arXiv subjects
Publications and source records attributed to Pierre-Cyrille Heam.
In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in other cryptographic domains. These preliminaries lead to a first proof of a cryptographically secure information hiding scheme.
This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of bits, but remains an open problem when this number becomes large. A running example is used throughout the paper. Finally, first statistical experiments of these generators are presented, they show how efficient and promising the proposed approach seems.
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distribution is calculated. Finally practical experiments show that the generators successfully pass the classical statistical tests.
In this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution.
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata representing reachable sets by merging some of their states with respect to simple syntactic criteria, or a combination of such criteria. The second approximation mechanism consists in manipulating an auxiliary automaton when applying a transducer representing the transition relation to an automaton encoding the initial states. In addition, for the second mechanism we propose a new approach to refine the approximations depending on a property of interest. The proposals are evaluated on examples of mutual exclusion protocols.
In the context of software testing, generating complex data inputs is frequently performed using a grammar-based specification. For combinatorial reasons, an exhaustive generation of the data -- of a given size -- is practically impossible, and most approaches are either based on random techniques or on coverage criteria. In this paper, we show how to combine these two techniques by biasing the random generation in order to optimise the probability of satisfying a coverage criterion.
In this proposal for the Journèes Codes et Stéganographie 2012, we define a new rigorous approach for steganalysis based on the complexity theory. It is similar to the definitions of security that can be found for hash functions, PRNG, and so on. We propose here a notion of \emph{secure hiding} and we give a first secure hiding scheme.