Controlling the Ultimate State of Projective Synchronization in Chaos: Application to Chaotic Encryption

Abstract

The ultimate state of projective synchronization is usually considered to be hardly controllable due to its close dependence on the initial conditions of both drive and response systems. In this letter, we show that the scaling factor of projective synchronization can be controlled to be proportional to a given scalar function with respect to time even without the knowledge of the initial conditions of response system. Further, we apply it to the chaotic encryption. Comparing with some existing implementations, it is found that the present scheme owns several remarkable advantages. To our knowledge, it is for the first time that the projective synchronization is applied to chaos-based encryption.

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

“…This method of recovering the unknown system parameters is applicable to cryptosystems that use the variable z(t) as the driving signal like those chaotic cryptosystems proposed in [13,14]. But it is not applicable to other two-channel cryptosystems driven by x(t) or y(t), like [12], because in those cases both conditional Lyapunov exponents are negative and the drive-response configuration is stable, in spite of being the drive and response parameters moderately different.…”

“…Cryptanalysis of the two-channel chaotic cryptosystem [13] In a recent article [13], Wang and Bu proposed a new encryption scheme based on PS. Following [19], the state vector of a partially linear system of ordinary differential equations is broken in two parts (u, z).…”

“…In order to avoid the weakness of the common chaotic masking scheme, a more elaborated mixing procedure was proposed by Jiang in 2002 [12] and later adopted by some other researchers [13,14]. They proposed to use two transmission channels instead of only one, where the first channel transmits an unmodified chaotic system variable, and the second channel conveys a signal that was a more complicated non-linear combination of the plaintext and one or more system variables, from which it is impossible to retrieve any of the components.…”

“…Therefore, in our attack, total knowledge of the communications system design is assumed. In the cryptosystems proposed in [13,14], the security relies on the secrecy of the system parameters, which play the role of secret key, hence the determination of the system parameters from the chaotic ciphertext is equivalent to breaking the system.…”

“…Then, in Secs. 3 and 4, it is shown how this method can be applied to break two different two-channel cryptosystems that use the Lorenz system [13,14]. Finally, Sec.…”