Logical Analysis and Verification of Cryptographic Protocols - Loria

Chapter 8
Conclusion and Perspectives
In our society, the use of electronic applications such as e-communication, evoting,
e-banking, e-commerce, etc is increasing. Among several important requirements,
security figures as one crucial aspect. To guarantee security, such
applications use cryptographic protocols. It is well-known that design of cryptographic
protocols is not sufficient to their deployment, they need to be formally
analysed. While the insecurity problem of cryptographic protocols has
been shown to be undecidable in the general case [111], several restrictions led
to decidable results with perfect and unperfect cryptography hypotheses.
In this thesis, we have relaxed the perfect cryptography hypothesis by taking
into account several algebraic properties of cryptographic primitives. Following
the symbolic approach (in particular the method based on the resolution
of constraint solving) to analyse cryptographic protocols, we provided decision
procedures for the insecurity problem of cryptographic protocols with a
bounded number of sessions.
In Chapter 3, we considered the collision vulnerability property of hash functions,
and we analysed the class of cryptographic protocols employing hash
functions having this property. We reduced the insecurity problem of our class
of cryptographic protocols to the ordered satisfiability problem for the intruder
exploiting the collision vulnerability property of hash functions. We provided
sufficient arguments that allowed us to conjecture that, following [74], the ordered
satisfiability problem for the intruder exploiting the collision vulnerability
property of hash functions can be reduced to the ordered satisfiability problem
for an intruder operating on words. We then proved the decidability of the
last problem. A natural extension of this work would be to prove the above
conjecture.
In Chapter 4, we considered the destructive exclusive ownership vulnerability
and the constructive exclusive ownership vulnerability properties for digital signature
schemes, and we showed the decidability of the insecurity problem for the two
classes of cryptographic protocols using signature schemes having respectively
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