Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application...Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application to cryptography. First, we give a simple method for selecting those GSS sequences whose least periods reach the maximum. Second, we give a method for describing and computing the auto-correlation coefficients of GSS sequences. Finally, we point out that some GSS sequences, when used as stream ciphers, have a security weakness.展开更多
This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period ...This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution.展开更多
Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking （GSS） sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomia...Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking （GSS） sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial ofL GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2^L-l linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.展开更多
文摘Generalized self-shrinking sequences, simply named the GSS sequences, are novel periodic sequences that have many advantages in cryptography. In this paper, we give several results about GSS sequence's application to cryptography. First, we give a simple method for selecting those GSS sequences whose least periods reach the maximum. Second, we give a method for describing and computing the auto-correlation coefficients of GSS sequences. Finally, we point out that some GSS sequences, when used as stream ciphers, have a security weakness.
文摘This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution.
基金Supported in part by the National Natural Science Foun-dation of China (No.60273084) and Doctoral Foundation (No.20020701013).
文摘Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking （GSS） sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial ofL GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2^L-l linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.
