Figure 1.
An Architecture of the WG-NLFSR
-
Previous Article
Repeated-root constacyclic codes of length $ 6lp^s $
- AMC Home
- This Issue
-
Next Article
The values of two classes of Gaussian periods in index 2 case and weight distributions of linear codes
February
2021, 15(1): 155-165.
doi: 10.3934/amc.2020050
Some properties of the cycle decomposition of WG-NLFSR
| a. | Science and Technology on Information Assurance Laboratory, Beijing, China |
| b. | Data Communication Science and Technology Research Institute, Beijing, China |
In this paper, we give some properties of the cycle decomposition of a nonlinear feedback shift register called WG-NLFSR which was presented by Mandal and Gong recently. First we give the parity of the state transition transformation of WG-NLFSR and then by the relation of the parity of a permutation and its number of cycles given in Theorem 2 in Section 1, we show that the number of cycles in the cycle decomposition of WG-NLFSR is even. Second we study the properties of the cycle decomposition of WG-NLFSR when the coefficients of the characteristic polynomial belong to the proper subfields of the finite field on which the WG-NLFSR is defined. Finally, we give some properties of the cycle decomposition of the filtering WG7-NLFSR.
Mathematics Subject Classification:
94A55, 94A60.
Citation:
Yujuan Li, Huaifu Wang, Peipei Zhou, Guoshuang Zhang. Some properties of the cycle decomposition of WG-NLFSR. Advances in Mathematics of Communications,
2021, 15
(1)
: 155-165.
doi: 10.3934/amc.2020050
![]()
References:
| [1] |
P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, 2nd Edition, Cambridge University Press, Cambridge, 1994.
doi: 10.1017/CBO9781139174237.
|
| [2] |
U. Cheng,
On the cycle structure of certain classes of nonlinear shift registers, Journal of Combinatorial Theory, 37 (1984), 61-68.
doi: 10.1016/0097-3165(84)90019-0. |
| [3] |
H. Dobbertin,
Kasami power functions, permutation polynomials and cyclic difference sets, Difference Sets, Sequences and Their Correlation Properties (Bad Windsheim, 1998), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht, 542 (1999), 133-158.
|
| [4] |
S. W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, Calif.-Cambridge-Amsterdam, 1967. |
| [5] |
G. Gong and A. M. Youssef,
Cryptographic properties of the Welch-Gong transformation sequence generators, IEEE Transactions on Information Theory, 48 (2002), 2837-2846.
doi: 10.1109/TIT.2002.804043. |
| [6] |
T. Helleseth,
Nonlinear shift registers - A survey and challenges, Algebraic Curves and Finite Fields, Radon Ser. Comput. Appl. Math., De Gruyter, Berlin, 16 (2014), 121-144.
|
| [7] |
K. Kjeldsen,
On the cycle structure of a set of nonlinear shift registers with symmetric feedback functions, Journal of Combinatorial Theory Ser. A, 20 (1976), 154-169.
doi: 10.1016/0097-3165(76)90013-3. |
| [8] |
K. Mandal and G. Gong,
Filtering nonlinear feedback shift registers using Welch-Gong transformations for securing RFID applications, ICST Trans. Security Safety, 3 (2016), e3.
|
| [9] |
J. Mykkeltveit, M. K. Siu and P. Tong,
On the cycle structure of some nonlinear shift register sequences, Information and Control, 43 (1979), 202-215.
doi: 10.1016/S0019-9958(79)90708-3. |
| [10] |
Z. X. Wan and Z. D. Dai, Nonlinear Feedback Shift Registers, Science Press, Beijing, 1975.
|
show all references
References:
| [1] |
P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, 2nd Edition, Cambridge University Press, Cambridge, 1994.
doi: 10.1017/CBO9781139174237.
|
| [2] |
U. Cheng,
On the cycle structure of certain classes of nonlinear shift registers, Journal of Combinatorial Theory, 37 (1984), 61-68.
doi: 10.1016/0097-3165(84)90019-0. |
| [3] |
H. Dobbertin,
Kasami power functions, permutation polynomials and cyclic difference sets, Difference Sets, Sequences and Their Correlation Properties (Bad Windsheim, 1998), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht, 542 (1999), 133-158.
|
| [4] |
S. W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, Calif.-Cambridge-Amsterdam, 1967. |
| [5] |
G. Gong and A. M. Youssef,
Cryptographic properties of the Welch-Gong transformation sequence generators, IEEE Transactions on Information Theory, 48 (2002), 2837-2846.
doi: 10.1109/TIT.2002.804043. |
| [6] |
T. Helleseth,
Nonlinear shift registers - A survey and challenges, Algebraic Curves and Finite Fields, Radon Ser. Comput. Appl. Math., De Gruyter, Berlin, 16 (2014), 121-144.
|
| [7] |
K. Kjeldsen,
On the cycle structure of a set of nonlinear shift registers with symmetric feedback functions, Journal of Combinatorial Theory Ser. A, 20 (1976), 154-169.
