## Anantharaman, Siva and Bouchard, Christopher and Narendran, Paliath and Rusinowitch, Michaël - Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

lmcs:808 - Logical Methods in Computer Science, February 9, 2014, Volume 10, Issue 1
Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

Authors: Anantharaman, Siva and Bouchard, Christopher and Narendran, Paliath and Rusinowitch, Michaël

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By interpreting a particular symbol of this signature suitably, the rewrite system can model several practical situations of interest. An inference procedure is presented for deciding the unification problem modulo this rewrite system. The procedure is modular in the following sense: any given problem is handled by a system of list-inferences', and the set of equations thus derived between the element-terms of the problem is then handed over to any (black-box') procedure which is complete for solving these element-equations. An example of application of this unification procedure is given, as attack detection on a Needham-Schroeder like protocol, employing the CBC encryption mode based on the associative-commutative (AC) operator XOR. The 2-sorted convergent rewrite system is then extended into one that fully captures a block chaining encryption-decryption mode at an abstract level, using no AC-symbols; and unification modulo this extended system is also shown to be decidable.

Source : oai:arXiv.org:1401.0445
DOI : 10.2168/LMCS-10(1:5)2014
Volume: Volume 10, Issue 1
Published on: February 9, 2014
Submitted on: August 7, 2013
Keywords: Computer Science - Logic in Computer Science