A Survey of Algebraic Properties Used in Cryptographic Protocols

A Survey of Algebraic Properties Used in Cryptographic Protocols. Véronique Cortier, Stéphanie Delaune, and Pascal Lafourcade. Journal of Computer Security, 14(1):1–43, IOS Press, 2006.

Download

[PDF] [PS]

Abstract

Cryptographic protocols are successfully analyzed using formal methods. However, formal approaches usually consider the encryption schemes as black boxes and assume that an adversary cannot learn anything from an encrypted message except if he has the key. Such an assumption is too strong in general since some attacks exploit in a clever way the interaction between protocol rules and properties of cryptographic operators. Moreover, the executability of some protocols relies explicitly on some algebraic properties of cryptographic primitives such as commutative encryption. We give a list of some relevant algebraic properties of cryptographic operators, and for each of them, we provide examples of protocols or attacks using these properties. We also give an overview of the existing methods in formal approaches for analyzing cryptographic protocols.

BibTeX

@article{CortierDL-JCS05,
  author =        {Cortier, V{\'e}ronique and Delaune, St{\'e}phanie and
                   Lafourcade, Pascal},
  journal =       {Journal of Computer Security},
  number =        {1},
  pages =         {1-43},
  publisher =     {{IOS} Press},
  title =         {A Survey of Algebraic Properties Used in
                   Cryptographic Protocols},
  volume =        {14},
  year =          {2006},
  abstract =      {Cryptographic protocols are successfully analyzed
                   using formal methods. However, formal approaches
                   usually consider the encryption schemes as black
                   boxes and assume that an adversary cannot learn
                   anything from an encrypted message except if he has
                   the key. Such an assumption is too strong in general
                   since some attacks exploit in a clever way the
                   interaction between protocol rules and properties of
                   cryptographic operators. Moreover, the executability
                   of some protocols relies explicitly on some algebraic
                   properties of cryptographic primitives such as
                   commutative encryption. We give a list of some
                   relevant algebraic properties of cryptographic
                   operators, and for each of them, we provide examples
                   of protocols or attacks using these properties. We
                   also give an overview of the existing methods in
                   formal approaches for analyzing cryptographic
                   protocols.},
}