New Classes of Even-Variable Boolean Functions with Optimal Algebraic Immunity and Very High Nonlinearity

2013 ◽  
Vol 5 (2) ◽  
pp. 419-428
Author(s):  
Huiting Han ◽  
Chunming Tang
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
High Nonlinearity ◽  
Very High

NEW CONSTRUCTIONS OF VECTORIAL BOOLEAN FUNCTIONS WITH GOOD CRYPTOGRAPHIC PROPERTIES

2012 ◽  
Vol 23 (03) ◽  
pp. 749-760
Author(s):  
DESHUAI DONG ◽  
LONGJIANG QU ◽  
SHAOJING FU ◽  
CHAO LI
Keyword(s):  
Boolean Functions ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
High Nonlinearity ◽  
Vectorial Boolean Functions ◽  
Very High

Vectorial Boolean functions play an important role in cryptography. How to construct vectorial Boolean functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper we present several constructions of balanced vectorial Boolean functions with high algebraic immunity, high(or optimum) algebraic degree, and very high nonlinearity. In some cases, the constructed functions also achieve optimum 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.

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