Cryptography inspires new group-theoretic problems and leads to important new ideas. The book includes exciting new improvements in the algorithmic theory of solvable groups. Another exceptional new development is the authors' analysis of the complexity of group-theoretic problems.

Cryptography inspires new group-theoretic problems and leads to important new ideas. Series: Mathematical Surveys and Monographs (Book 177).

oceedings{utativeCA, title {Non-Commutative Cryptography and Complexity of Group-Theoretic Problems}, author {Alexei G. Myasnikov and Vladimir Shpilrain and Alexander Ushakov}, year {2011} }. Alexei G. Myasnikov. Myasnikov, Vladimir Shpilrain, Alexander Ushakov. This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography.

Mathematical Surveys and Monographs Volume 177. Non-commutative Cryptography and Complexity of. . Non-commutative Cryptography and Complexity of Group-theoretic Problems Alexei Myasnikov Vladimir Shpilrain Alexander Ushakov With an appendix by Natalia Mosina. American Mathematical Society. Preface In this book, we explore non-commutative ideas in cryptography that have appeared in the literature over the last decade or so. Since all three authors have backgrounds in combinatorial and computational group theory, we pay particular attention to what can be called group-based cryptography, . cryptography that uses non-commutative group theory one way or another.

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Alexei Myasnikov; Vladimir Shpilrain; Alexander Ushakov Non-Commutative Cryptography and Complexity of.Cryptography inspires new group-theoretic problems and leads to important new ideas.

Alexei Myasnikov; Vladimir Shpilrain; Alexander Ushakov Non-Commutative Cryptography and Complexity of Group-Theoretic Problems (Mathematical Surveys and Monographs). ISBN 13: 9780821853603. Non-Commutative Cryptography and Complexity of Group-Theoretic Problems (Mathematical Surveys and Monographs).

Alexei Myasnikov; Vladimir Shpilrain; Alexander Ushakov. with an Appendix by Natalia Mosina. Non-commutative Cryptography and Complexity of Group-theoretic Problems. Base Product Code Keyword List: surv; SURV; surv/177; SURV/177; surv-177; SURV-177. Print Product Code: SURV/177.

Alexei Myasnikov, Vladimir Shpilrain, and Alexander Ushakov. In part two of the book we find methods of using the complexity of non-commutative groups in public-key cryptography. Publisher: American Mathematical Society. Mathematical Surveys and Monographs 177. Price: 10. 0. The authors call this canonical cryptography and discuss it in chapter four. In chapter five we have an analysis of several groups to determine whether they can be used as platforms for cryptographic public-key protocols.

Non-commutative cryptography and complexity of group-theoretic problems. V Shpilrain, A Ushakov. International Conference on Applied Cryptography and Network Security, 151-163, 2005. AG Myasnikov, V Shpilrain, A Ushakov. American Mathematical So. 2011. Thompson’s group and public key cryptography. Length based attack and braid groups: cryptanalysis of ld key exchange protocol. AD Myasnikov, A Ushakov. International Workshop on Public Key Cryptography, 76-88, 2007.

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In book: Non-commutative Cryptography and Complexity of Group-theoretic Problems, p. 41-145. In this paper we investigate how the complexity of the shortest vector problem in a lattice Λ depends on the cycle structure of the additive group Zn/Λ. Cite this publication. Stevens Institute of Technology. City College of New York. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices Λ where Zn/Λ has n-1 cycles