On the ANF and Degree of Data-dependent Rotation

In this article we consider data-dependent rotation (DDR) as a vectorial boolean function and show that all its component functions are algebraic degree k+1 where 2k is the bit-length of its operands. Besides, we obtain the algebraic normal form (ANF) of the component functions. These results give us insight into the algebraic nature of this seemingly complex operation and have applications in studying higher order differential attacks on block ciphers like RC5 which heavily rely on DDR as their main building block, and may possibly be used in mounting Courteous algebraic attack on such ciphers.