Single Cycle Invertible Function and its Cryptographic Applications

摘要

Single cycle invertible functions(SCIF) are studied in this paper. We show that i f β+ γ = k~(2n - a ) , 2~a β +α≡ 1 (mod 4), and α + k ≡C≡ 1 ( mod 2), g(x) = αx + β(x > b) + γ(x b) + C is a single cycle invertiblefunction and some cryptographic properties are studied; new ways based on SCIF and linear feedback shift registers are introduced to generate longer periods state which can be used as the state transition function in stream ciphers. At last, a new stream cipher proposal which is based on SCIF and LFSR is introduced and its cryptographic properties are studied.