A New Adaptable Construction of Modulo Addition with Scalable Security for Stream Ciphers

In recent years, attacks involving polynomial cryptanalysis have become an important tool in evaluating encryption algorithms involving stream ciphers. Stream cipher designs are difficult to implement since they are prone to weaknesses based on usage, with properties being similar to one-time pad key-stream are subjected to very strict requirements. Contemporary stream cipher designs are highly vulnerable to Algebraic cryptanalysis based on linear algebra, in which the inputs and outputs are formulated as multivariate polynomial equations. Solving a nonlinear system of multivariate equations will reduce complexity, which in turn yields the targeted secret information. Recently, Addition Modulo \(2^n\) has been suggested over logic XOR as a mixing operator to guard against such attacks. However, it has been observed that the complexity of Modulo Addition can be drastically decreased with the appropriate formulation of polynomial equations and probabilistic conditions. A new model for enhanced Addition Modulo is proposed. The framework for the new design is characterized by user-defined expandable security for stronger encryption and does not impose changes in the existing layout for stream ciphers such as SNOW 2.0, BIVIUM, CryptMT, Grain Family, etc. The structure of the proposed design is highly scalable, boosts the Algebraic degree and thwarts the probabilistic conditions by maintaining the original hardware complexity without changing the integrity of the Addition Modulo \(2^n\).