Lecture 4 1 Honnor Projects Supervised by Catuscia Palamidessi The  -calculus, a small language for specification and verification of concurrency and mobility The generalized dining philosophers, a paradigm for resource allocation The spi-calculus, a small language for specification and verification of security protocols

Lecture 4 2 Project 1: The  -calculus Completed. With Shawna Daigle Implementation of (a fragment of) the  - calculus, a small language for specification and verification of concurrent process which communicate via mobile links

Lecture 4 3 The  -calculus   Example of link mobility   Representation of systems whose Connection structure changes over time

Lecture 4 4 Prj.2: Generalized Dining Philosophers Current project. With Michael Pilquist The problem: coordinate the activity of several processes (philosophers), who share common resources (forks), and need more than one resource to perform a certain activity (eat). We want to avoid deadlock and starvation Generalized means that a philosopher can need more than two forks and that a fork can be shared by more than two philosophers

Lecture 4 5 Dining Philosophers: classic case Each fork is shared by exactly two philosophers

Lecture 4 6 Dining Philosophers: deadlock Each philosopher is holding one fork

Lecture 4 7 Dining Philosophers: generalized case Each fork can be shared by more than two philosophers

Lecture 4 8 Project 3: The spi-calculus Current project. With Jennifer McCord Investigation of the spi-calculus, a small language to express and verify security protocols and their properties, like Secrecy messages, keys, etc. remain secret Authentication guarantees about the parties involved in the protocol Non-repudiation evidence of the involvement of the other party Anonymity protecting the identity of agents wrt particular events Formal tools for automatic verification

Lecture 4 9 Example: The dining cryptographers Crypt (0) Crypt (1) Crypt (2) Master pays.0notpays.0 An example of achieving anonymity

Lecture 4 10 The dining cryptographers The Problem: Three cryptographers share a meal The meal is paid either by the organization (master) or by one of them. The master decides who pays Each of the cryptographers is informed by the master whether or not he is paying GOAL: The cryptographers would like to know whether the meal is being paid by the master or by one of them, but without knowing who is paying (if it is one of them).

Lecture 4 11 The dining cryptographers: Solution Solution: Each cryptographer tosses a coin. Each coin is in between two cryptographers. The result of each coin-tossing is visible to the adjacent cryptographers, and only to them. Each cryptographer examines the two adjacent coins If he is paying, he announces “agree” if the results are the same, and “disagree” otherwise. If he is not paying, he says the opposite Claim: if the number of “disagree” is even, then the master is paying. Otherwise, one of them is paying. In the latter case, the non paying cryptographers will not be able to deduce whom exactly is paying

Lecture 4 12 The dining cryptographers: Solution Crypt (0) Crypt (1) Crypt (2) Master Coin( 2) Coin (1) Coin (0) pays.0notpays.0 look.2.0 out.1