Combinatorics, Probability, and Information Theory

  • Jeffrey Hoffstein
  • Jill Pipher
  • Joseph H. Silverman
Part of the Undergraduate Texts in Mathematics book series (UTM)


In considering the usefulness and practicality of a cryptographic system, it is necessary to measure its resistance to various forms of attack. Such attacks include simple brute-force searches through the key or message space, somewhat faster searches via collision or meet-in-the-middle algorithms, and more sophisticated methods that are used to compute discrete logarithms, factor integers, and find short vectors in lattices.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jeffrey Hoffstein
    • 1
  • Jill Pipher
    • 1
  • Joseph H. Silverman
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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