ROTATION SYMMETRIC BOOLEAN FUNCTION

Abstract

Over the years, the Rotational Symmetric Boolean Function has an important significance in cryptosystem. Rotational Symmetric Functions are invariant under circular transformation of indices. For secret key cryptosystems, nonlinearity, correlation immunity, balanced-ness, algebraic degrees are the different criteria for choosing a Boolean function for cryptographic applications. Rotational Symmetric Boolean Functions have good combination of these properties. The search space of Boolean functions is very large, i.e. 220 n-variables. It is not possible to check some desired properties for n ~t 7 (with current computational power). RSBFs reduced this search space to 20(n) [1], where g(n) = tIn 0(t) 2n/t, where 0 is the Euler phi function. So, it can be possible to perform experiments on this reduced search space. But the functions having high nonlinearity are good for cryptographic applications. So we will have to increase the search to find the function having high nonlinearity. So, we have increased the search space by performing partitions on input vector and performed the circular rotations on these partitions, such type of functions are known as 2-part rotation symmetric Boolean function.