A T-junction 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.
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