Chaotic Cryptosystems: Cryptanalysis and Identifiability

A general framework based on the identifiability concept for the cryptanalysis of a large class of chaotic cryptosystems is proposed. A systematic methodology is provided, in order to test, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not. A connection between robustness against brute force attacks, uniqueness in the parameters and identifiability is pointed out. Two approaches, the outputs equality approach and the input/output relation approach, are presented to test the identifiability of the system parameters. The second approach is constructive in the sense that not only it allows to conclude on the identifiability of the parameters but it also provides a systematic technique, based on solving a set of algebraic equations, to retrieve the parameters in the context of a known plaintext attack. It turns out that cryptosystems involving polynomial nonlinearities, chaotic or not, are weak against such an attack, called algebraic attack

[1]  Erik Frisk,et al.  RESIDUAL GENERATION FOR FAULT DIAGNOSIS , 2001 .

[2]  Meng Zhan,et al.  Error function attack of chaos synchronization based encryption schemes. , 2003, Chaos.

[3]  Hu Guojie,et al.  Chosen ciphertext attack on chaos communication based on chaotic synchronization , 2003 .

[4]  R. Marino,et al.  Global adaptive observers for nonlinear systems via filtered transformations , 1992 .

[5]  Yvo Desmedt,et al.  Advances in Cryptology — CRYPTO ’94 , 2001, Lecture Notes in Computer Science.

[6]  Maciej Ogorzalek,et al.  Taming chaos. I. Synchronization , 1993 .

[7]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[8]  Benoit B. Mandelbrot,et al.  Les objets fractals : forme, hasard et dimension , 1989 .

[9]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[10]  P. G. Vaidya,et al.  Decoding chaotic cryptography without access to the superkey , 2003 .

[11]  Ercan Solak.  Cryptanalysis of Observer Based Discrete-Time Chaotic Encryption Schemes , 2005, Int. J. Bifurc. Chaos.

[12]  Tao Yang,et al.  A SURVEY OF CHAOTIC SECURE COMMUNICATION SYSTEMS , 2004 .

[13]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[14]  Miguel Romera,et al.  Cryptanalyzing a discrete-time chaos synchronization secure communication system , 2003, nlin/0311046.

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

[16]  Gérard Bloch,et al.  Global adaptive synchronization based upon polytopic observers , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[17]  Martin Hasler,et al.  Synchronization of chaotic systems and transmission of information , 1998 .

[18]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[19]  Maciej Ogorzalek,et al.  Identification of chaotic systems based on adaptive synchronization , 1997 .

[20]  G. Bloch,et al.  Message-Embedded Cryptosystems: Cryptanalysis and Identifiability , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  Gérard Bloch,et al.  Considering the attractor structure of chaotic maps for observer-based synchronization problems , 2005, Math. Comput. Simul..

[22]  Helmut Knebl,et al.  Introduction to Cryptography , 2002, Information Security and Cryptography.

[23]  E. Solak.  On the security of a class of discrete-time chaotic cryptosystems , 2004 .

[24]  C. Moog,et al.  Identifiability of discrete-time nonlinear systems , 2004 .

[25]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[26]  Qinghua Zhang,et al.  Adaptive Observer for Discrete Time Linear Time Varying Systems , 2003 .

[27]  M. Fliess,et al.  Nonlinear observability, identifiability, and persistent trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[28]  Qinghua Zhang,et al.  Global adaptive observer for a class of nonlinear systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[29]  Latifa Boutat-Baddas,et al.  Observability Bifurcations: Application to Cryptography , 2005 .

[30]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[31]  Lin Wang,et al.  Analysis of a type of digital chaotic cryptosystem , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[32]  M. Hénon.  A two-dimensional mapping with a strange attractor , 1976 .

[33]  Jamal Daafouz,et al.  Input independent chaos synchronization of switched systems , 2004, IEEE Transactions on Automatic Control.

[34]  Gonzalo Alvarez,et al.  Breaking projective chaos synchronization secure communication using filtering and generalized synchronization , 2004, Chaos, Solitons & Fractals.

[35]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[36]  Thomas Beth,et al.  Cryptanalysis of Cryptosystems Based on Remote Chaos Replication , 1994, CRYPTO.

[37]  Henk Nijmeijer,et al.  c ○ World Scientific Publishing Company ADAPTIVE OBSERVER-BASED SYNCHRONIZATION FOR COMMUNICATION , 1999 .

[38]  Jamal Daafouz,et al.  Unknown Input Observers for Message-Embedded Chaos Synchronization of Discrete-Time Systems , 2004, Int. J. Bifurc. Chaos.

[39]  Guanrong Chen,et al.  Breaking a chaos-noise-based secure communication scheme. , 2004, Chaos.