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Birkhäuser - Birkhäuser Mathematics | Group-based Cryptography

Group-based Cryptography

Myasnikov, Alexei, Shpilrain, Vladimir, Ushakov, Alexander

2008

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  • Increased interest in applications of combinatorial group theory to cryptography
  • First monograph exploring the area of "non-commutative cryptography"
  • Employing decision problems (as opposed to search problems) in public key cryptography allows us to construct cryptographic protocols with new properties
  • First presentation of a rigorous mathematical justification of security for protocols based on infinite groups, as an alternative to the security model known as semantic security

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory.

Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far.

Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.

Content Level » Graduate

Keywords » Finite - Group theory - average - complexity - cryptography - mathematics

Related subjects » Birkhäuser Mathematics

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