Abstract
We put forward an efficient method to study the algebraic immunity of H Boolean functions with Hamming weight of 2 n -1 + 2 n -2 , getting the existence of the higher-order algebraic immunity functions with correlation immunity. We also prove the existing problem of the above 2-order algebraic immunity functions and the optimal algebraic immunity functions. Meanwhile, we solve the compatibility of algebraic immunity and correlation immunity. What is more, the main theoretical results are verified through the examples and are revealed to be correct. Such researches are important in cryptographic primitive designs, and have significance and role in the theory and application range of cryptosystems.
Highlights
The cipher security is the core of the cryptosystem, and only a cryptosystem with good security has an existing significance
Boolean functions with a variety of secure cipher properties are the key factors to design the cryptosystem with the ability to resist multiple cipher attacks and good safety performance. It is of great importance for a security cryptosystem to study some properties of Boolean functions, which make the cryptosystem resist various attacks [1], such as high algebraic degree, high nonlinearity, the strict avalanche criterion and propagation, higher-order correlation immunity and higher-order algebraic immunity
When we study the correlation immunity and algebraic immunity of the H Boolean functions, it is equivalent to study the compatibility of the propagation property, algebraic immunity and correlation immunity of Boolean functions
Summary
The cipher security is the core of the cryptosystem, and only a cryptosystem with good security has an existing significance. Boolean functions with a variety of secure cipher properties are the key factors to design the cryptosystem with the ability to resist multiple cipher attacks and good safety performance. It is of great importance for a security cryptosystem to study some properties of Boolean functions, which make the cryptosystem resist various attacks [1], such as high algebraic degree, high nonlinearity, the strict avalanche criterion and propagation, higher-order correlation immunity and higher-order algebraic immunity. In this paper, using the derivative and e-derivative [7~9] as research tools, we study the importance of study cryptographic properties of H Boolean function with Hamming weight of 2n1 2n2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
