Logical Analysis and Verification of Cryptographic Protocols - Loria

Abstract
This thesis is developed in the framework of symbolic analysis of cryptographic
protocols. The contributions of this thesis can be split into three mains parts:
1. We analyse the three classes of cryptographic protocols using respectively collision
vulnerable hash functions, key substitution vulnerable digital signature
schemes, and cryptographic primitives represented by convergent equational theories
having the finite variant property.
• We conjecture that the verification problem of the first class of protocols can
be reduced to the verification problem of the class of cryptographic protocols
using an associative symbol of concatenation, and we show the decidability
of the verification problem for the last class.
• We show the decidability of the verification problem for the second two
classes of protocols.
2. We show the decidability of the ground entailment problem for a new fragment
of first order logic, and we show the application of this result on the verification
problem of cryptographic protocols.
3. We analyse the electronic-voting protocols, and we give a formal definition for
the voter-verifiability property. We also show that some well-known electronic
voting protocols satisfy this property.
Keywords: Security protocols, electronic-voting protocols, decision procedures,
algebraic primitives, constraint systems, first order clauses, resolution,
saturation, applied π calculus.
This thesis is presented and defended at Toulouse on the 9 th of December
2009, was performed under the supervision of Yannick Chevalier and
Philippe Balbiani. The author obtained the degree of Docteur en Informatique
de l’Université de Toulouse.
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