Based on a constructive theorem of generalized synchronization (GS) for discrete-time chaos system (DTCS \cite{ZangMin07}), a GS DTCS is constructed via a Henon-like map. A new DTCS-based pseudorandom number generator (PNG) is introduced. The FIPS 140-2 randomness tests show that the PNG has good pseudo-randomness. Combining the DTCS and the PNG, an image encryption scheme with digital signature is established. This scheme is able successfully to encrypt and decrypt original information without any loss. The scheme is sensitive to the perturbations of the PNG parameters and the seeds of the PNG. The key space of the scheme is as large as $10^{158}$. The analysis of the key space, sensitivity of key parameters show that this scheme has sound security. Numerical simulations show that our scheme is effective to be used in secure communication.
['Hongyan Zang', 'Lequan Min', 'Li Cao']
An Image Encryption and Digital Signature Scheme Based on Generalized Synchronization Theorem