Rain: Reversible Addition with Increased Nonlinearity

This paper proposes a reversible, balanced and nonlinear vectorial Boolean function called ‘Rain’. Traditional integer addition modulo 2 has several features like reversibility, balancedness and nonlinearity. However, the bias for the best linear approximation of the output bits and their linear combinations is quite high. This leads to several attacks on stream cipher like NLS, which employs addition modulo 2. In this paper, it has been proved mathematically that the bias of the each output bit and their non-zero linear combinations of the proposed vectorial Boolean function decreases exponentially with the bit position. Also as a case study, it has been shown that attacks against stream cipher NLS is prevented through the incorporation of Rain.