Stream cipher designs are difficult to implement since they are prone to
weaknesses based on usage, with properties being similar to one-time pad
besides keystream is 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 the complexity, which in turn yields the targeted
secret information. Recently, Addition Modulo 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 design for 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 existing layout for any
stream cipher such as SNOW 2.0, SOSEMANUK, CryptMT, Grain Family, etc. The
structure of the proposed design is highly scalable, which boosts the
algebraic degree and thwarts the probabilistic conditions by maintaining the
original hardware complexity without changing the integrity of the Addition
Modulo.
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