Balancedness and Correlation Immunity of Symmetric Boolean Functions

2003 ◽  
Vol 15 ◽  
pp. 176-181 ◽  
Author(s):  
Palash Sarkar ◽  
Subhamoy Maitra
Keyword(s):  
Boolean Functions ◽  
Symmetric Boolean Functions ◽  
Correlation Immunity

Algebraic Immunity, Correlation Immunity and other Cryptographic Properties of Quadratic Rotation Symmetric Boolean Functions

2014 ◽  
Vol 989-994 ◽  
pp. 2593-2598
Author(s):  
Jing Lian Huang ◽  
Zhuo Wang ◽  
Mei Rong He
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity ◽  
Rotation Symmetry ◽  
Symmetric Boolean Functions ◽  
Application Range ◽  
Correlation Immunity ◽  
Cryptographic Primitive ◽  
Rotation Symmetric ◽  
The Relationship ◽  
Rotation Symmetric Boolean Functions

Boolean functions with a variety of secure cipher properties are the key factors to design cryptosystem with the ability to resist multiple cipher attacks and good safety performance. In this paper, using the derivative of the Boolean functions and the e-derivative defined by ourselves as the main research tools, we study algebraic immunity, correlation immunity and other cryptographic properties of the quadratic rotation symmetric Boolean functions. We determine the quadratic rotation symmetric Boolean functions which are H Boolean functions, and the range of weight distribution of the quadratic rotation symmetry H Boolean functions. Besides, we get the compatibility among propagation, balance, correlation immunity and algebraic immunity of the quadratic rotation symmetry H Boolean functions, and also focus on the relationship of balance, correlation immunity and dimension. Furthermore, we check the existence of the cubic rotation symmetry H Boolean functions, and obtain the relationship between existence and dimension of the cubic rotation symmetry H Boolean functions. Moreover, we obtain a more convenient method for solving annihilator. Such researches are important in cryptographic primitive designs, and have significance and role in the theory and application range of cryptosystems.

Algorithms of Constructing Symmetric Boolean Functions with Second-Order Correlation-Immunity

2013 ◽  
Vol 411-414 ◽  
pp. 67-71
Author(s):  
Cao Hao ◽  
Shi Min Wei ◽  
Hui Ge Wang
Keyword(s):  
Boolean Functions ◽  
Second Order ◽  
Symmetric Boolean Functions ◽  
Binary Field ◽  
Correlation Immunity ◽  
Equivalent Equation

Constructing n-variable symmetric Boolean Functions with Second-Order Correlation-Immunity is equivalent to solving the equation in the binary field. By discussing the relationships between the solutions of the equation, and using the characteristics of the equation and its equivalent equation, algorithms of constructing symmetric Boolean Functions with Second-Order Correlation-Immunity is proposed.

On 1-stable perfectly balanced Boolean functions

2017 ◽  
Vol 27 (2) ◽  
Author(s):  
Stanislav V. Smyshlyaev
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
The Other ◽  
Correlation Immunity ◽  
Other Hand

AbstractThe paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the 1-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is 1-stable.

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