Perfect Algebraic Immune Functions
The study of the cryptanalysis of the filter and combination generators of stream ciphers based on Linear Feedback Shift Registers (LFSRs) has resulted in a wealth of cryptographic criteria for Boolean functions, such as balancedness, high algebraic degree, high nonlinearity, high correlation immunity and so on. An overview of cryptographic criteria for Boolean functions with extensive bibliography is given in. A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two.