[BOOK][B] Non-commutative cryptography and complexity of group-theoretic problems
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 …
to public key cryptography, assess the generic-case performance of various algorithms, and …
[BOOK][B] Group-based cryptography
This book is about relations between three di? erent areas of mathematics and
theoreticalcomputer science: combinatorialgroup theory, cryptography, and c-plexity theory …
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 …
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 …
theoretic problems in braid groups have been proposed. We survey these cryptosystems …
Random subgroups and analysis of the length-based and quotient attacks
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 …
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
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 …
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 …
nilpotent group G. Let Sat (G, k) be the set of all satisfiable equations over G in k variables …
Exponentially generic subsets of groups
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 …
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 …
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 …
decision problems in Thompson's groups F, T, V and some generalizations. The …