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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Evaluation of Chaotic Properties of CBC Mode of Encryption Embedded with RC5 Block Cipher Algorithm

Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 607--618 | DOI:10.5890/DNC.2020.12.013

Abdessalem Abidi$^1$ , Christophe Guyeux$^2$, Mohsen Machhout$^1$

$^1$ Electronics and Microelectronics Laboratory, Faculty of Sciences of Monastir, University of Monastir, Tunisia

$^2$ FEMTO-ST Institute, UMR 6174 CNRS, DISC Computer Science Department, University of Bourgogne Franche-Comt'e, 16, Route de Gray, 25000 Besanc{c}on, France

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It has been recently proven that, under ad hoc conditions, the Cipher Block Chaining (CBC) mode of operation can behave chaotically according to the mathematical definition of Devaney, on the infinite discrete product set of finite memory coupled with (finite) media of unbounded size. This occurs when the chosen block cipher function satisfies some properties related to a well defined associated graph. Rudimentary examples taken from so-called transposition cipher methods have formerly been proposed as illustrative examples. In this paper, the same canvas will be followed by regarding the conditions under which the CBC mode behaves chaotically. But the encryption function is now the Rivest Cipher 5 (RC5) one, a very famous symmetric key block cipher algorithm. Therefore, our goal is to prove the chaotic behavior of RC5-CBC encryption algorithm according to the reputed Devaney's definition. Then, this unpredictability was checked in hardware through such sensitivity tests which allowed us to validate that RC5-CBC exhibits a high degree of randomness, key and plain sensitivity, in addition to the so-called avalanche effect.


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