基于RSA模数的一类新型广义割圆序列的迹表示

doi:10.3969/j.issn.0372-2112.2019.07.015

电子学报 ›› 2019, Vol. 47 ›› Issue (7): 1512-1517.DOI: 10.3969/j.issn.0372-2112.2019.07.015

基于RSA模数的一类新型广义割圆序列的迹表示

陈智雄¹, 刘华宁², 杨阳³

1. 莆田学院福建省高校应用数学重点实验室, 福建莆田 351100;
2. 西北大学数学学院, 陕西西安 710127;
3. 福建师范大学数学与信息学院, 福建福州 350007

收稿日期:2018-05-18 修回日期:2019-03-07 出版日期:2019-07-25
- 作者简介:
- 陈智雄 男,生于1972年,福建莆田人.2006年毕业于西安电子科技大学,密码学博士.现为莆田学院教授、硕士生导师、福建省高校应用数学重点实验室主任,中国密码学会高级会员.主要研究方向为序列密码.E-mail:ptczx@126.com;刘华宁 男,生于1979年,湖南永州人.2007年毕业于西北大学,理学博士.现为西北大学教授、博士生导师.主要研究方向为伪随机数列.E-mail:hnliu@nwu.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61772292，No.11571277）; 国家自然科学基金国际合作交流项目NSFC-RFBR (No.61911530130）; 福建省自然科学基金 (No.2018J01425）; 陕西省工业科技攻关项目 (No.2016GY-077，No.2016GY-080）

Trace Representation of New Generalized Cyclotomic Sequences Based on RSA Moduli

CHEN Zhi-xiong¹, LIU Hua-ning², YANG Yang³

1. School of Mathematics and Financial, Putian University, Putian, Fujian 351100, China;
2. School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China;
3. School of Mathematics and Information, Fujian Normal University, Fuzhou, Fujian 350007, China

Received:2018-05-18 Revised:2019-03-07 Online:2019-07-25 Published:2019-07-25
- Supported by:
- National Natural Science Foundation of China (No.61772292, No.11571277); NSFC-RFBR International Coorperation and Exchange Program (No.61911530130); Natural Science Foundation of Fujian Province, China (No.2018J01425); Industrial Science and Technology Research and Development Project of Shaanxi Province (No.2016GY-077, No.2016GY-080)

摘要/Abstract

摘要： 针对最近研究的周期为pq（两个不同的大素数的乘积）的一类广义割圆序列，通过计算该序列的离散傅里叶变换系数，从而确定了该序列的Mattson-Solomon多项式，并由此得到了序列的迹表示形式.

关键词: 流密码, RSA模数, 广义割圆类, 广义割圆序列, Mattson-Solomon 多项式, 迹表示

Abstract: For a new family of generalized cyclotomic sequences of period pq, a product of two large distinct primes, we calculate the discrete Fourier transform and hence determine Mattson-Solomon polynomial, which helps us to describe the sequences via trace functions.

Key words: stream cipher, RSA moduli, generalized cyclotomy, generalized cyclotomic sequence, Mattson-Solomon polynomial, trace representation

中图分类号:

TN918.4

陈智雄, 刘华宁, 杨阳. 基于RSA模数的一类新型广义割圆序列的迹表示[J]. 电子学报, 2019, 47(7): 1512-1517.

CHEN Zhi-xiong, LIU Hua-ning, YANG Yang . Trace Representation of New Generalized Cyclotomic Sequences Based on RSA Moduli[J]. Acta Electronica Sinica, 2019, 47(7): 1512-1517.

