椭圆曲线上的二元门限序列的构造

Design of Pseudorandom Binary Threshold Sequences over Elliptic Curves

鉴于椭圆曲线密码的高度安全性,利用椭圆曲线生成伪随机序列得到了高度的重视,但目前的研究主要集中在素域上的椭圆曲线。该文在定义于扩张域上的椭圆曲线上,定义取值在[0,1)区间上的伪随机数,并利用这类伪随机数给出了一类二元门限序列的构造。通过分析伪随机数的偏差,得到了二元门限序列的一致分布测度与l阶相关测度的上界,证明中应用了指数和以及偏差与上述两种测度的联系。此外,应用l阶相关测度,给出了二元门限序列的线性复杂度轮廓的下界。

Due to the high security level of elliptic curve cryptography, the constructions of pseudorandom sequences generated from elliptic curves have been paid more attention recently. But the study mainly is concentrated upon the application of elliptic curves over prime fields. This paper defines pseudorandom numbers in the interval （0,1） by using elliptic curves over extension fields and presents a construction of binary threshold sequences. A discrepancy bounds for the pseudorandom numbers is derived and used to study the pseudorandomness of the binary threshold sequences in terms of estimating upper bounds on the well-distribution measure and the correlation measure of order/, both introduced by Mauduit and Sarkozy. The proofs are based on bounds on exponential sums and earlier relations of Mauduit, Niederreiter and Sarkozy between discrepancy and both measures above. Moreover, a lower bound on the linear complexity profile of the binary threshold sequences is presented in terms of the correlation measure of order l.