Abstract
Rotation symmetric Boolean functions (RSBFs) are nowadays studied a lot because of its easy operations and good performance in cryptosystem. This paper constructs a new class of odd-variable RSBFs with optimal algebraic immunity (AI). The nonlinearity of the new function, 2 n-1 -( k n-1 )+2 k-4 (k-3)(k-2), is the highest among all existing RSBFs with optimal AI and known nonlinearity, and its algebraic degree is also almost highest. Besides, the class of functions have almost optimal fast algebraic immunity (FAI) at least for n <; 17, which is actually the highest possible value for the designated number of variables.
Highlights
Boolean functions play an important role in cryptosystems of stream ciphers
In 2003, the algebraic attack was proposed by Courtois and Meier in [1]
Was introduced in [17], which works as a measurement of the ability of Boolean functions to resist fast algebraic attacks
Summary
Boolean functions play an important role in cryptosystems of stream ciphers They are required to satisfy kinds of cryptographic properties in order to resist many attacks. Was introduced in [17], which works as a measurement of the ability of Boolean functions to resist fast algebraic attacks. In 2017, Sun and Fu [35] presented two classes of even-variable RSBFs with optimal AI, high nonlinearity and high fast algebraic immunity. Presented a class of odd-variable RSBFs with optimal AI and higher nonlinearity. These two classes of functions have almost optimal immunity for n = 11, 13 and n = 11, 13, 15, respectively. We here construct a new type of odd-variable RSBFs with the following properties: i) They are balanced with optimal.
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