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(2014)
Notes on thin matrix groups, Thin groups and superstrong approximation
R. Zimmer (1984)
Ergodic Theory and Semisimple Groups
D. Ruinskiy, A. Shamir, B. Tsaban (2006)
Length-based cryptanalysis: the case of Thompson's group, 1
A. Jackson, B. Lautrup, P. Johansen, M. Nielsen (2002)
Products of random matrices.Physical review. E, Statistical, nonlinear, and soft matter physics, 66 6 Pt 2
A. Lenstra, H. Lenstra, L. Lovász (1982)
Factoring polynomials with rational coefficientsMathematische Annalen, 261
H. Furstenberg (1963)
Noncommuting random productsTransactions of the American Mathematical Society, 108
A. Lubotsky, S. Mozes, M. Raghunathan, H. Iwaniec, Wenzhi Luo, P. Sarnak, L. Stolovitch (2000)
The word and Riemannian metrics on lattices of semisimple groupsPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 91
Irit Dinur, Guy Kindler, S. Safra (2003)
Approximating CVP to Within Almost-Polynomial Factors is NP-HardCombinatorica, 23
Sanjeev Arora, L. Babai, J. Stern, E. Sweedyk (1993)
The hardness of approximate optima in lattices, codes, and systems of linear equationsProceedings of 1993 IEEE 34th Annual Foundations of Computer Science
A. Shamir (1982)
A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)
G. Margulis (1991)
Discrete Subgroups of Semisimple Lie Groups
Y. Gurevich, P. Schupp (2007)
Membership Problem for the Modular GroupSIAM J. Comput., 37
L. Lovász, E. Szemerédi, Bolyai Társulat (1985)
Theory of algorithms
Mohit Singh, Kunal Talwar (2021)
Approximation AlgorithmsProceedings of the 1997 International Symposium on Parallel Architectures, Algorithms and Networks (I-SPAN'97)
J. Tsitsiklis, V. Blondel (1997)
The Lyapunov exponent and joint spectral radius of pairs of matrices are hard—when not impossible—to compute and to approximateMathematics of Control, Signals and Systems, 10
M. Gromov, Graham Niblo, M. Roller (1993)
Asymptotic invariants of infinite groups
L. Babai (1986)
On Lovász’ lattice reduction and the nearest lattice point problemCombinatorica, 6
D. Collins (1971)
Review: K. A. Mihajlova, (Problema vhozdenia did pramyh proizvedenij grupp):The Occurrence Problem for Direct Products of GroupsJournal of Symbolic Logic, 36
P. Bougerol, J. Lacroix (1985)
Products of Random Matrices with Applications to Schrödinger Operators
E. Page (1982)
Théorèmes limites pour les produits de matrices aléatoires
D. Garber, S. Kaplan, M. Teicher, B. Tsaban, U. Vishne (2004)
Probabilistic Solutions of Equations in the Braid GroupAdv. Appl. Math., 35
Hyunjoong Kim (2017)
Functional Analysis I
A. Joux, J. Stern (1998)
Lattice Reduction: A Toolbox for the CryptanalystJournal of Cryptology, 11
Abstract Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we consider an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out strong approximation algorithms (i.e., whose approximation factors depend only on dimension) analogous to LLL in the general case.
Groups Complexity Cryptology – de Gruyter
Published: Nov 1, 2015
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