On the Propagation Criterion of Boolean Functions

2004 ◽  
pp. 153-168 ◽  
Author(s):  
Aline Gouget
Keyword(s):  
Boolean Functions ◽  
Propagation Criterion

scholarly journals A New Family of Boolean Functions with Good Cryptographic Properties

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 42
Author(s):  
Guillermo Sosa-Gómez ◽  
Octavio Paez-Osuna ◽  
Omar Rojas ◽  
Evaristo José Madarro-Capó
Keyword(s):  
Boolean Functions ◽  
Linear Codes ◽  
Bent Functions ◽  
New Family ◽  
Propagation Criterion ◽  
Daunting Task ◽  
Wide Range ◽  
Algebraic Codes ◽  
New Construction

In 2005, Philippe Guillot presented a new construction of Boolean functions using linear codes as an extension of the Maiorana–McFarland’s (MM) construction of bent functions. In this paper, we study a new family of Boolean functions with cryptographically strong properties, such as non-linearity, propagation criterion, resiliency, and balance. The construction of cryptographically strong Boolean functions is a daunting task, and there is currently a wide range of algebraic techniques and heuristics for constructing such functions; however, these methods can be complex, computationally difficult to implement, and not always produce a sufficient variety of functions. We present in this paper a construction of Boolean functions using algebraic codes following Guillot’s work.

Relationship between Algebraic Immunity, Correlation Immune and Propagation of Boolean Functions

2013 ◽  
Vol 321-324 ◽  
pp. 2649-2652
Author(s):  
Jing Lian Huang ◽  
Zhuo Wang ◽  
Chun Ling Zhang
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Algebraic Immunity ◽  
Correlation Immunity ◽  
Propagation Criterion ◽  
Function Correlation ◽  
The Relationship ◽  
Research Tools

Using the derivative of the Boolean function and thee-derivative defined by ourselves as research tools, we study the problem of relationship between algebraic immunity,correlation immunity and propagation of H Boolean functions with weight of and satisfying the 1st-order propagation criterion togetherwith the problem of their compatibility. We get the results , suchas the relationship between the number of annihilators and correlation immunityorder, the relationship between the number of correlation immunity order and algebraic immune degree together with theircompatibility and the largest propagations of H Boolean function, the relationships between propagationsof Boolean function, correlation immunity order and algebraic immune degree.

Noise Sensitivity of Boolean Functions and Percolation

2015 ◽  
Author(s):  
Christophe Garban ◽  
Jeffrey E. Steif
Keyword(s):  
Boolean Functions ◽  
Noise Sensitivity

CLASS OF BOOLEAN FUNCTIONS CONSTRUCTED USING SIGNIFICANT BITS OF LINEAR RECURRENCES OVER THE RING ℤ2n

2019 ◽  
Vol 6 (2) ◽  
pp. 90-94
Author(s):  
Hernandez Piloto Daniel Humberto
Keyword(s):  
Linear Function ◽  
Boolean Functions ◽  
Hamming Distance ◽  
Linear Recurrences ◽  
Maximum Period ◽  
Non Linear ◽  
The Given ◽  
Class Of Functions

In this work a class of functions is studied, which are built with the help of significant bits sequences on the ring ℤ2n. This class is built with use of a function ψ: ℤ2n → ℤ2. In public literature there are works in which ψ is a linear function. Here we will use a non-linear ψ function for this set. It is known that the period of a polynomial F in the ring ℤ2n is equal to T(mod 2)2α, where α∈ , n01- . The polynomials for which it is true that T(F) = T(F mod 2), in other words α = 0, are called marked polynomials. For our class we are going to use a polynomial with a maximum period as the characteristic polyomial. In the present work we show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

On the Signal-to-Noise Ratio for Boolean Functions

2020 ◽  
Vol E103.A (12) ◽  
pp. 1659-1665
Author(s):  
Yu ZHOU ◽  
Wei ZHAO ◽  
Zhixiong CHEN ◽  
Weiqiong WANG ◽  
Xiaoni DU
Keyword(s):  
Boolean Functions ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Noise Ratio
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