Relation between the Irreducible Polynomials that Generates the Same Binary Sequence Over Odd Characteristic Field

Md. Arshad Ali; Yuta Kodera; Taehwan Park; Takuya Kusaka; Yasuyuki Nogmi; Howon Kim

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자료유형: 학술저널

저자정보: Md. Arshad Ali (Okayama University) Yuta Kodera (Okayama University) Taehwan Park (Pusan National University) Takuya Kusaka (Okayama University) Yasuyuki Nogmi (Okayama University) Howon Kim (Pusan National University)

저널정보: 한국정보통신학회JICCE Journal of information and communication convergence engineering Journal of information and communication convergence engineering Vol.16 No.3

발행연도: 2018.9

수록면: 166 - 172 (7page)

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A pseudo-random sequence generated by using a primitive polynomial, trace function, and Legendre symbol has been researched in our previous work. Our previous sequence has some interesting features such as period, autocorrelation, and linear complexity. A pseudo-random sequence widely used in cryptography. However, from the aspect of the practical use in cryptographic systems sequence needs to generate swiftly. Our previous sequence generated by utilizing a primitive polynomial, however, finding a primitive polynomial requires high calculating cost when the degree or the characteristic is large. It’s a shortcoming of our previous work. The main contribution of this work is to find some relation between the generated sequence and irreducible polynomials. The purpose of this relationship is to generate the same sequence without utilizing a primitive polynomial. From the experimental observation, it is found that there are (p − 1) ⁄ 2 kinds of polynomial, which generates the same sequence. In addition, some of these polynomials are non-primitive polynomial. In this paper, these relationships between the sequence and the polynomials are shown by some examples. Furthermore, these relationships are proven theoretically also.

#Irreducible polynomial #Legendre symbol #Odd characteristic field #Pseudo-random sequence #Trace function

참고문헌 (10)

참고문헌 신청

[단행본] - T. W. Cusick / 1998 / Stream Ciphers and Number Theory / Elsevier

[단행본] - S. W. Golomb / 1967 / Shift Register Sequences / Holden-Day

[단행본] - S. W. Golomb / 2005 / Sequence Design for Good Correlation / Cambridge University Press

[단행본] - A. J. Menezes / 1996 / Handbook of Applied Cryptography / CRC Press

[학술지(정기간행물)] - N. Zierler / 1959 / Linear recurring sequences / Journal of the Society for Industrial and Applied Mathematics 7 (1) : 31 ~ 48

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