Finite and infinite field cryptography analysis and applications

Most of the currently used cryptosystems are defined over finite fields and use modular arithmetic. Their security is often based on the difficulty of solving certain number theoretic problems. In recent years, a large amount of work for introducing of systems defined on infinite field in the design of new cryptosystems has been published. Many studies have been done by introducing of chaotic and fractal functions into the design of symmetric and asymmetric encryption scheme. This paper aims to discuss the advantages and drawbacks of using these new types of mathematics methods behind computer and network security that emerge as a result of integrating between communication and information sciences. In this paper the analysis and the comparison studies between these two disciplines is discussed in terms of their efficiency and security, to identify a common framework for the guidelines that address main issues for implementation and security analysis. Conclusions on their performance are inferred.

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