Designing correlation immune boolean functions with minimal hamming weight using various genetic programming methods

2019 ◽  
Author(s):  
Jakub Husa
Keyword(s):  
Genetic Programming ◽  
Boolean Functions ◽  
Hamming Weight

scholarly journals Evolutionary Algorithms for Boolean Functions in Diverse Domains of Cryptography

2016 ◽  
Vol 24 (4) ◽  
pp. 667-694 ◽  
Author(s):  
Stjepan Picek ◽  
Claude Carlet ◽  
Sylvain Guilley ◽  
Julian F. Miller ◽  
Domagoj Jakobovic
Keyword(s):  
Evolutionary Algorithms ◽  
Genetic Programming ◽  
Evolutionary Computation ◽  
Boolean Functions ◽  
Coding Theory ◽  
Design Criteria ◽  
Hamming Weight ◽  
High Quality ◽  
Distinct Role

The role of Boolean functions is prominent in several areas including cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged over the years. There are still many combinations of design criteria left unexplored and in this matter evolutionary computation can play a distinct role. This article concentrates on two scenarios for the use of Boolean functions in cryptography. The first uses Boolean functions as the source of the nonlinearity in filter and combiner generators. Although relatively well explored using evolutionary algorithms, it still presents an interesting goal in terms of the practical sizes of Boolean functions. The second scenario appeared rather recently where the objective is to find Boolean functions that have various orders of the correlation immunity and minimal Hamming weight. In both these scenarios we see that evolutionary algorithms are able to find high-quality solutions where genetic programming performs the best.

scholarly journals On the confusion coefficient of Boolean functions

2021 ◽  
Vol 16 (1) ◽  
pp. 1-13
Author(s):  
Yu Zhou ◽  
Jianyong Hu ◽  
Xudong Miao ◽  
Yu Han ◽  
Fuzhong Zhang
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Power Analysis ◽  
Signal To Noise Ratio ◽  
Sum Of Squares ◽  
Hamming Weight ◽  
Signal To Noise ◽  
Trade Offs ◽  
Cryptographic Algorithms ◽  
Transparency Order

Abstract The notion of the confusion coefficient is a property that attempts to characterize confusion property of cryptographic algorithms against differential power analysis. In this article, we establish a relationship between the confusion coefficient and the autocorrelation function for any Boolean function and give a tight upper bound and a tight lower bound on the confusion coefficient for any (balanced) Boolean function. We also deduce some deep relationships between the sum-of-squares of the confusion coefficient and other cryptographic indicators (the sum-of-squares indicator, hamming weight, algebraic immunity and correlation immunity), respectively. Moreover, we obtain some trade-offs among the sum-of-squares of the confusion coefficient, the signal-to-noise ratio and the redefined transparency order for a Boolean function.

Effects of the Internal Structure of H Boolean Functions on Algebraic Immunity and Algebraic Degree

2013 ◽  
Vol 774-776 ◽  
pp. 1721-1724
Author(s):  
Jing Lian Huang ◽  
Xiu Juan Yuan ◽  
Jian Hua Wang
Keyword(s):  
Boolean Function ◽  
Internal Structure ◽  
Boolean Functions ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
Hamming Weight ◽  
Relationship Of ◽  
The Relationship

We go deep into the internal structure of the Boolean functions values, and study the relationship of algebraic immunity and algebraic degree of Boolean functions with the Hamming weight with the diffusion included. Then we get some theorems which relevance together algebraic immunity, annihilators and algebraic degree of H Boolean functions by the e-derivative which is a part of the H Boolean function. Besides, we also get the results that algebraic immunity and algebraic degree of Boolean functions can be linked together by the e-derivative of H Boolean functions and so on.

Relationship between Correlation Immune Order and Algebraic Immunity Order of Boolean Functions

2013 ◽  
Vol 740 ◽  
pp. 273-278
Author(s):  
Jing Lian Huang ◽  
Zhuo Wang ◽  
Ya Jing Liu
Keyword(s):  
Boolean Function ◽  
Internal Structure ◽  
Boolean Functions ◽  
Necessary Conditions ◽  
Algebraic Immunity ◽  
Hamming Weight ◽  
Analytic Combinatorics ◽  
Sufficient And Necessary Conditions ◽  
Research Tools

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we go deep into the internal structure of the Boolean function values. Additionally, by the methods of cascade calculations and analytic combinatorics, cryptographic properties such as correlation immune and algebraic immunity of H Boolean functions with Hamming weight of with diffusibility are studied. Then we prove the existing of m order correlation immune H Boolean functions ,and get the result of the sufficient and necessary conditions of algebraic immunity order is 1 of Boolean function with correlation immune order is m.

Some Cryptographic Properties of H Boolean Functions

2013 ◽  
Vol 740 ◽  
pp. 279-283
Author(s):  
Jing Lian Huang ◽  
Zhuo Wang ◽  
Ya Jing Liu
Keyword(s):  
Boolean Function ◽  
Internal Structure ◽  
Boolean Functions ◽  
Mathematical Expression ◽  
Algebraic Degree ◽  
Algebraic Immunity ◽  
Hamming Weight ◽  
The Relationship ◽  
Research Tools

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we go deep into the internal structure of the Boolean function values. Cryptographic properties such as algebraic immunity, correlation immune and algebraic degree of H Boolean functions with Hamming weight of with diffusibility and the relationship between these properties are studied. Then we get the results of the mathematical expression of linear annihilators, the values of algebraic degree and correlation immune order, and so on.

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