Applications to montgomery modular multiplication of karatsuba multiplication without overlapped summation

Karatsuba Multiplication Algorithm is commonly used in modular multiplications of public-key cryptosystems with large key sizes. The overlapped summation in Karatsuba Multiplication is difficult for parallel acceleration in hardware implementations. This paper proposes a method of avoiding the overlapped summation under the circumstances of calculating Montgomery Modular Multiplication. The proposed method has fewer addition rows and better parallelism.