Abstract
Wu et al. proposed a generalized Tu-Deng conjecture over $\mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}}$ , and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open. Based on Wu’s work and assuming that the conjecture is true, we come up with a new class of balanced Boolean functions which has optimal algebraic degree, high nonlinearity and optimal algebraic immunity. The Boolean function also behaves well against fast algebraic attacks. Meanwhile we construct another class of Boolean functions by concatenation, which is 1-resilient and also has other good cryptographic properties.
Highlights
It is difficult to construct Boolean function satisfying all main criteria, including balancedness, optimal algebraic immunity (AI), high algebraic degree, high nonlinearity, etc
Fast algebraic immunity (FAI) is usually computed by computer to evaluate the ability of Boolean functions to resist fast algebraic attack, but some work is to obtain accurate fast algebraic immunity or its lower bound by mathematical proof [1]–[4]
We present a class of balanced Boolean functions over F2rm × F2m which are proved to obtain optimal AI, optimal deg, high nonlinearity and good behavior against fast algebraci attack (FAA)
Summary
It is difficult to construct Boolean function satisfying all main criteria, including balancedness, optimal algebraic immunity (AI), high algebraic degree (deg), high nonlinearity, etc. Work was done to prove the Tu-Deng conjecture [12] This class of Boolean functions does not perform well against fast algebraic attack (FAA). We present a class of balanced Boolean functions over F2rm × F2m which are proved to obtain optimal AI, optimal deg, high nonlinearity and good behavior against fast algebraci attack (FAA). We construct another class of Boolean functions with good cryptographic properties by concatenating with Wu’s function proposed in [16].
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