CAJ | 학술논문

Brandst?tter等人(2011)结合割圆序列与Sidel’nikov序列的概念定义了一个新序列双素数(p,q) Sidel’nikov序列，并且分析了双素数Sidel’nikov序列的均衡性、自相关函数、相关测度和线性复杂度轮廓，证明了双素数Sidel’nikov序列有好的伪随机特性。该文主要研究d=gcd(p, q)=2的双素数Sidel’nikov序列的自相关函数，借助于数论中的Legendre符号和有限域中的指数和理论，得到自相关函数的3个定理。通过与Brandst?tter论文中自相关函数的界进行比较，本文定理2和定理3中的界O(q1/2)和O(p1/2)比Brandst?tter的界O((p+q)/2)更紧，同时当p>>q或q>>p时，本文定理4中的界O((p q)1/2)比Brandst?tter的界O((p+q)/2+(p q)1/2)更优。
Brandst?tter등인(2011)결합할원서렬여Sidel’nikov서렬적개념정의료일개신서렬쌍소수(p,q) Sidel’nikov서렬，병차분석료쌍소수Sidel’nikov서렬적균형성、자상관함수、상관측도화선성복잡도륜곽，증명료쌍소수Sidel’nikov서렬유호적위수궤특성。해문주요연구d=gcd(p, q)=2적쌍소수Sidel’nikov서렬적자상관함수，차조우수론중적Legendre부호화유한역중적지수화이론，득도자상관함수적3개정리。통과여Brandst?tter논문중자상관함수적계진행비교，본문정리2화정리3중적계O(q1/2)화O(p1/2)비Brandst?tter적계O((p+q)/2)경긴，동시당p>>q혹q>>p시，본문정리4중적계O((p q)1/2)비Brandst?tter적계O((p+q)/2+(p q)1/2)경우。
Brandst?tter et al. (2011) combined the concepts of the two-prime generator and Sidel’nikov sequence to define a new sequence called two-prime (p, q) Sidel’nikov sequence, and analyzed the balance, the autocorrelation, the correlation measure and the linear complexity profile of the sequence. They showed that this sequence has many nice pseudorandom properties. With the help of the Legendre symbol in number theory and the exponential sums in finite field, this paper investigates the autocorrelation of the two-prime Sidel’nikov sequence with d=gcd(p, q)=2. Three theorems are got about the autocorrelation functions. The detailed comparison results show that the bounds O(q1/2) and O(p1/2) on the autocorrelation function in theorem 2 and theorem 3 are tighter than the Brandst?tter’s bound O((p+q)/2), besides, the bound O((p q) 1/2) in theorem 4 are tighter than the Brandst?tter’s bound O((p+q)/2+(p q) 1/2) when p>>q or q>>p.