Abstract
It is difficult to find Boolean functions achieving many good cryptographic properties. Recently, Tu and Deng obtained two classes of Boolean functions with good properties based on a combinatorial conjecture about binary strings. In this paper, using different approaches, we prove this conjecture is true in some cases. This conjecture has resisted different attempts of proof since it is hard to find a recursive method. In this paper we give a recursive formula in a special case.
Highlights
Tu and Deng obtained two classes of Boolean functions with good properties based on a combinatorial conjecture about binary strings
In this paper, using different approaches, we prove this conjecture is true in some cases
In this paper we give a recursive formula in a special case
Summary
Tu and Deng obtained two classes of Boolean functions with good properties based on a combinatorial conjecture about binary strings. In this paper, using different approaches, we prove this conjecture is true in some cases. [1] Tu and Deng proposed the following conjecture. Tu and Deng [1] constructed two classes of Boolean functions with many good cryptographic properties.
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