Self-synchronizing stream ciphers and dynamical systems: state of the art and open issues

International audienceDynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in ''chaos-based'' private communications and in stream ciphers over finite fields. In the former case, they get the form of automata named as Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved at the transmitter and the receiver part. In this paper, we focus on a special class of symmetric ciphers, namely the Self-Synchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they get interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature and fully-specified algorithms are detailed for illustration purpose. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developped. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end

Security proof of the canonical form of self-synchronizing stream ciphers

International audienceThis paper studies the security level expected by the canon-ical form of the Self-Synchronizing Stream Cipher (SSSC). A SSSC can be viewed as the combination of a shift register together with a filtering function. The maximum security of such a cipher is reached when the filtering function is random. However, in practice, Pseudo Random Functions (PRF) are used as filtering functions. In this case, we show that the security against chosen ciphertext attacks (IND-CCA security) cannot be reached for the canonical form of the SSSC, but it is however secure against chosen plaintext attacks (IND-CPA secure). Then, a weaker property than pseudo-randomness is introduced in order to characterize the security of the canonical SSSC from its filtering function. A connection with the left-or-right indistinguishability (LOR-IND) is made. This property provides a necessary and sufficient condition to characterize the indistinguishablity of SSSC

Une approche intrinsèque des observateurs linéaires à entrées inconnues

On donne des conditions nécessaires et suffisantes d'existence d'observateurs à entrées inconnues, pour les systèmes linéaires invariants, à temps continu ou discret. Une structure générique valable quel que soit le degré relatif est alors proposé en monovariable, qui peut être étendue au multivariable. Deux exemples, dont l'un avec simulations numériques, sont examinés

Synchronization of Boolean Dynamical Systems: a Spectral Characterization

International audienceIn this paper a spectral characterization of the synchronization property of Boolean dynamical systems is provided. Conditions on the spectrum of the next-state function are derived for two systems coupled in a unidirectional way - also called master-slave configuration - to guarantee self-synchronization. Two kinds of self-synchronization are discussed: the statistical one and the finite one. Next, some conditions are stated for a specific input sequence to allow the system to be self-synchronizing. Some of the results are based on the notion of influence of variables, a notion that is extended to vectorial Boolean functions for the purpose of the paper. A potential application to cryptography is finally given

Towards a spectral approach for the design of self-synchronizing stream ciphers

International audienceThis paper addresses the problem of characterizing the func- tions that can be used in the design of self-synchronizing stream ciphers. We propose a general framework based on a spectral characterization through correlation matrices or equivalently through Walsh matrices. Two modes of self-synchronization are discussed: the finite time one and the statistical one

Matrix representations of vectorial boolean functions and eigenanalysis

International audienceThis paper aims at giving a unified overview on the various representations of vectorial Boolean functions, namely the Walsh matrix, the correlation matrix and the adjacency matrix. A new representation called polynomial matrix is introduced. It is shown that those different representations are similar. For a vectorial Boolean function with the same number of inputs and outputs, an eigenanalysis of those representations is performed. It is shown how eigenvalues and eigenvectors are related to the structure of the graph associated to this function

Chaos Synchronization for a class of discrete dynamical systems on the N- dimensional torus

In this paper, a class of dynamical systems on T^N (the N-dimensional torus) is investigated. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that the sequences produced are equidistributed for almost every initial data. The above results are then extended to switched affine transformations of T^N. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup

Bounded State Reconstruction Error for LPV Systems With Estimated Parameters

International audienceThis note deals with the state reconstruction of a class of discrete-time systems with time-varying parameters. While usually the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability

Self-synchronizing stream ciphers and dynamical systems: state of the art and open issues

Dynamical systems play a central role in the design of symmetric cryptosystems. Their use has been widely investigated both in "chaos-based" private communications and in stream ciphers over finite fields. In the former case, they get the form of automata named as Moore or Mealy machines. The main charateristic of stream ciphers lies in that they require synchronization of complex sequences generated by the dynamical systems involved at the transmitter and the receiver part. In this paper, we focus on a special class of symmetric ciphers, namely the SelfSynchronizing Stream Ciphers. Indeed, such ciphers have not been seriously explored so far although they get interesting properties of synchronization which could make them very appealing in practice. We review and compare different design approaches which have been proposed in the open literature and fully-specified algorithms are detailed for illustration purpose. Open issues related to the validation and the implementation of Self-Synchronizing Stream Ciphers are developped. We highlight the reason why some concepts borrowed from control theory appear to be useful to this end