Qianxue Wang

Qianxue Wang, Simin Yu

Plaintext non-delayed chaotic cipher (PNDCC) means that in the diffusion equation, plaintext has no delay terms while ciphertext has a feedback term. In existing literature, chaotic cipher diffusions invariably take this form. Since its introduction, PNDCC has attracted attention but also doubts. Designers of chaotic ciphers usually claim PNDCC security by statistical tests, while rigorous cryptographic proofs are absent. Thus, it is necessary to re-examine its design rationale and empirical security. To address this issue, we present a typical example of a three-stage permutation-diffusion-permutation PNDCC, which contains multiple security vulnerabilities. Although all of its statistical indicators show good performance, we are able to break it using four different attacks. The first is a differential attack based on homogeneous operations; the second is an S-PTC attack; the third is a novel impulse-step-based differential attack (ISBDA), proposed in this paper, and the fourth is a novel chain attack, also introduced here. These results demonstrate that the fulfilment of statistical criteria is not a sufficient condition for the security of PNDCC. Then, based on a mathematical model of multi-stage PNDCC, we show that the proposed chain attack can successfully break a class of multi-stage PNDCCs. The key technique of the chain attack depends on how to reveal all permutations. To address this key problem, we summarize the chaining rules and show that, from the attacker's perspective, if the same decryption chain can be reconstructed then all permutations can be deciphered. To that end, the entire diffusion process can be broken by solving a system of simultaneous equations. Finally, as a secure improvement, we propose a new scheme termed plaintext-delayed chaotic cipher (PDCC) that can resist various cryptanalytic attacks.

Zhuosheng Lin, Christophe Guyeux, Qianxue Wang et al.

To guarantee the integrity and security of data transmitted through the Internet, hash functions are fundamental tools. But recent researches have shown that security flaws exist in the most widely used hash functions. So a new way to improve their security performance is urgently demanded. In this article, we propose new hash functions based on chaotic iterations, which have chaotic properties as defined by Devaney. The corresponding diffusion and confusion analyzes are provided and a comparative study between the proposed hash functions is carried out, to make their use more applicable in any security context.

Christophe Guyeux, Qianxue Wang, Xiole Fang et al.

The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state machines can behave chaotically regarding the slight alteration of their inputs. This behavior is explained using Turing machines and formalized thanks to a special family of discrete dynamical systems called chaotic iterations. An illustrative example is finally given in the field of hash functions.

Zhuosheng Lin, Christophe Guyeux, Simin Yu et al.

Investigating how to construct a secure hash algorithm needs in-depth study, as various existing hash functions like the MD5 algorithm have recently exposed their security flaws. At the same time, hash function based on chaotic theory has become an emerging research in the field of nonlinear information security. As an extension of our previous research works, a new chaotic iterations keyed hash function is proposed in this article. Chaotic iterations are used both to construct strategies with pseudorandom number generator and to calculate new hash values using classical hash functions. It is shown that, by doing so, it is possible to apply a kind of post-treatment on existing hash algorithms, which preserves their security properties while adding Devaney's chaos. Security performance analysis of such a post-treatment are finally provided.

Xiaole Fang, Christophe Guyeux, Qianxue Wang et al.

Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos have been proposed. In this article, we summarize these contributions and propose applications in the fields of pseudorandom number generation, hash functions, and symmetric cryptography. For all these applications, the proofs of chaotic properties are outlined.

Qianxue Wang, Simin Yu, Christophe Guyeux et al.

In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to the Devaney's definition of chaos. Furthermore, an analog-digital hybrid circuit is also developed for realizing the designed basic IDCS. In the IDCS circuit design, chaos generation strategy is realized through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence, which plays a key role in circuit implementation. The experimental observations further validate the proposed systematic methodology for the first time.

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, 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.