| 单圈 T-函数的 2-adic 复杂度和 1-错 2-adic 复杂度 |
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| 引用本文： | 游伟,戚文峰.单圈 T-函数的 2-adic 复杂度和 1-错 2-adic 复杂度[J].通信学报,2014,35(3):15-139. |
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| 作者姓名： | 游伟 戚文峰 |
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| 作者单位： | 1. 国家数字交换系统工程技术研究中心，河南 郑州 450002；2. 解放军信息工程大学 四院，河南 郑州 450002；
3. 解放军信息工程大学 数学工程与先进计算国家重点实验室，河南 郑州 450002 |
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| 基金项目： | 国家自然科学基金资助项目(61070178) |
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| 摘 要： | 研究了由 上单圈T-函数所导出权位序列的2-adic复杂度，设 为整数， 。结论表明，第 权位序列2-adic复杂度的上界为 。另外，讨论了与所有单圈 T-函数所导出第 权位序列相对应的2-adic整数的分布，分布情况说明这个上界是可以达到的。最后，研究了权位序列的1-错2-adic复杂度。研究结果表明对所有 ，权位序列 的1-错2-adic 复杂度都与其2-adic复杂度相同。
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| 关 键 词： | 序列密码 2-adic复杂度 -错2-adic复杂度 单圈T-函数 权位序列 |
The 2-adic complexity and the 1-error 2-adic
complexity of single cycle T-functions |
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| Wei YOU,Wen-feng QI.The 2-adic complexity and the 1-error 2-adic
complexity of single cycle T-functions[J].Journal on Communications,2014,35(3):15-139. |
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| Authors: | Wei YOU Wen-feng QI |
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| Affiliation: | 1. National Digital Switching System Engineering ＆ Technological Research Center,Zhengzhou 450002,China;2. Fourth Institute,PLA Information Engineering University,Zhengzhou 450002,China;3. State Key Laboratory of Mathematical Engineering and Advanced Computing,PLA Information Engineering University,Zhengzhou 450002,China |
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| Abstract: | The 2-adic complexities of the coordinate sequences derived from single cycle T-functions over were investigated. Let be an integer such that . It is shown that the 2-adic complexity of the th coordinate sequence is upper bounded by . The distribution of the corresponding 2-adic number associated with the th coordinate sequence of all single cycle T-functions was also discussed, which implies that the upper bound is attainable. Moreover, 1-error 2-adic complexity was also studied. It was proved that the 1-error 2-adic complexity of the th coordinate sequence is equal to its 2-adic complexity except for . |
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| Keywords: | stream cipher 2-adic complexity -error 2-adic complexity single cycle T-functions coordinate sequences |
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