A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis

Abstract

This paper describes a method about how to determine parameters of some double-scroll chaotic systems, including the Lorenz system and the Chua's circuit, from one of its variables. The geometric properties of the system are exploited firstly to reduce the parameter search space. Then, a synchronization-based approach, with the help of the same geometric properties as coincidence criteria, is implemented to determine the parameter values with the wanted accuracy. The method is not affected by a moderate amount of noise in the waveform. As an example of its effectiveness, the method is applied to cryptanalyze two two-channel chaotic cryptosystems, figuring out how the secret keys can be directly derived from the driving signal z(t).

Real-time image encryption using a low-complexity discrete 3D dual chaotic cipher

“…This is significantly better than using a periodic signal to blur the return map as in [24], which was broken in [25]. Geometry attacks [26,27] will also be ineffective because the discrete Lorenz generator used in the proposed technique has additional parameters g i , one in each of the three difference equations. Since the g i can be assigned different values, they represent three additional key parameters beyond those of the differential equations of the continuous Lorenz generator, and so provide an additional level of security.…”

“…Since the proposed encryption algorithm is based on a discrete Lorenz system, it is important to consider attacks against the corresponding continuous Lorenz system. These attacks are based on the system synchronization and are primarily return map and geometry attacks [23][24][25][26][27]. The attacker uses the encrypted signal as the driving signal to synchronize their master generator in an attempt to obtain the Lorenz attractor parameters.…”

Cryptanalysis of a Classical Chaos-Based Cryptosystem with Some Quantum Cryptography Features

“…Different random values were generated for the initial conditions and the coupling parameters. In each different configuration the gradient descend algorithm in [Orue et al, 2010] was used to get an estimation of x A 0 , y A 0 , w A 0 , and ε Ex . As it is drawn from Fig.…”

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

“…Regarding power-spectral filtering, even when the power spectra of some chaotic systems seem to be good, significant spectrum peaks can be found in the spectra by removing the symmetries of the chaotic attractors [62,86,85]. For instance, the spectrum of x(t) in the Lorenz System is relatively good, but that of |x(t)| has a significant peak.…”