Many computers are interconnected through networks, the biggest of them being Internet. Communications over these networks are ruled by protocols: physical networks are just wires (or radio waves) linking computers, providing channels where data can be transmitted; protocols define how data are formatted to go through these channels, and also provide additional features such as error detection and correction. More precisely, a protocol is a sequence of messages exchanged between (two or more) principals. A principal can be a computer, but also—more generally—a (human) user, a process, a server, etc. Sometimes, the identities of the principals involved are important: one must be sure of the other’s identity to proceed. For example, when you connect to your bank’s website, you want be sure that you are really talking to your bank and that nobody is spying on you. You cannot just assume that there is an armored pipe between you and your bank: actually, your messages must go through several intermediate entities (wires, switches, routers), and each of them can be watched or controlled by a possibly malicious intruder. A protocol resistant to intermediate malicious actions is a security protocol. Two main properties are targeted when designing such protocols: authentication and secrecy. These are achieved using cryptography (public-key, shared-key or both), so such protocols are also called cryptographic protocols. This report is mainly about verification of the security properties of cryptographic protocols. We consider especially authentication protocols, for which Clark and Jacob give a survey in [9]. The main target of this report is to present and compare some formal approaches to protocol verification (based on proof systems), and to present in detail a semantics for one of them and prove the corresponding soundness. In this report, formal frameworks are especially considered, where some simplifying assumptions—such as perfect cryptography, uniquely interpretable

Proof Theory

Analysis of authentication protocols Intership report

Some computational issues on abduction are discussed in a framework of the first order sequent calculus. Starting from revising the meaning of “good” abduction, a new criterion of abduction called intuitive-minimal abduction (IMA) is introduced.

Intuitive Minimal Abduction in Sequent Calculi

Propositional intuitionistic multiple-conclusion calculus via proof graphs

We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.

On Structural Features of the Implication Fragment of Frege’s Grundgesetze

This paper focuses on globally sound but possibly locally unsound analytic sequent calculi for quantifier macros defined by sequences of quantifiers. It is demonstrated that no locally sound analytic representation based on the usual eigenvariable condition exists. In consequence, representations by globally sound but possibly locally unsound analytic sequent calculi are used. Cut-elimination is shown by translating proofs into LK and retranslating cut-free proofs into the desired format. Finally, criteria are given for sequents to be proved without reference to the extended eigenvariable conditions.

Proof Theory

Citations

Analysis of authentication protocols Intership report

Intuitive Minimal Abduction in Sequent Calculi

Propositional intuitionistic multiple-conclusion calculus via proof graphs

On Structural Features of the Implication Fragment of Frege’s Grundgesetze

Towards a proof theory for quantifier macros

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