Notes on DIMACS Work

These are notes based on discussions at DIMACS in May 2008. 1 Dining Cryptographers Figures 1, 2, and 3 describe the master process, the signature and state set of a cryptographer, and the transition relation of a cryptographer, respectively. In the definitions above, each action name is a task. Thus, one of the tasks is {pay i(T ), pay i(F )}. From the discussion about the correctness of Dining Cryptographers we ended up with the following informal formulation of correctness: for every scheduler σ and every observation o of player 0, μσ(M1‖C0‖C1‖C2)(o) = μσ(M2‖C0‖C1‖C2)(o), where with the notation μσ(M1‖C0‖C1‖C2)(o) we mean the probability of o in the probabilistic execution of M1‖C0‖C1‖C2 induced by σ. In other words, for every scheduler σ cryptographer 0 has no way to distinguish the situation in which cryptographer 1 is paying from the situation in which cryptographer 2 is paying. The scheduler has to be restricted in power, and we reached the conclusion that according to the definition given in the CONCUR paper of Chatzikokolakis and Palamidessi [3] using task schedulers should be ok. We take this definition for granted, given that we derived it from the CONCUR paper mentioned above. However, we will need to see whether there are alternative definitions (e.g., by exchanging quantifications) that are equivalent or more interesting. An observation of a cryptographer should be seen as the actual execution performed by the cryptographer. Thus, in the framework of task PIOAs, we can reformulate the correctness condition as follows: let Pi, i ∈ {0, 1, 2}, be Mi‖C0‖C1‖C2. Then,