Constructing Vectorial Boolean Functions with High Algebraic Immunity Based on Group Decomposition
Boolean functions play a very critical role in symmetric cryptographic systems. There are many criteria for a Boolean function to be a so-called "Good" function, such as balancedness, high nonlinearity, high algebraic degree, and correlation immunity. In 2003, Courtois and Meier proposed a standard algebraic attack upon some well-known stream cryptographic systems(i.e. LILI128 and Toyocrypt), which was then improved by Armknecht. After that, algebraic attack has become an effective method to analyze stream ciphers, block ciphers. Besides LILI128 and Toyocrypt, many other cryptographic systems were investigated by the means of algebraic attack. At the same time, algebraic immunity, which is used to measure a Boolean function's ability for resisting algebraic attack, has become a very important criterion to design Boolean functions.