论文信息 - Lyapunov Exponent Evaluation of the CBC Mode of Operation

Lyapunov Exponent Evaluation of the CBC Mode of Operation

The Cipher Block Chaining (CBC) mode of encryption was invented in 1976, and it is currently one of the most commonly used mode. In our previous research works, we have proven that the CBC mode of operation exhibits, under some conditions, a chaotic behavior. The dynamics of this mode has been deeply investigated later, both qualitatively and quantitatively, using the rigorous mathematical topology field of research. In this article, which is an extension of our previous work, we intend to compute a new important quantitative property concerning our chaotic CBC mode of operation, which is the Lyapunov exponent.

Mohsen Machhout | Jacques Demerjian | Christophe Guyeux | Abdessalem Abidi | Belagacem Bouallegue

[1] Verónica Fernández Mármol,et al. On the inadequacy of the logistic map for cryptographic applications , 2008, 0805.4355.

[2] Belgacem Bouallegue,et al. Proving Chaotic Behavior of CBC Mode of Operation , 2016, Int. J. Bifurc. Chaos.

[3] Douglas Lind,et al. An Introduction to Symbolic Dynamics and Coding , 1995 .

[4] Jacques M. Bahi,et al. Topological chaos and chaotic iterations application to hash functions , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[5] Enrico Formenti. Automates cellulaires et chaos : de la vision topologique a la vision algorithmique , 1998 .

[6] Jacques M. Bahi,et al. Evaluating Quality of Chaotic Pseudo-Random Generators: Application to Information Hiding , 2011, ArXiv.

[7] Jacques M. Bahi,et al. A Topological Study of Chaotic Iterations Application to Hash Functions , 2016, Computational Intelligence for Privacy and Security.

[8] M. Bernhard. Introduction to Chaotic Dynamical Systems , 1992 .

[9] X. Liao,et al. A block cipher with dynamic S-boxes based on tent map , 2009 .

[10] David Richeson,et al. Chain recurrence rates and topological entropy , 2008, 0801.1635.

[11] Belgacem Bouallegue,et al. Quantitative evaluation of chaotic CBC mode of operation , 2016, 2016 2nd International Conference on Advanced Technologies for Signal and Image Processing (ATSIP).

[12] Jacques M. Bahi,et al. Hash Functions Using Chaotic Iterations , 2017, ArXiv.