Some Permutation Trinomials over Finite Fields F22m

Jump To References Section

Authors

  • P. L. Sharma
     Department of Mathematics & Statistics, H. P. University, Shimla ,IN
  • Mansi Harish
     Department of Mathematics & Statistics, H. P. University, Shimla ,IN
  • Sushil Kumar
     Department of Mathematics & Statistics, H. P. University, Shimla ,IN

DOI:

https://doi.org/10.18311/jims/2024/32894

Keywords:

Finite Fields, Permutation Polynomials, Permutation Trinomials, Trace Function.

Abstract

Permutation trinomials play an important role in various fields such as finite geometry, combinatorial design and cryptography. Here, we present the constructions of some new classes of permutation trinomials of the form xrh(x 2m−1 ) over the finite field F22m using the permutation of the unit circle µ2m+1.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2024-07-01

How to Cite

Sharma, P. L., Harish, M., & Kumar, S. (2024). Some Permutation Trinomials over Finite Fields F<sub>2</sub><sup>2m</sup>. The Journal of the Indian Mathematical Society, 91(3-4), 470–477. https://doi.org/10.18311/jims/2024/32894

Issue

Volume 91, Issue 3-4, July-December 2024

Section

Articles

License

Copyright (c) 2024 P. L. Sharma, Mansi Harish, Sushil Kumar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC
Received 2023-02-03
Accepted 2023-07-19
Published 2024-07-01

 

References

S. Ball and M. Zieve, Sympectic spreads and permutation polynomials, Finite Fields Appl., Lect. Notes Comput. Sci., 2948 (2004), 79 - 88.

W. Cherowitzo, α-Flocks and hyperovals, Geom. Dedic., 72 (1998), 221 - 246.

C. Ding, L. Qu, Q. Wang, J. Yuan and P. Yuan, Permutation trinomials over finite fields with even characteristic, SIAM J. Discrete Math., 29 (2015), 79 - 92.

H. Dobbertin, Almost perfect nonlinear power functions on GF(2n): the Welch case, IEEE Trans. Inf. Theory, 45 (1999), 1271 - 1275.

R. Gupta, P. Gahlyan and R. K. Sharma, New classes of permutation trinomials over Fq3, Finite Fields Appl., 84, Art. No. 102110, (2022), 21 pages.

R. Gupta and R. K. Sharma, Some new classes of permutation trinomials over finite field with even characteristic, Finite Fields Appl., 41 (2016), 89 - 96.

H. D. L. Hollmann and Q. Xiang, A proof of the Welch and Niho conjectures on cross-correlations of binary m-sequences, Finite Fields Appl., 7 (2001), 253 - 286.

X. Hou, Determination of a type of permutation trinomials over finite fields, II, Finite Fields Appl., 35 (2015), 16 - 35.

X. Hou, Permutation polynomials over finite fields – a survey of recent advances, Finite Fields Appl., 32 (2015), 82 - 119.

X. Hou and V. Pallozzi Lavorante, A general construction of permutation polynomials of Fq2, Finite Fields Appl., 89, Art. No. 102193, (2023), 30 pages.

J. B. Lee and Y. H. Park, Some permutation trinomials over finite fields, Acta Math. Sci., 17 (1997), 250 - 254.

N. Li and T. Helleseth, Several classes of permutation trinomials from Niho exponents, Cryptogr. Commun., 9 (2017), 693 - 705.

K. Li, L. Qu and X. Chen, New classes of permutation binomials and permutation trinomials over finite fields, Finite Fields Appl., 43 (2017), 69 - 85.

K. Li, L. Qu, C. Li and S. Fu, New permutation trinomials constructed from fractional polynomials, Acta Arithmetica, 183 (2018), 101 - 116.

R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Application, Addision-Wesley, Reading, MA. 20 1983.

G. L. Mullen and D. Panario, Handbook of Finite Fields, Taylor & Francis, Boca Raton, 2013.

A. Rai and R. Gupta, Further results on a class of permutation trinomials, Cryptogr. Commun., https://doi.org/10.1007/s12095-023-00640-8.

P. L. Sharma, S. Kumar, Ashima and N. Dhiman, On permutation polynomials modulo 7n, J. Discret. Math. Sci. Cryptogr., (Accepted for publication).

X. Xie, N. Li, L. Xu, X. Zeng and X. Tang, Two new classes of permutation trinomials over Fq3 with odd characteristic, https://ia.cr/2022/485.

D. Wan and R. Lidl, Permutation polynomials of the form xrh(x(q−1)/d) and their group structure, Monatshefte Math., 31 (1991), 12 - 24.

D. Wu, P. Yuan, C. Ding and Y. Ma, Permutation trinomials over F2m: a corrected version, DOI:10.48550/arXiv.2209.04762.

Z. Zha, L. Hu and S. Fan, Further results on permutation trinomials over finite fields with even characteristic, Finite Fields Appl., 45 (2017), 43 - 52.

M. E. Zieve, Some families of permutation polynomials over finite fields, Int. J. Number Theory, 4 (2008), 851 - 857.