Luo, Yonglong; Qi, Wenfeng Pattern distributions of sequences based on single-cycle T-function. (Chinese. English summary) Zbl 1212.94013 J. Wuhan Univ., Nat. Sci. Ed. 55, No. 4, 395-398 (2009). Summary: 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 \(1\leqslant s\leqslant m\leqslant n\). Here \(n\) is the word length of single-cycle T-function, \(m\) is the word length of truncated sequences of single-cycle T-function. MSC: 94A60 Cryptography 94A55 Shift register sequences and sequences over finite alphabets in information and communication theory 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) Keywords:stream cipher; single-cycle T-function; truncated sequence; pattern distribution PDFBibTeX XMLCite \textit{Y. Luo} and \textit{W. Qi}, J. Wuhan Univ., Nat. Sci. Ed. 55, No. 4, 395--398 (2009; Zbl 1212.94013)