Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

Siva Anantharaman 1 Christopher Bouchard 2 Paliath Narendran 2 Michaël Rusinowitch 3
3 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : 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: {\em list\/} and {\em 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.
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Siva Anantharaman, Christopher Bouchard, Paliath Narendran, Michaël Rusinowitch. Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2014, 10 (1:5), pp. 1--26. ⟨10.2168/LMCS-10(1:5)2014⟩. ⟨hal-00854841v3⟩

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