Abstract
In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desired Walsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
Highlights
Boolean functions are fundamental components of a cryptographic algorithm
We introduced four new constructions of cryptographic boolean functions by using Cayley graph products
These boolean functions are constructed from smaller ones and the
Summary
Boolean functions are fundamental components of a cryptographic algorithm. Designing boolean functions with desired cryptographic properties is an important problem. Boolean functions should have some properties like balancedness, high non-linearity, algebraic immunity, correlation immunity and propagation criterion to be used in a symmetric algorithm. These properties make the cipher resistant against attacks like differential and linear cryptanalysis, correlation and algebraic attacks and statistical tests. Algebraic attacks will be more efficient if boolean functions have low degrees. All cryptographic properties can be measured by the Walsh spectrum of a boolean function. We aim to propose four new methods to construct larger boolean functions from smaller ones with predictable cryptographic properties
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