## A Survey of Algebraic Properties Used in Cryptographic Protocols

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

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### 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{CDL05-survey,
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.},
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},
lsv-category = {jour},
wwwpublic = {public and ccsb},
}