New Constructions of Balanced Boolean Functions with Maximum Algebraic Immunity, High Nonlinearity and Optimal Algebraic Degree

  • Dheeraj Kumar SHARMA Department of Electronics & Communication Engineering, National Institute of Technology Kurukshetra, 136119, India
  • Rajoo PANDEY Department of Electronics & Communication Engineering, National Institute of Technology Kurukshetra, 136119, India
Keywords: Boolean function, Nonlinearity, Cyclotomic coset, Algebraic degree, Algebraic immunity

Abstract

This paper consists of proposal of two new constructions of balanced Boolean function achieving a new lower bound of nonlinearity along with high algebraic degree and optimal or highest algebraic immunity. This construction has been made by using representation of Boolean function with primitive elements. Galois Field,  used in this representation has been constructed by using powers of primitive element such that greatest common divisor of power and  is 1. The constructed balanced  variable Boolean functions achieve higher nonlinearity, algebraic degree of , and algebraic immunity of   for odd ,  for even . The nonlinearity of Boolean function obtained in the proposed constructions is better as compared to existing Boolean functions available in the literature without adversely affecting other properties such as balancedness, algebraic degree and algebraic immunity.

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Author Biographies

Dheeraj Kumar SHARMA, Department of Electronics & Communication Engineering, National Institute of Technology Kurukshetra, 136119, India

Assistant Professor, Electronics and Communication Engineering Department, National Institute of Technology Kurukshetra, India

Rajoo PANDEY, Department of Electronics & Communication Engineering, National Institute of Technology Kurukshetra, 136119, India

Professor, Electronics and Communication Engineering Department, National Institute of Technology Kurukshetra

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Published
2020-07-01
How to Cite
SHARMA, D. K., & PANDEY, R. (2020). New Constructions of Balanced Boolean Functions with Maximum Algebraic Immunity, High Nonlinearity and Optimal Algebraic Degree. Walailak Journal of Science and Technology (WJST), 17(7), 639-654. Retrieved from http://wjst.wu.ac.th/index.php/wjst/article/view/5999