rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Group-based Cryptography
  name:
    name part: Myasnikov, Alexei.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ushakov, Alexander.
    role:
      role term: author.
  name:
    name part: Shpilrain, Vladimir.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 183 p. online resource.
  abstract: 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.
  table of contents: Background on Groups, Complexity, and Cryptography -- Background on Public Key Cryptography -- Background on Combinatorial Group Theory -- Background on Computational Complexity -- Non-commutative Cryptography -- Canonical Non-commutative Cryptography -- Platform Groups -- Using Decision Problems in Public Key Cryptography -- Generic Complexity and Cryptanalysis -- Distributional Problems and the Average-Case Complexity -- Generic Case Complexity -- Generic Complexity of NP-complete Problems -- Asymptotically Dominant Properties and Cryptanalysis -- Asymptotically Dominant Properties -- Length-Based and Quotient Attacks.
  note: by Alexei Myasnikov, Alexander Ushakov, Vladimir Shpilrain.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Computer mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Combinatorics
  subject:
    topic: Computational Mathematics and Numerical Analysis
  classification: QA174-183
  classification: 512.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Advanced Courses in Mathematics - CRM Barcelona, Centre de Recerca Matemàtica
  identifier: 9783764388270
  identifier: http://dx.doi.org/10.1007/978-3-7643-8827-0
  record info:
    record creation date: 100301
    record change date: 20151123155909.0
    record identifier: 978-3-7643-8827-0