Cryptographic properties of nonlinear pseudorandom number generators

The cryptographic properties of keystreams generated by stream ciphers based on t-functions are studied. These constructions are of great interest as they allow building highly efficient and secure cryptographic primitives. The randomness of the coordinate sequences generated by such mappings is analyzed in terms of the autocorrelation function. The results derived are valid for all t-functions regardless the type of construction and indicate the existence of nonrandomness. As the problem of the efficient implementation of secure s-boxes is open, the nonlinearity of t-functions is also analyzed. It is shown how some cryptographically undesirable properties, can be solved by application of similarity transformations.

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