Algebrical Properties of Modular Addition Modulo 2t with r Operant

Modular addition modulo 2t is one of the most applicable operators in symmetric cryptography. Therefore, investigating the properties of this operator has a significant role in design and analysis of symmetric ciphers. Algebraic properties of this operator have been studied for two operands in [1]. In this contribution, to obtain more accurate results in this area, we generalize some of the algebraic properties of this operator for operands. More precisely, we consider the algebraic degree of the component Boolean functions of modular addition as a vectorial Boolean function and determine the number of terms and variables in these Boolean functions. After some theoretical analysis in special cases, we propose an efficient algorithm for finding the degree of these Boolean functions general case. Using this algorithm, the algebraic degree of the component Boolean functions for modular addition modulo 232, with three up to eight operands is calculated.