den Ji Jerry Hartog

Verifying probabilistic programs using a Hoare-like logic

Probability, be it inherent or explicitly introduced, has become an important issue in the verification of programs. In this paper we study a formalism which allows reasoning about programs which can act probabilistically. To describe probabilistic programs, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language. To specify propertics of probabilistic programs, standard first order logic predicates are insufficient, so a notion of probabilistic predicates is introduced. A Hoare-style proof system to check properties of probabilistic programs is given. The proof system for a sublanguage is shown to be sound and complete; the properties that can be derived are exactly the valid properties. Finally some typical examples illustrate the use of the probabilistic predicates and the proof system.

Verifying Probabilistic Programs Using a Hoare like Logic

Hoare logic can be used to verify properties of deterministic programs by deriving correctness formulae, also called Hoare triples. The goal of this paper is to extend the Hoare logic to be able to deal with probabilistic programs. To this end a generic non-uniform language Lpw with a probabilistic choice operator is introduced and a denotational semantics D is given for the language. A notion of probabilistic predicate is defined to express claims about the state of a probabilistic program. To reason about the probabilistic predicates a derivation system pH, similar to that of standard Hoare logic, is given. The derivation system is shown to be correct with respect to the semantics D. Some basic examples illustrate the use of the system.

An operation-based metric for CPA resistance

Differential power analysis (DPA) is a strong attack upon cryptographic devices such as smartcards. Correlation power analysis (CPA) is a specific form of DPA where the Hamming-weight and the correlation coefficient are employed. In this paper we investigate the intrinsic vulnerability of the individual operations that are targeted in DPA attacks. We find that under the typical circumstances, there is a difference in resistance to the attack between the operations. We then provide a precise definition of CPA resistance and capture it in a simple yet effective metric to rank operations. The metric is validated with both simulations and experiments on actual hardware.