参考文献

[1] Graham S,Shparlinski I.On RSA moduli with almost half of the bits prescribed[J].Discrete Applied Mathematics,2008,156(16):3150-3154.
[2] Shparlinski I.On the uniformity of distribution of the RSA pairs[J].Mathematics of Computation,2001,70(234):801-808.
[3] Shparlinski I.On RSA moduli with prescribed bit patterns[J].Designs,Codes and Cryptography,2006,39(1):113-122.
[4] Whiteman A.A family of difference sets[J].Illinois Journal of Mathematics,1962,6:107-121.
[5] Bai E,Fu X,Xiao G.On the linear complexity of generalized cyclotomic sequences of order four over Z_pq[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2005,88:392-395.
[6] Bai E,Liu X,Xiao G.Linear complexity of new generalized cyclotomic sequences of order two of length pq[J].IEEE Transactions on Information Theory,2005,51:1849-1853.
[7] 常祖领,周玉倩,柯品惠.一类新的pqr长2阶广义分圆序列的线性复杂度[J].电子学报,2015,43(1):166-170. Chang Zuling,Zhou Yuqian,Ke Pinhui.Linear complexity of new generalized cyclotomic sequences of order two and length pqr[J].Acta Electronica Sinica,2015,43(1):166-170.(in Chinese)
[8] Ding C.Linear complexity of generalized cyclotomic binary sequences of order 2[J].Finite Fields and Their Applications,1997,3:159-174.
[9] Ding C.Autocorrelation values of generalized cyclotomic sequences of order two[J].IEEE Transactions on Information Theory,1998,44:1699-1702.
[10] Ding C.Cyclotomic constructions of cyclic codes with length being the product of two primes[J].IEEE Transactions on Information Theory,2012,58(4):2231-2236.
[11] Du X,Yan T,Xiao G.Trace representation of some generalized cyclotomic sequences of length pq[J].Information Sciences,2008,178(16):3307-3316.
[12] 柯品惠,李瑞芳,张胜元.一类新的周期为p^m+1qⁿ⁺¹的二元广义分圆序列的线性复杂度[J].电子学报,2014,42(5):1009-1013. Ke Pinhui,Li Ruifang,Zhang Shengyuan.The linear complexity of a new class of generalized cyclotomic binary sequences of length p^m+1qⁿ⁺¹[J].Acta Electronica Sinica,2014,42(5):1009-1013.(in Chinese)
[13] Li S,Chen Z,Sun R,et al.On the randomness of generalized cyclotomic sequences of order two and length pq[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2007,E90-A:2037-2041.
[14] 刘华宁,陈晓林.一类新的广义割圆序列的线性复杂度及其自相关值[J].数学学报,2019,62(2):233-246. Liu Huaning,Chen Xiaolin.Autocorrelation values and linear complexity of new generalized cyclotomic sequences[J].Acta Mathematica Sinica Chinese Series,2019,62(2):233-246.(in Chinese)
[15] 刘龙飞,杨凯,杨晓元.新的周期为p^m的GF(h)上广义割圆序列的线性复杂度[J].通信学报,2017,38(9):39-45. Liu Longfei,Yang Kai,Yang Xiaoyuan.On the linear complexity of a new generalized cyclotomic sequence with length p^m over GF(h)[J].Journal on Communications,2017,38(9):39-45.(in Chinese)
[16] Qi M,Xiong S,Yuan J,et al.Trace representation over F_r of binary Jacobi sequences with period pq[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2015,98-A(3):912-917.
[17] Yan T,Du X,Xiao G,et al.Linear complexity of binary Whiteman generalized cyclotomic sequences of order 2^k[J].Information Sciences,2009,179(7):1019-1023.
[18] Hu L,Yue Q.Autocorrelation value of Whiteman generalized cyclotomic sequence[J].Journal of Mathematical Research with Applications,2012,32(4):415-422.
[19] Hu L,Yue Q,Wang M.The linear complexity of Whiteman's generalized cyclotomic sequences of period p^m+1qⁿ⁺¹[J].IEEE Transactions on Information Theory,2012,58(8):5534-5543.
[20] Dai Z,Gong G,Song H.A trace representation of binary Jacobi sequences[J].Discrete Mathematics,2009,309(6):1517-1527.
[21] 杜小妮,李芝霞,万韫琦,李晓丹.基于费马商的r元序列的迹表示[J].电子学报,2017,45(10):2439-2442. Du Xiaoni,Li Zhixia,Wan Yunqi,et al.Trace representation of r-ary sequences derived from Fermat quotients[J].Acta Electronica Sinica,2017,45(10):2439-2442.(in Chinese)
[22] Blahut R.Transform techniques for error control codes[J].IBM Journal of Research and Development,1979,23(3):299-315.
[23] Chen Z.Trace representation and linear complexity of binary sequences derived from Fermat quotients[J].SCIENCE CHINA Information Sciences,2014,57(11):1-10.
[24] Chen Z.Linear complexity and trace representation of quaternary sequences over Z ₄ based on generalized cyclotomic classes modulo pq[J].Cryptography and Communications,2017,9(4):445-458.
[25] Chen Z,Du X,Marzouk R.Trace representation of pseudorandom binary sequences derived from Euler quotients[J].Applicable Algebra in Engineering,Communication and Computing,2015,26(6):555-570.
[26] Dai Z,Gong G,Song H,et al.Trace representation and linear complexity of binary e-th power residue sequences of period p[J].IEEE Transactions Information Theory,2011,57(3):1530-1547.
[27] Du X,Chen Z.Trace representation of binary generalized cyclotomic sequences with length p^m[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2011,94-A(2):761-765.
[28] Du X,Chen Z,Shi A,et al.Trace representation of a new class of sextic residue sequences of period p=3(mod8)[J].IEICE Transactions,2009,92-A(2):668-670.
[29] Helleseth T,Kim S,No J.Linear complexity over F_p and trace representation of Lempel-Cohn-Eastman sequences[J].IEEE Transactions Information Theory,2003,49(6):1548-1552.
[30] Kim J,Song H.Trace representation of Legendre sequences[J].Designs,Codes and Cryptography,2001,24(3):343-348.
[31] No J,Lee H,Chung H,et al.Trace representation of Legendre sequences of Mersenne prime period[J].IEEE Transactions Information Theory,1996,42(6):2254-2255.
[32] Qi M,Xiong S,Yuan J,et al.A simpler trace representation of Legendre sequences[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2015,98-A(4):1026-1031.

基于RSA模数的一类新型广义割圆序列的迹表示

Trace Representation of New Generalized Cyclotomic Sequences Based on RSA Moduli

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