[图书][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 …

Cryptographic algorithms on groups and algebras

AS Kuzmin, VT Markov, AA Mikhalev… - Journal of Mathematical …, 2017 - Springer
We analyze algorithms for open construction of a key on some noncommutative group.
Algorithms of factorization and decomposition for associative algebras (of small dimension) …

Factoring in skew-polynomial rings over finite fields

M Giesbrecht - Journal of Symbolic Computation, 1998 - Elsevier
Efficient algorithms are presented for factoring polynomials in the skew-polynomial ringF [x;
σ], a non-commutative generalization of the usual ring of polynomialsF [x], whereFis a finite …

Algorithms based on*-algebras, and their applications to isomorphism of polynomials with one secret, group isomorphism, and polynomial identity testing

G Ivanyos, Y Qiao - SIAM Journal on Computing, 2019 - SIAM
We consider two basic algorithmic problems concerning tuples of (skew-) symmetric
matrices. The first problem asks us to decide, given two tuples of (skew-) symmetric matrices …

Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms

J Voight - Quadratic and higher degree forms, 2013 - Springer
We discuss the relationship between quaternion algebras and quadratic forms with a focus
on computational aspects. Our basic motivating problem is to determine if a given algebra of …

Computing irreducible representations of finite groups

L Babai, L Rónyai - Mathematics of computation, 1990 - ams.org
We consider the bit-complexity of the problem stated in the title. Exact computations in
algebraic number fields are performed symbolically. We present a polynomial-time algorithm …

Basic module theory over non-commutative rings with computational aspects of operator algebras

J Gómez-Torrecillas - Algebraic and Algorithmic Aspects of Differential and …, 2014 - Springer
LNCS 8372 - Basic Module Theory over Non-commutative Rings with Computational Aspects of
Operator Algebras Page 1 Basic Module Theory over Non-commutative Rings with …

Computation of lattice isomorphisms and the integral matrix similarity problem

W Bley, T Hofmann, H Johnston - Forum of Mathematics, Sigma, 2022 - cambridge.org
Let K be a number field, let A be a finite-dimensional K-algebra, let denote the Jacobson
radical of A and let be an-order in A. Suppose that each simple component of the …

Bounded round interactive proofs in finite groups

L Babai - SIAM Journal on Discrete Mathematics, 1992 - SIAM
This paper considers “black box groups,” ie, finite groups whose elements are uniquely
encoded by strings of uniform length, with group operations being performed by a group …

Decompositions of algebras over ℝ and ℂ

W Eberly - Computational Complexity, 1991 - Springer
We consider the boolean complexity of the decomposition of matrix algebras over ℂ and ℝ
with bases consisting of matrices over a number field. Deterministic polynomial time …