Construction of <Emphasis Type="Italic">k</Emphasis>-ary pseudorandom elliptic curve sequences |
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Authors: | Chenhuang Wu Xin Weng Zhixiong Chen |
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Institution: | WU Chenhuang1,2,WENG Xin3,CHEN Zhixiong1,2 1.Department of Mathematics,Putian University,Putian 351100,Fujian,China,2.State Key Laboratory of Information Security/Institute of Software,Chinese Academy of Sciences,Beijing 100049,3.School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei |
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Abstract: | 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 ?, 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 ? 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. |
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Keywords: | pseudorandom sequences discrete logarithms elliptic curves character sums |
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