Abstract：Algebraic immunity is one of the most significant cryptographic properties for Boolean functions. In order to resist algebraic attack, high algebraic immunity is necessary for those Boolean functions used in stream ciphers. This paper constructed more than one even-variable rotation symmetric Boolean functions with optimum algebraic immunity by giving an even n. Based on majority function, some orbits of different hamming weights were chosen, then the values of functions on these orbits were changed. Given a sufficient condition of Boolean functions with optimum algebraic immunity, the new constructed Boolean functions were proved to satisfy the condition. Therefore, it shows the algebraic immunity of the functions is optimum. Thus, algebraic attacks can be resisted effectively.
2014, Vol. 34 
