When designing a stream cipher

pattern distribution is one of the most important aspects to weigh the pseudo-randomness of the keystream.Based on the property of bit sequences of single-cycle T-function

the pattern distributions of single-cycle T-function sequences and their truncated sequences are studied in this correspondence.It shows that the pattern distributions of length s are all balanced in the truncated sequences of single-cycle T-function when 1≤s ≤m≤n.Here n is the word length of single-cycle T-function

m is the word length of truncated sequences of single-cycle T-function.