Abstract
To resist Binary Decision Diagrams (BDD) based attacks, a Boolean function should have a high BDD size. The hidden weighted bit function (HWBF), introduced by Bryant in 1991, seems to be the simplest function with exponential BDD size. In [28], Wang et al. investigated the cryptographic properties of the HWBF and found that it is a very good candidate for being used in real ciphers. In this paper, we modify the HWBF and construct two classes of functions with very good cryptographic properties (better than the HWBF). The new functions are balanced, with almost optimum algebraic degree and satisfy the strict avalanche criterion. Their nonlinearity is higher than that of the HWBF. We investigate their algebraic immunity, BDD size and their resistance against fast algebraic attacks, which seem to be better than those of the HWBF too. The new functions are simple, can be implemented efficiently, have high BDD sizes and rather good cryptographic properties. Therefore, they might be excellent candidates for constructions of real-life ciphers.
Highlights
To resist the main known attacks, Boolean functions used in real ciphers should be balanced, with high algebraic degree, with high algebraic immunity, with high nonlinearity and with good immunity to fast algebraic attacks
The new functions are balanced, with almost optimum algebraic de- gree and satisfy the strict avalanche criterion. Their nonlinearity is higher than that of the hidden weighted bit function (HWBF).We investigate their algebraic immunity, Binary Decision Diagrams (BDD) size and their resistance against fast algebraic attacks, which seem to be better than those of the HWBF too
A Boolean function f should have a high algebraic immunity, which implies that the nonlinearity of f is not very low since, according to Lobanov’s bound [17]
Summary
To resist the main known attacks, Boolean functions used in real ciphers should be balanced, with high algebraic degree, with high algebraic immunity, with high nonlinearity and with good immunity to fast algebraic attacks It would be better if the function is non-normal and satisfies the strict avalanche criterion. Key words and phrases: Hidden weighted bit function, algebraic immunity, nonlinearity, strict avalanche criterion, BDD-based attack. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number
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