scholarly journals A Lower Bound of Fast Algebraic Immunity of a Class of 1-Resilient Boolean Functions

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 90145-90151 ◽  
Author(s):  
Yindong Chen ◽  
Liu Zhang ◽  
Jianlong Xu ◽  
Weihong Cai
Keyword(s):  
Lower Bound ◽  
Boolean Functions ◽  
Algebraic Immunity

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

2020 ◽  
Vol 17 (7) ◽  
pp. 639-654
Author(s):  
Dheeraj Kumar SHARMA ◽  
Rajoo PANDEY
Keyword(s):  
Lower Bound ◽  
Boolean Function ◽  
Boolean Functions ◽  
Primitive Element ◽  
Galois Field ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
Greatest Common Divisor ◽  
Primitive Elements ◽  
High Nonlinearity

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.

CONSTRUCTING ODD VARIABLE BOOLEAN FUNCTIONS WITH OPTIMAL ALGEBRAIC IMMUNITY

2013 ◽  
Vol 24 (03) ◽  
pp. 409-417
Author(s):  
ZIRAN TU ◽  
YUPENG JIANG ◽  
XIANGYONG ZENG
Keyword(s):  
Lower Bound ◽  
Boolean Functions ◽  
Algebraic Degree ◽  
Algebraic Immunity

Based on Carlet-Feng functions, we present a method to construct odd variable Boolean functions with optimal algebraic immunity in this paper. The proposed functions can have the highest algebraic degree and a lower bound on the nonlinearity is also established.

On the Number of Balanced Even-Variable Boolean Functions with Maximum Algebraic Immunity

2011 ◽  
Vol 58-60 ◽  
pp. 1647-1650
Author(s):  
Hai Xin ◽  
Shao Jing Fu ◽  
Chao Li
Keyword(s):  
Lower Bound ◽  
Boolean Functions ◽  
Algebraic Immunity ◽  
The Third

Enumeration of Boolean functions with maximum algebraic immunity (MAI) is investigated in this paper. The even-variable Boolean functions with maximum AI were divided into 3 classes. First, we can obtain the number of the first two classes, and then we give a construction which provides large number of Boolean functions with maximum AI belong to the third classes. As a result, the lower bound on the number of balanced even-variable Boolean functions with maximum AI was improved.

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