1 - 10 of 14 articles
After reviewing the importance of the Word Problem and the Conjugacy Problem for group-based cryptosystems, this paper offers an efficient method for solving both problems in the Shuffle Group.
The object of this paper is to give a proof of the following theorem: S / P ≅ ण mn ⊆ ℚ + , where S / P is a certain torsion-free factor group of the Baumslag-Solitar group 〈 a, b ; a –1 b m a = b n | m ≠ 0, n ≠ 0, m, n ∈ ℤ〉, with m and n are relatively prime, and ण mn is a subgroup of the...
If two groups are residually-𝑃, their free product is not necessarily so; however, it is known that the free product of residually torsion-free nilpotent groups is again residually torsion-free nilpotent. In this paper it is shown that the free metabelian product of a free nilpotent group of...
Ben Fine observed that a theorem of Magnus on normal closures of elements in free groups is first order expressible and thus holds in every elementarily free group. This classical theorem, vintage 1931, asserts that if two elements in a free group have the same normal closure, then either they...
We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative) semigroup, i.e., to recovering X from X –1 AX and A ....
A generalized tetrahedron group is defined to be a group admitting the following presentation: , 2 ≤ l, m, n, p, q, r , where each W i ( a, b ) is a cyclically reduced word involving both a and b . These groups appear in many contexts, not least as fundamental groups of certain hyperbolic...
A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable / polycyclic group is suggested. In the process we review recent progress in non-abelian cryptography and post some open problems that naturally arise from...
It is an open problem whether the shifted conjugacy (decision) problem in B ∞ is solvable. We settle this problem by reduction to an instance of the simultaneous conjugacy problem in B n for some n ∈ ℕ.
This is the first in a two-part survey of current techniques in algebraic cryptanalysis. After introducing the basic setup of algebraic attacks and discussing several attack scenarios for symmetric cryptosystems, public key cryptosystems, and stream ciphers, we discuss a number of individual...
This paper is concerned with the question of determining which groups have their word problems lying in a given complexity class. Our main results give sufficient conditions for the existence of groups whose word problem is contained in some specified space complexity class but is not contained...
Read and print from thousands of top scholarly journals.
Continue with Facebook
Sign up with Google
Log in with Microsoft
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.