Four kinds of sequences generated by single cycle triangular function （T-function） are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on the special properties of single cycle T-function and an algorithm due to Wei, linear complexities of these four kinds of sequence are all acquired. The results show that single cycle T-function sequences have high linear complexity. Therefore, T-function satisfies the essential requirements being a basic component of stream cipher.
Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.
