A new method to construct Boolean functions with good cryptographic properties

• A new method to construct Boolean functions was put forward.
• Balanced functions with high algebraic immunity and nonlinearity was constructed.
• The function might achieve the maximum nonlinearity among balanced functions with AI⩾n−12.

To resist fast correlation attacks, Boolean functions used in stream ciphers should have high nonlinearity. n  -variable bent functions have the maximum nonlinearity. However, they are not balanced and their algebraic degrees are at most n2. Therefore, they cannot be used directly as filter functions. In this paper, we give a new method to construct cryptographically significant Boolean functions. As an example, based on bent functions, we construct an infinite class of functions with good cryptographic properties: balancedness, optimum algebraic degree, almost optimum algebraic immunity and an almost optimum nonlinearity (higher than all other infinite classes of balanced functions with high algebraic immunity).