Boolean Functions with Maximum Algebraic Immunity Based on Properties of Punctured Reed–Muller Codes

2016 ◽  
pp. 3-16 ◽  
Author(s):  
Konstantinos Limniotis ◽  
Nicholas Kolokotronis
Keyword(s):  
Boolean Functions ◽  
Algebraic Immunity

On Algebraic Immunity of Weight Symmetric H Boolean Functions

2014 ◽  
Vol 643 ◽  
pp. 124-129
Author(s):  
Jing Lian Huang ◽  
Zhuo Wang ◽  
Juan Li
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Theoretical Basis ◽  
Research Method ◽  
Algebraic Immunity ◽  
Correlation Immunity ◽  
Cryptographic Property ◽  
Cryptographic Primitive ◽  
New Research ◽  
The Relationship

Using the derivative of Boolean functions and the e-derivative defined by ourselves as research tools, we discuss the relationship among a variety of cryptographic properties of the weight symmetric H Boolean functions in the range of the weight with the existence of H Boolean functions. We also study algebraic immunity and correlation immunity of the weight symmetric H Boolean functions and the balanced H Boolean functions. We obtain that the weight symmetric H Boolean function should have the same algebraic immunity, correlation immunity, propagation degree and nonlinearity. Besides, we determine that there exist several kinds of H Boolean functions with resilient, algebraic immunity and optimal algebraic immunity. The above results not only provide a theoretical basis for reducing nearly half of workload when studying the cryptographic properties of H Boolean function, but also provide a new research method for the study of secure cryptographic property of Boolean functions. Such researches are important in cryptographic primitive designs.

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