A contribution to the identification of switched dynamical systems over finite fields

In this paper, we address specific issues related to the problem of parameter identification for switched linear systems over finite fields. Peculiarities related to the consideration of finite fields are pointed out. In particular, one of the main contributions of the paper is the reconsideration of the usual Persistently Exciting conditions. Indeed they are important in that they guarantee unicity in the solution of the identification procedure but they actually do no longer make sense on finite fields. In this paper, we provide alternative conditions. Such an issue has a cryptographic interest since identification amounts to an attack in cryptography, that is a way of recovering the secret key played by the parameters of the dynamical system.

[1]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[2]  A. Benveniste,et al.  Dynamical systems over Galois fields and DEDS control problems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[3]  Vincent Rijmen,et al.  Correlated Keystreams in Moustique , 2008, AFRICACRYPT.

[4]  Jamal Daafouz,et al.  Left invertibility, flatness and identifiability of switched linear dynamical systems: a framework for cryptographic applications , 2010, Int. J. Control.

[5]  A. Benveniste,et al.  Hybrid dynamical systems theory and nonlinear dynamical systems over finite fields , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[6]  Jamal Daafouz,et al.  A connection between chaotic and conventional cryptography , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  Jacob Roll,et al.  Input-output realization of piecewise affine state space models , 2007, 2007 46th IEEE Conference on Decision and Control.

[8]  G. Millérioux,et al.  FLAT DYNAMICAL SYSTEMS AND SELF-SYNCHRONIZING STREAM CIPHERS , 2008 .

[9]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[10]  René Vidal,et al.  Identification of Deterministic Switched ARX Systems via Identification of Algebraic Varieties , 2005, HSCC.

[11]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[12]  D. Segal.  ALGEBRA: (Graduate Texts in Mathematics, 73) , 1982 .

[13]  S. Weiland,et al.  On the equivalence of switched affine models and switched ARX models , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.