In this paper some new mathematical technique used in the design and analysis of cipher systems have been reviewed. Firstly, some modern cryptosystems like stream ciphers, permutation-based systems and public key encryption systems are described and the mathematical tools used in their design have been outlined. Special emphasis has been laid on the problems related to application of computational complexity to cryptosystems. Recent work on the design of the systems based on a combined encryption and coding for error correction has also been reviewed. Some recent system-oriented techniques of cryptanalysis have been discussed. It has been brought out that with the increase in the complexity of the cryptosystems it is necessary to apply some statistical and classification techniques for the purpose of identifying a cryptosystem as also for classification of the total key set into smaller classes. Finally, some very recent work on the application of artificial intelligence technique in cryptography and cryptanalysis has been mentioned.
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