本文用迹函数及m—序列的结构特性构造并研究了一类GF(q^m)上的非线性伪随机序列。这类序列的取值分布、游程及自相关函数均与m—序列一致,且满足移位相加特性,但这类新序列的数量是m—序列的[multiply from f=1 to (m-1)((q^m-q^l)-m)...本文用迹函数及m—序列的结构特性构造并研究了一类GF(q^m)上的非线性伪随机序列。这类序列的取值分布、游程及自相关函数均与m—序列一致,且满足移位相加特性,但这类新序列的数量是m—序列的[multiply from f=1 to (m-1)((q^m-q^l)-m)]/m倍。展开更多
Ⅰ. INTRODUCTIONPseudorandom sequences are useful in security communications, and M-sequences have been studied extensively, m-sequences cannot be used as key-streams because of their small quantity and small linear c...Ⅰ. INTRODUCTIONPseudorandom sequences are useful in security communications, and M-sequences have been studied extensively, m-sequences cannot be used as key-streams because of their small quantity and small linear complexity. However, most of the M-sequences展开更多
Ⅰ. INTRODUCTIONLet s=（S<sub>0</sub>, s<sub>1</sub>, s<sub>2</sub>,…） be an infinite sequence on GF（q）, s<sup>n</sup>=(s<sub>0</sub>, s<sub>1</...Ⅰ. INTRODUCTIONLet s=（S<sub>0</sub>, s<sub>1</sub>, s<sub>2</sub>,…） be an infinite sequence on GF（q）, s<sup>n</sup>=(s<sub>0</sub>, s<sub>1</sub>,…,s<sub>n-1</sub>). The linear complexity of the sequence s<sup>n</sup> is defined to be L<sub>n</sub>（s）=min{1: s<sub>j</sub>=-sum from i=1 to l(C<sub>i</sub>S<sub>j-1</sub>), j=1, 1+1,…, n-1, c<sub>1</sub>,c<sub>2</sub>,…,c<sub>1</sub>∈GF（q）}, i.e. L<sub>n</sub>（s）is the smallest nonnegative integer L such that there exist the constants c<sub>1</sub>, c<sub>2</sub>,…,c<sub>1</sub> for展开更多
设S=(S_0,S_1,S_2,…)为有限域GF(q)上的无穷序列,S^n=(S_0,S_1,…,3_(n-1)),序列S^n的线性复杂度L_n(S)=min{l:S_j=-sum from i=1 to l(C_iS_(j-i),j=l,l+1,…,n-1,C_1,C_2,…,C_1∈CF(q)},序列的线性复杂度曲线为L=(L_0(S),L_1(S),L_1...设S=(S_0,S_1,S_2,…)为有限域GF(q)上的无穷序列,S^n=(S_0,S_1,…,3_(n-1)),序列S^n的线性复杂度L_n(S)=min{l:S_j=-sum from i=1 to l(C_iS_(j-i),j=l,l+1,…,n-1,C_1,C_2,…,C_1∈CF(q)},序列的线性复杂度曲线为L=(L_0(S),L_1(S),L_1(S),L_2(S),…)。由序列的随机性与复杂度关系可知,适合作为序列密码密钥的伪随机序列。展开更多
基金Project supported by University Science and Technology Foundation of China.
文摘Ⅰ. INTRODUCTIONPseudorandom sequences are useful in security communications, and M-sequences have been studied extensively, m-sequences cannot be used as key-streams because of their small quantity and small linear complexity. However, most of the M-sequences
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTIONLet s=（S<sub>0</sub>, s<sub>1</sub>, s<sub>2</sub>,…） be an infinite sequence on GF（q）, s<sup>n</sup>=(s<sub>0</sub>, s<sub>1</sub>,…,s<sub>n-1</sub>). The linear complexity of the sequence s<sup>n</sup> is defined to be L<sub>n</sub>（s）=min{1: s<sub>j</sub>=-sum from i=1 to l(C<sub>i</sub>S<sub>j-1</sub>), j=1, 1+1,…, n-1, c<sub>1</sub>,c<sub>2</sub>,…,c<sub>1</sub>∈GF（q）}, i.e. L<sub>n</sub>（s）is the smallest nonnegative integer L such that there exist the constants c<sub>1</sub>, c<sub>2</sub>,…,c<sub>1</sub> for
文摘设S=(S_0,S_1,S_2,…)为有限域GF(q)上的无穷序列,S^n=(S_0,S_1,…,3_(n-1)),序列S^n的线性复杂度L_n(S)=min{l:S_j=-sum from i=1 to l(C_iS_(j-i),j=l,l+1,…,n-1,C_1,C_2,…,C_1∈CF(q)},序列的线性复杂度曲线为L=(L_0(S),L_1(S),L_1(S),L_2(S),…)。由序列的随机性与复杂度关系可知,适合作为序列密码密钥的伪随机序列。
