Chaotic Cryptosystems: Cryptanalysis and Identifiability

Abstract

A general framework and a systematic methodology for the cryptanalysis of a large class of chaotic cryptosystems are proposed. More precisely, it is tested, a priori, during the design stage, whether the parameters of a chaotic cryptosystem may play the role of the secret key or not. Robustness against brute force attacks is first considered. A connection between 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 to retrieve the parameters in the context of a known plaintext attack. It is shown that cryptosystems involving polynomial nonlinearities, chaotic or not, are weak against this attack, called algebraic attack.

Masking Digital Image using a Novel technique based on a Transmission Chaotic System and SPIHT Coding Algorithm

“…One of the most important properties of cryptographic systems is the existence of a secret key which defines the level of security of the cryptosystem [27][28]. The better secret key is designed, the larger is the key space hence and the more secure is the cryptosystem.…”

Cryptanalysis of image encryption with compound chaotic sequence

“…The decryption is straightforward. Using the secret parameters, x 0 , y 0 , we use (1), (2) and (4) to produce K, ρ and σ. We go from C to M using (8) then (7).…”

“…Synchronization based cryptosystems can generate ciphertext with desirable statistical properties. However, these systems are weak against adaptive synchronization and identification attacks [2], [3], [4].…”

Secure Data Transmission Based on Multi-Input Multi-Output Delayed Chaotic System

“…It is known that some of the designed secure data transmission systems based on chaos with single input have been broken (Pérez et al, 1995), (Short, 1994), (Yang et al, 1998), (Anstett et al, 2006). Particularly, it has been recently shown in (Anstett et al, 2006) that traditional methods of data transmission by synchronization of chaotic systems suffer from the serious drawback of not being robust with respect to known plain-text attacks.…”

“…Particularly, it has been recently shown in (Anstett et al, 2006) that traditional methods of data transmission by synchronization of chaotic systems suffer from the serious drawback of not being robust with respect to known plain-text attacks. More precisely, according to the famous Kerkhoff assumption (Kerkhoff, 1883), it is assumed that hackers know all the details about the cryptosystem but the secret key.…”