A new Modulo Addition with enhanced scalable security against algebraic attack

In recent years, Algebraic Attack has emerged to be an important cryptanalysis method in evaluating encryption algorithms. The attack exploits algebraic equations between the inputs and outputs of a cipher to solve for the targeted information. The complexity of the attack depends on the algebraic degree of the equations, the number of equations, and the probabilistic conditions employed. Addition Modulo 2n had been suggested over logic XOR as a mixing element to better defend against Algebraic Attack. However, it has been discovered that the complexity of the traditional Modulo Addition can be greatly reduced with the right equations and probabilistic conditions. The presented work introduces a new Modulo Addition structure that includes an Input Expansion, Modulo Addition, and Output Compaction. The security of the new structure is scalable and user-defined as the new structure increases the algebraic degree and thwarts the probabilistic conditions.