Garber - Braids: Introductory lectures on braids, configurations …, 2010 - World Scientific
In the last decade, a number of public-key cryptosystems based on combinatorial group
theoretic problems in braid groups have been proposed. We survey these cryptosystems …

Random subgroups and analysis of the length-based and quotient attacks

AG Myasnikov, A Ushakov - Journal of Mathematical Cryptology, 2008 - degruyter.com
In this paper we discuss generic properties of “random subgroups” of a given group G. It
turns out that in many groups G (even in most exotic of them) the random subgroups have a …

An authentication scheme based on the twisted conjugacy problem

V Shpilrain, A Ushakov - Applied Cryptography and Network Security: 6th …, 2008 - Springer
The conjugacy search problem in a group G is the problem of recovering an x∈ G from
given g∈ G and h= x− 1 gx. The alleged computational hardness of this problem in some …

Random equations in nilpotent groups

RH Gilman, A Myasnikov, V Romanʼkov - Journal of Algebra, 2012 - Elsevier
In this paper we study satisfiability of random equations in an infinite finitely generated
nilpotent group G. Let Sat (G, k) be the set of all satisfiable equations over G in k variables …

Exponentially generic subsets of groups

R Gilman, A Miasnikov, D Osin - Illinois Journal of Mathematics, 2010 - projecteuclid.org
In this paper, we study the generic, ie, typical, behavior of finitely generated subgroups of
hyperbolic groups and also the generic behavior of the word problem for amenable groups …

[BOOK][B] Semirings as building blocks in cryptography

M Durcheva - 2019 - books.google.com
Semirings as an algebraic structure have been known since 1934, but remained unapplied
for mathematical purposes for a long time. It has only been in the past decade that they have …

Algorithms and classification in groups of piecewise-linear homeomorphisms

F Matucci - arxiv preprint arxiv:0807.2871, 2008 - arxiv.org
This manuscript represents the author's PhD dissertation thesis. The first part studies
decision problems in Thompson's groups F, T, V and some generalizations. The …