Control theory for synchronization in private communications – THE CASCADE

The specificity and the originality of the project is the combination of modern tools from
control theory and timely cryptographic purposes. Indeed, synchronization can be interpreted as a state reconstruction problem while
the recovery of the information at the receiver side can be viewed as a left inversion problem.

Synchronization
- Necessary and sufficient conditions of self-synchronization in terms of graphical conditions ensuring the property of flatness [I2b]
- conditions of synchronization for different classes of Linear Parameter Varying (LPV) systems [I1b, I3b, I4b]
- General methodology of constructing stream ciphers having the self-synchronization property based on the result [I2b]
- Polynomial time algorithm for the search of all the flat ouputs of a system [I5b][J2b]
- Flatness characterization for PieceWiseLinear systems based on the spectral radius [J1b]

Securiy
- A unified representation of vectorial Boolean functions [J1a]
- Proof of the IND-CPA security of the canonical form of self-syncjronizing stream ciphers [I2a][J2b]
- Statistical attacks, algebraic attacks and physical attacks. In particular, for the first time regarding the literature, fault induction attacks on SSSC (publication in progress)

Implémentation
- ISC/SCADA platfom incorporating our SSSC algorithms

Synchronization
- Extension of the graphical characterization of flatness for MIMO systems

Securiy
- Further investigation regarding the cryptanalysis

Architecture and implementation
- Comparison of performances with respect to existing SSSC algorithms and potential enhancements

For the sake of space limitation, the scientific production has been splitted into the french and english dedicated columns. Appologize

International Conference papers
[I2a] B. DRAVIE, P. GUILLOT and G. MILLERIOUX, April 2015 Security Proof of the Canonical Form of Self-Synchronizing Stream Cipher. In proceeding of the ninth Workshop on Coding and Cryptography (WCC'15), Paris, France.

[I1b] G. MILLERIOUX and J. PARRIAUX , 2015, Discrete time-varying delayed systems for secure
communication, Proc. of International Symposium on Circuits and Systems (ISCAS'15), Lisboa, Portugal.

[I2b] G. MILLERIOUX and T. BOUKHOBZA, 2015, Characterization of flat outputs for LPV discrete-time systems : a graph-oriented approach., Proc. of 54th Conference on Decision and Control (CDC'15), Osaka, Japon.

[I3b] M. HALIMI, G. MILLERIOUX and J. DAAFOUZ, 2014, Mode detection and discernability as a framework for the estimation of time-varying delays, Proc. of 13th European Control Conference
(ECC'14), Strasbourg, France.

[I4b] G. MILLERIOUX. Chaotic cryptosystems in communication within an LPV framework. In Proc. of 9th IEEE International Symposium on Communication Systems, Networks and Digital
Signal Processing (CSNDSP14), Manchester, UK, 25-27 July, 2014.

[I5b] G. MILLERIOUX and T. BOUKHOBZA, 2016, Graphical characterization of the set of all flat outputs for structured linear discrete-time systems, Proc. of 6th Symposium on System Structure
and Control, (SSSC 2016), Istanbul, Turkey.

[I6b] B. DRAVIE, T. BOUKHOBZA and G. MILLERIOUX , 2017, A mixed algebraic/graph- oriented approach for flatness of SISO LPV discrete-time systems, Proc. of American Control
Conference, (ACC 2017), Seattle, USA (submitted)

Synchronization is not only an ubiquitous phenomenon in natural world, but can also be an interesting solution for different problems encountered in engineering area. In particular, it turns out that synchronization between coupled entities in a unidirectional way, that is in a master-slave configuration, is a mechanism used in private communication, more precisely in cryptographic setups involving ciphers called self-synchronizing stream ciphers. The main principle of such ciphers is based on generators delivering complex sequences used to conceal information. Those generators must be synchronized at the transmitter (ciphering) and receiver (deciphering) sides for proper information recovery. The aim of the project THE CASCADE is to propose new self-synchronizing architectures for private communications. On the upgrowing field of group communications, self-synchronization is a key feature for high speed communications like PMR (Professional Mobile Radio) systems and for a lot of new devices which are small, mobile, at low consumption and low cost such as some Bluetooth equipments, RFID tags, sensors that require lightweight cryptography, survivable Cyber-Physical Systems.

The specificity and the originality of the project is the combination of modern tools from control theory and timely cryptographic purposes. More precisely, the use of dynamical systems and modern control theoretical concepts will allow to provide and suggest new self-synchronizing architectures.

Clearly, even though control theory is central for the purpose of the project, issues related to security assessment and implementation will also be deeply examined. Hence, investigations for provable security will be carried out and resistance to distinct attacks will be assessed: algebraic attacks addressed as aparameter identifiability problem, distinguisher-based attacks, side channel attacks. Some of the attacks will be particularized owing to the specificity of the generators which will be proposed. A real-world communication platform for tests and validation will be designed by the companies involved in the project.