Cryptographic applications of T-functions

A T-function is a mapping in which the i-th bit of the output can depend only on bits 0, 1,..., i of the input. All the bitwise machine operations and most of the numeric machine operations in modern processors are T-functions, and their compositions are also T-functions. In this paper we show that T-functions can be used to construct exceptionally efficient cryptographic building blocks which can be used as nonlinear maximal length state transition functions in stream ciphers, as large S-boxes in block ciphers, and as non-algebraic multipermutations in hash functions.