Cryptographic Properties of Stream Ciphers Based on T-functions

The cryptographic properties of keystreams that are generated by stream ciphers based on T-functions are studied in this paper. Such constructions, which have been lately proposed by Klimov and Shamir, are of great interest as they allow building efficient and secure cryptographic primitives. By using concepts from the analysis of sequences, namely the linear complexity, we are able to derive simple linear equations of small weight satisfied by all T-functions. This indicates the non-randomness exhibited by state sequences produced from such mappings. Furthermore, we consider the particular class of algebraic T-functions and give necessary and sufficient conditions to generate a single cycle