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
The security of certain classes of the generalized self-shrinking sequence （GSS） generators is analyzed. Firstly, it is shown that the security of these GSS generators is equivalent to the security of the GSS genera...The security of certain classes of the generalized self-shrinking sequence （GSS） generators is analyzed. Firstly, it is shown that the security of these GSS generators is equivalent to the security of the GSS generators of the class-1, after which two effective key recovery attacks on the GSS generators of the class-1 are developed to evaluate their security.展开更多
m-Sequences have been used widely in many applications, but the corresponding computation of the correlation-detection is overwhelming N2 operations, where N is the length of the m-sequence, such that it is unpracti...m-Sequences have been used widely in many applications, but the corresponding computation of the correlation-detection is overwhelming N2 operations, where N is the length of the m-sequence, such that it is unpractical. In this paper, a transform from p-ary m-sequence matrices to generalized Hadamard matrices is developed; and then by the fast generalized Hadamard matrices transform, a fast p-ary m-sequence transform is developed. The results show that the computation can be dramatically reduced from N2 to Nlog pN operations, so the fast p-ary m-sequence transform could enable a rapid correlation-detection at the receiver.展开更多
Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functi...Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.展开更多
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.
基金the National Natural Science Foundation of China (60273084).
文摘The security of certain classes of the generalized self-shrinking sequence （GSS） generators is analyzed. Firstly, it is shown that the security of these GSS generators is equivalent to the security of the GSS generators of the class-1, after which two effective key recovery attacks on the GSS generators of the class-1 are developed to evaluate their security.
基金TheNationalScienceFoundationofChina (No .6 0 30 2 0 15 )andtheFoundamentalScienceFoun dationofSouthwestJiaotongUniversity (No .2 0 0 3B0 5 )
文摘m-Sequences have been used widely in many applications, but the corresponding computation of the correlation-detection is overwhelming N2 operations, where N is the length of the m-sequence, such that it is unpractical. In this paper, a transform from p-ary m-sequence matrices to generalized Hadamard matrices is developed; and then by the fast generalized Hadamard matrices transform, a fast p-ary m-sequence transform is developed. The results show that the computation can be dramatically reduced from N2 to Nlog pN operations, so the fast p-ary m-sequence transform could enable a rapid correlation-detection at the receiver.
文摘Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.
