Abstract
Encryption algorithm has an important application in ensuring the security of the Internet of Things. Boolean function is the basic component of symmetric encryption algorithm, and its many cryptographic properties are important indicators to measure the security of cryptographic algorithm. This paper focuses on the sum-of-squares indicator of Boolean function; an upper bound and a lower bound of the sum-of-squares on Boolean functions are obtained by the decomposition Boolean functions; some properties and a search algorithm of Boolean functions with the same autocorrelation (or cross-correlation) distribution are given. Finally, a construction method to obtain a balanced Boolean function with small sum-of-squares indicator is derived by decomposition Boolean functions. Compared with the known balanced Boolean functions, the constructed functions have the higher nonlinearity and the better global avalanche characteristics property.
Highlights
The Internet of Things is an important part of the new generation of information technology and an important stage of information development
Theorem 20 provides a construction for use in lightweight dynamic cryptographic algorithms, especially some 3-variable or 4-variable Boolean functions for encryption algorithm in the Internet of Things [2]; that is, we find many alternative cryptographic components with the same cryptographic properties
We put up a new definition of two pairs of Boolean functions; this definition plays an important role in our construction. We believe that these conclusions and properties can be widely studied in designing the stream ciphers and block ciphers
Summary
The Internet of Things is an important part of the new generation of information technology and an important stage of information development. In 1995, Zhang and Zheng introduced the global avalanche characteristic (GAC [4]: the sum-of-squares indicator (σf), the absolute indicator (△f)) for an n-variable Boolean function f(x), and they gave the lower and the upper bounds on the two indicators. In 2010, [9] generalized the GAC and put up a new criterion based on the cross-correlation functions: the sum-of-squares indicator (σf,g) and the absolute indicator (△f,g) for two n-variable Boolean functions f(x), g(x); they gave the lower and the upper bounds on the two indicators. Reference [10] derived a new bound on the sum-of-squares indicator and gave a method to construct balanced Boolean functions with n(n ≥ 6) variables by the disjoint spectra functions, where n is an even integer, satisfying strict avalanche criterion, high nonlinearity, and lower GAC.
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