Study on Single-Cycle Function Sequences
Bing Shen · Information Security and Communications Privacy · 2011
In designing stream cipher,a random source is usually used,and generally LFSR is employed as the random source. After the suggested notion of single-cycle T function by Klimov A. and Shamir A.,many scholars adopt single-cycle T function as random source in designing stream cipher. In order to obtain new random source,the notion of single-cycle T function is extended. The notions of single-cycle function and single-cycle function sequence are defined. The least period of single-cycle function sequence is computed. The expression of cyclotomic polynomial over finite field is given,and the two relative theorems are presented. Based on these theorems,the lower bound of linear complexity of the single-cycle function sequence is derived. It is supposed that,under many conditions,the linear complexity of the single-cycle function sequence is far greater than this lower bound.