On the pseudorandom properties of d-ary generalized two-prime Sidelnikov sequences

Shimeng SHEN , Huaning LIU

Front. Math. China ›› 2023, Vol. 18 ›› Issue (5) : 341 -351.

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Front. Math. China ›› 2023, Vol. 18 ›› Issue (5) : 341 -351. DOI: 10.3868/s140-DDD-023-0028-x
RESEARCH ARTICLE

On the pseudorandom properties of d-ary generalized two-prime Sidelnikov sequences

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Abstract

Let p and q be two distinct odd primes and let d=(p1,q1). In this paper, we construct d-ary generalized two-prime Sidelnikov sequences and study the autocorrelation values and linear complexity.

Keywords

Two-prime sequence / Sidelnikov sequence / character sum / autocorrelation value / linear complexity

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Shimeng SHEN, Huaning LIU. On the pseudorandom properties of d-ary generalized two-prime Sidelnikov sequences. Front. Math. China, 2023, 18(5): 341-351 DOI:10.3868/s140-DDD-023-0028-x

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References

[1]

Brandstätter N, Pirsic G. Correlation of the two-prime Sidelnikov sequence. Des Codes Cryptogr 2011; 59(1/3): 59–68

[2]

Brandstätter N, Winterhof A. Some notes on the two-prime generator of order 2. IEEE Trans Inform Theory 2005; 51(10): 3654–3657

[3]

Ding C. Pattern distributions of Legendre sequences. IEEE Trans Inform Theory 1998; 44(4): 1693–1698

[4]

Ding C, Helleseth T. On cyclotomic generator of order r. Inform Process Lett 1998; 66(1): 21–25

[5]

Ding C, Helleseth W. On the linear complexity of Legendre sequences. IEEE Trans Inform Theory 1998; 44(3): 1276–1278

[6]

Green D H, Green P R. Polyphase power-residue sequences. R Soc Lond Proc Ser A, Math Phys Eng Sci 2003; 459(2032): 817–827

[7]

Ke P H, Ye Z F, Zhou Z C, Shen J. Autocorrelation of the modified binary two-prime Sidelnikov sequence. Internat J Found Comput Sci 2017; 28(4): 391–409

[8]

Kim Y, Kim D, Song H. New M-ary sequence families with low correlation from the array structure of Sidelnikov sequences. IEEE Trans Inform Theory 2015; 61(1): 655–670

[9]

Kim Y, Song M, Kim D. . Properties and crosscorrelation of decimated Sidelnikov sequences. IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences 2014; E97.A(12): 2562–2566

[10]

Mauduit C, Sárközy A. On finite pseudorandom binary sequences I. Measure of pseudorandomness, the Legendre symbol. Acta Arith 1997; 82(4): 365–377

[11]

Mauduit C, Sárközy A. On finite pseudorandom sequences of k symbols. Indag Math (N S) 2002; 13(1): 89–101

[12]

SchmidtW M. Equations over Finite Fields, An Elementary Approach. Lecture Notes in Mathematics, Vol 536. Berlin: Springer-Verlag, 1976

[13]

Sidel'nikov V M. Some k-valued pseudo-random sequences and nearly equidistant codes. Problems Inform Transmission 1969; 5(1): 12–16

[14]

SuM. On the d-ary generalized Legendre-Sidelnikov sequence. In: Sequences and Their Applications SETA 2012. Lecture Notes in Comput Sci, Vol 7280. Heidelberg: Springer-Verlag, 2012, 233–244

[15]

Su M. On the linear complexity of Legendre-Sidelnikov sequences. Des Codes Cryptogr 2015; 74(3): 703–717

[16]

Su M, Winterhof A. Autocorrelation of Legendre-Sidelnikov sequences. IEEE Trans Inform Theory 2010; 56(4): 1714–1718

[17]

Su M. Correlation measure of order k and linear complexity profile of Legendre-Sidelnikov sequence. IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences 2012; E95.A(11): 1851–1854

[18]

TopuzogluAWinterhofA. Pseudorandom sequences. In: Topics in Geometry, Coding Theory and Cryptography. Algebr Appl, Vol 6. Dordrecht: Springer-Verlag, 2007, 135–166

[19]

WinterhofA. Linear complexity and related complexity measures. In: Selected Topics in Information and Coding Theory. Ser Coding Theory Cryptol, Vol 7. Hackensack, NJ: World Sci Publ, 2010, 3–40

[20]

Yan T J, Liu H D, Sun Y H. Autocorrelation of modified Legendre-Sidelnikov sequence. IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences 2015; E98.A(2): 771–775

[21]

Yue Z, Gao J T, Xie J. Autocorrelation of the two-prime sidelnikov sequence. Journal of Electronics & Information Technology 2013; 35(11): 2602–2607

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