The properties and the software implementation for the proposed scheme are discussed in details. The proposed scheme is analyzed and discussed from the attacker viewpoint to prove that the scheme provides essential security requirements. The message is accepted only if the verification process is success, otherwise the message is ignored. By comparing the received hash with the calculated one the verification process is performed to identify the integrity of the message. At the receiver side, the hash function is constructed for the received encrypted message, after decryption. Using the advantages of fractal image coding (FIC), the fractal codes of a digital signature are added to the encrypted message to be transmitted. In the proposed scheme the message is encrypted using an efficient encrypted method, and a secure digital signature is constructed using hash function. An efficient signcryption scheme using the compression capability of fractal encoding and decoding scheme is proposed in this paper. The functionality combining of an encryption scheme with that of a signature scheme is called signcryption. This can be satisfied using digital signature followed by encryption. The major aim of the computer and the commutation security research is to achieve secure and authenticated message delivery/storage. The convergence rate has been discussed in the case of affine maps, and the conditions to decrease the convergence rate by a factor of 16 have been presented, based on the locally linear behaviour of the weakly coupled map. Two different observers have been designed. The model is a deterministic one, but exhibits spectral properties (spectrum, correlation and autocorrelation) close to those of random signals, and successfully passed all the statistical tests for closeness to random signals (NIST). Unlike these papers, in our work we present the analysis of a new ultra weakly coupled maps system introduced by Lozi. Moreover, most of the time these properties, however essential for the chaotic encryption, are simply neglected. However, most of the papers dealing with synchronization and observer synthesis consider maps exhibiting poor statistical and spectral properties. In some engineering applications, such as chaotic encryption, chaotic maps have to exhibit required statistical and spectral properties close to those of random signals.
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