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Algebraic methods in difference sets and bent functions

Year 2021, Volume: 8 Issue: 2, 139 - 148, 20.05.2021
https://doi.org/10.13069/jacodesmath.940192

Abstract

We provide some applications of a polynomial criterion for difference sets. These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions. We also consider the question about the bentness of certain Boolean functions introduced by Carlet when the $\mathcal{C}$-condition introduced by him doesn't hold.

References

  • [1] T. Becker, V. Weispfennig, Groebner bases a computational approach to commutative algebra, Springer (1993).
  • [2] C. Carlet, Two new classes of bent functions, Advances in Cryptology-EUROCRYPT’93, LNCS vol 765 (Ed. T. Hellseth) Springer-Verlag (1994) 77–101.
  • [3] D. Cox, J. Little, D. O’Shea, Ideals, varieties and algorithms, Springer Verlag, New York Inc (2007).
  • [4] J. F. Dillon, Elementary hadamard difference sets, Ph. D. Thesis, University of Maryland (1974).
  • [5] P. H. Keskar, P. Kumari, Polynomial criterion for abelian difference sets, Indian Journal of Pure and Applied Mathematics 51(1) (2020) 233–249.
  • [6] N. Kolomeec, The graph of minimal distances of bent functions and its properties, Designs, Codes and Cryptography 85 (2017) 395–410.
  • [7] B. Mandal, P. Stanica, S. Gangopadhyay, E. Pasalic, An analysis of the C class of bent functions, Fundamenta Informaticae 146(3) (2016) 271–292.
  • [8] E. H. Moore, H. S. Pollatsek, Difference sets, connecting algebra, combinatorics, and geometry, american mathematical society (2013).
  • [9] N.Tokareva, Bent functions: Results and applications to cryptography, Elsevier (2015).
  • [10] A. van den Essen, Polynomial automorphisms and the jacobian conjecture, Birkhauser (2000).
Year 2021, Volume: 8 Issue: 2, 139 - 148, 20.05.2021
https://doi.org/10.13069/jacodesmath.940192

Abstract

References

  • [1] T. Becker, V. Weispfennig, Groebner bases a computational approach to commutative algebra, Springer (1993).
  • [2] C. Carlet, Two new classes of bent functions, Advances in Cryptology-EUROCRYPT’93, LNCS vol 765 (Ed. T. Hellseth) Springer-Verlag (1994) 77–101.
  • [3] D. Cox, J. Little, D. O’Shea, Ideals, varieties and algorithms, Springer Verlag, New York Inc (2007).
  • [4] J. F. Dillon, Elementary hadamard difference sets, Ph. D. Thesis, University of Maryland (1974).
  • [5] P. H. Keskar, P. Kumari, Polynomial criterion for abelian difference sets, Indian Journal of Pure and Applied Mathematics 51(1) (2020) 233–249.
  • [6] N. Kolomeec, The graph of minimal distances of bent functions and its properties, Designs, Codes and Cryptography 85 (2017) 395–410.
  • [7] B. Mandal, P. Stanica, S. Gangopadhyay, E. Pasalic, An analysis of the C class of bent functions, Fundamenta Informaticae 146(3) (2016) 271–292.
  • [8] E. H. Moore, H. S. Pollatsek, Difference sets, connecting algebra, combinatorics, and geometry, american mathematical society (2013).
  • [9] N.Tokareva, Bent functions: Results and applications to cryptography, Elsevier (2015).
  • [10] A. van den Essen, Polynomial automorphisms and the jacobian conjecture, Birkhauser (2000).
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Pradipkumar H. Keskar This is me 0000-0001-5463-4189

Priyanka Kumari This is me

Publication Date May 20, 2021
Published in Issue Year 2021 Volume: 8 Issue: 2

Cite

APA Keskar, P. H., & Kumari, P. (2021). Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(2), 139-148. https://doi.org/10.13069/jacodesmath.940192
AMA Keskar PH, Kumari P. Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications. May 2021;8(2):139-148. doi:10.13069/jacodesmath.940192
Chicago Keskar, Pradipkumar H., and Priyanka Kumari. “Algebraic Methods in Difference Sets and Bent Functions”. Journal of Algebra Combinatorics Discrete Structures and Applications 8, no. 2 (May 2021): 139-48. https://doi.org/10.13069/jacodesmath.940192.
EndNote Keskar PH, Kumari P (May 1, 2021) Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications 8 2 139–148.
IEEE P. H. Keskar and P. Kumari, “Algebraic methods in difference sets and bent functions”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 2, pp. 139–148, 2021, doi: 10.13069/jacodesmath.940192.
ISNAD Keskar, Pradipkumar H. - Kumari, Priyanka. “Algebraic Methods in Difference Sets and Bent Functions”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/2 (May 2021), 139-148. https://doi.org/10.13069/jacodesmath.940192.
JAMA Keskar PH, Kumari P. Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:139–148.
MLA Keskar, Pradipkumar H. and Priyanka Kumari. “Algebraic Methods in Difference Sets and Bent Functions”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 2, 2021, pp. 139-48, doi:10.13069/jacodesmath.940192.
Vancouver Keskar PH, Kumari P. Algebraic methods in difference sets and bent functions. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(2):139-48.