CONSTRUCTIONS OF ROTATION SYMMETRIC BENT FUNCTIONS AND BENT IDEMPOTENT FUNCTIONS

The class of rotation symmetric functions is extremely rich in terms of cryptographical significance. However, few constructions of rotation symmetric bent functions, which can correspond to bent idempotent functions, have been presented in the literature. In this paper, for any even integer n & GE; 4, we first construct an n-variable rotation symmetric bent function by modifying the truth table of Rothaus's bent function on the vector space Fn2 , and then obtain a bent idempotent function by corresponding it to the finite field F2n . By generalizing the proposed n-variable Boolean function, we obtain a family of Boolean functions which are rotation symmetric bent on the vector space Fn2 and bent idempotent over the finite field F2n .