scholarly journals OPPORTUNITIES TO MINIMIZE HARDWARE AND SOFTWARE COSTS FOR IMPLEMENTING BOOLEAN FUNCTIONS IN STREAM CIPHERS

2019 ◽  
pp. 443-452
Author(s):  
Alexandr Kuznetsov ◽  
Oleksandr Potii ◽  
Nikolay Poluyanenko ◽  
Serhii Ihnatenko ◽  
Igor Stelnyk ◽  
...  
Keyword(s):  
Boolean Functions ◽  
Linear Complexity ◽  
Random Sequence ◽  
Algebraic Degree ◽  
Main Subject ◽  
De Bruijn Sequence ◽  
De Bruijn ◽  
Design Characteristics ◽  
Sequence Characteristics ◽  
Minimal Hardware

Currently, nonlinear Boolean functions are actively investigated worldwide. However, many questions remain unanswered. The theory of nonlinear Boolean functions that are suitable for use in cryptographically strong algorithms is significantly incomplete. Despite the existence of numerous publications on these themes, many issues related to the interconnection of design characteristics affecting the generator’s performance and its cryptographic characteristics still remain unsolved. The possibility of generating a special type of sequence, called de Bruijn sequence, at minimal hardware and software costs to implement nonlinear Boolean functions in stream encryption systems, is the main subject of this work. The paper presents the possible structure boundaries (algebraic degree of a Boolean function, the number of monomials in a function) of iterative de Bruijn sequence bitrate generators for various generated sequence characteristics, such as linear complexity and autocorrelation function. The profile of the linear complexity of the studied sequences is close to the expected value of the linear complexity, as well as for a truly random sequence.

scholarly journals The discrepancy of the lex-least de Bruijn sequence

2010 ◽  
Vol 310 (6-7) ◽  
pp. 1152-1159 ◽  
Author(s):  
Joshua Cooper ◽  
Christine Heitsch
Keyword(s):  
De Bruijn Sequence ◽  
De Bruijn

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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