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Construction of k-ary Pseudorandom Elliptic Curve Sequences

Construction of k-ary Pseudorandom Elliptic Curve Sequences
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摘要 We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography. We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.
作者 WU Chenhuang WENG Xin CHEN Zhixiong
机构地区 Department of Mathematics State Key Laboratory of Information Security/Institute ofSoftware School of Mathematics and Statistics
出处 《Wuhan University Journal of Natural Sciences》 CAS 2011年第5期452-456,共5页 武汉大学学报（自然科学英文版）
基金 Supported by the National Natural Science Foundation of China (61063041) the Program for New Century Excellent Talents in Fujian Province University (JK2010047) the Open Funds of State Key Laboratory of Information Security (01-01-1)
关键词 pseudorandom sequences discrete logarithms elliptic curves character sums pseudorandom sequences discrete logarithms elliptic curves character sums
分类号 TN918 [电子电信—通信与信息系统]
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参考文献17

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Wuhan University Journal of Natural Sciences
2011年 第5期

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