doi: 10.1016/0097-3165(76)90013-3. |
| [8] |
K. Mandal and G. Gong,
Filtering nonlinear feedback shift registers using Welch-Gong transformations for securing RFID applications, ICST Trans. Security Safety, 3 (2016), e3.
|
| [9] |
J. Mykkeltveit, M. K. Siu and P. Tong,
On the cycle structure of some nonlinear shift register sequences, Information and Control, 43 (1979), 202-215.
doi: 10.1016/S0019-9958(79)90708-3. |
| [10] |
Z. X. Wan and Z. D. Dai, Nonlinear Feedback Shift Registers, Science Press, Beijing, 1975.
|
| [1] |
Amin Sakzad, Mohammad-Reza Sadeghi, Daniel Panario. Cycle structure of permutation functions over finite fields and their applications. Advances in Mathematics of Communications, 2012, 6 (3) : 347-361. doi: 10.3934/amc.2012.6.347 |
| [2] |
Nataša Djurdjevac Conrad, Ralf Banisch, Christof Schütte. Modularity of directed networks: Cycle decomposition approach. Journal of Computational Dynamics, 2015, 2 (1) : 1-24. doi: 10.3934/jcd.2015.2.1 |
| [3] |
Stefano Barbero, Emanuele Bellini, Rusydi H. Makarim. Rotational analysis of ChaCha permutation. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021057 |
| [4] |
Washiela Fish, Jennifer D. Key, Eric Mwambene. Partial permutation decoding for simplex codes. Advances in Mathematics of Communications, 2012, 6 (4) : 505-516. doi: 10.3934/amc.2012.6.505 |
| [5] |
Dmitry N. Kozlov. Cobounding odd cycle colorings. Electronic Research Announcements, 2006, 12: 53-55. |
| [6] |
Nian Li, Qiaoyu Hu. A conjecture on permutation trinomials over finite fields of characteristic two. Advances in Mathematics of Communications, 2019, 13 (3) : 505-512. doi: 10.3934/amc.2019031 |
| [7] |
Ethel Mokotoff. Algorithms for bicriteria minimization in the permutation flow shop scheduling problem. Journal of Industrial and Management Optimization, 2011, 7 (1) : 253-282. doi: 10.3934/jimo.2011.7.253 |
| [8] |
Ricardo P. Beausoleil, Rodolfo A. Montejo. A study with neighborhood searches to deal with multiobjective unconstrained permutation problems. Journal of Industrial and Management Optimization, 2009, 5 (2) : 193-216. doi: 10.3934/jimo.2009.5.193 |
| [9] |
Xiang Wang, Wenjuan Yin. New nonexistence results on perfect permutation codes under the hamming metric. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021058 |
| [10] |
Hotaka Udagawa, Taiji Okano, Toshimichi Saito. Permutation binary neural networks: Analysis of periodic orbits and its applications. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022097 |
| [11] |
Xiu Ye, Shangyou Zhang. A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh. Electronic Research Archive, 2021, 29 (6) : 3609-3627. doi: 10.3934/era.2021053 |
| [12] |
Claudio Qureshi, Daniel Panario, Rodrigo Martins. Cycle structure of iterating Redei functions. Advances in Mathematics of Communications, 2017, 11 (2) : 397-407. doi: 10.3934/amc.2017034 |
| [13] |
Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems and Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035 |
| [14] |
Stefano Bianchini, Daniela Tonon. A decomposition theorem for $BV$ functions. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1549-1566. doi: 10.3934/cpaa.2011.10.1549 |
| [15] |
Ben Niu, Weihua Jiang. Dynamics of a limit cycle oscillator with extended delay feedback. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1439-1458. doi: 10.3934/dcdsb.2013.18.1439 |
| [16] |
Valery A. Gaiko. The geometry of limit cycle bifurcations in polynomial dynamical systems. Conference Publications, 2011, 2011 (Special) : 447-456. doi: 10.3934/proc.2011.2011.447 |
| [17] |
Zhiqin Qiao, Deming Zhu, Qiuying Lu. Bifurcation of a heterodimensional cycle with weak inclination flip. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 1009-1025. doi: 10.3934/dcdsb.2012.17.1009 |
| [18] |
Yu-Hsien Chang, Guo-Chin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure and Applied Analysis, 2006, 5 (4) : 779-792. doi: 10.3934/cpaa.2006.5.779 |
| [19] |
Domingo Gomez-Perez, Ana-Isabel Gomez, Andrew Tirkel. Arrays composed from the extended rational cycle. Advances in Mathematics of Communications, 2017, 11 (2) : 313-327. doi: 10.3934/amc.2017024 |
| [20] |
Qigang Yuan, Yutong Sun, Jingli Ren. How interest rate influences a business cycle model. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3231-3251. doi: 10.3934/dcdss.2020190 |
2021 Impact Factor: 1.015
Tools
Metrics
Other articles
by authors
[Back to Top]