Abdessalem Abidi

Abdessalem Abidi, Samar Tawbi, Christophe Guyeux et al.

In cryptography, block ciphers are the most fundamental elements in many symmetric-key encryption systems. The Cipher Block Chaining, denoted CBC, presents one of the most famous mode of operation that uses a block cipher to provide confidentiality or authenticity. In this research work, we intend to summarize our results that have been detailed in our previous series of articles. The goal of this series has been to obtain a complete topological study of the CBC block cipher mode of operation after proving his chaotic behavior according to the reputed definition of Devaney.

Abdessalem Abidi, Christophe Guyeux, Jacques Demerjian et al.

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.

Abdessalem Abidi, Qianxue Wang, Belgacem Bouallegue et al.

The cipher block chaining (CBC) block cipher mode of operation was invented by IBM (International Business Machine) in 1976. It presents a very popular way of encrypting which is used in various applications. In this paper, we have mathematically proven that, under some conditions, the CBC mode of operation can admit a chaotic behaviour according to Devaney. Some cases will be properly studied in order to put in evidence this idea.

Abdessalem Abidi, Christophe Guyeux, Bechara Al Bouna et al.

In cryptography, the Cipher Block Chaining (CBC), one of the most commonly used mode in recent years, is a mode of operation that uses a block cipher to provide confidentiality or authenticity. In our previous research work, we have shown that this mode of operation exhibits, under some conditions, a chaotic behaviour. We have studied this behaviour by evaluating both its level of sensibility and expansivity. In this paper, we intend to deepen the topological study of the CBC mode of operation and evaluate its property of topological mixing. Additionally, other quantitative evaluations are performed, and the level of topological entropy has been evaluated too.

Abdessalem Abidi, Qianxue Wang, Belgacem Bouallègue et al.

The cipher block chaining (CBC) block cipher mode of operation presents a very popular way of encrypting which is used in various applications. In previous research work, we have mathematically proven that, under some conditions, this mode of operation can admit a chaotic behavior according to Devaney. Proving that CBC mode is chaotic is only the beginning of the study of its security. The next step, which is the purpose of this paper, is to develop the quantitative study of the chaotic CBC mode of operation by evaluating the level of sensibility and expansivity for this mode.