Speeding Modular Squaring Algorithms of Larger-Number Using CRT

Modular exponentiation can be decomposed into several modular squaring and modular multiplication.So we can accelerate the computation of modular exponentiation by optimizing modular squaring of larger number,and we can resolve question of slowly calculating of the public-key cryptography systems.An algorithm of optimizing modular squaring using Chinese remainder theorem is introduced. At the same time another algorithm of optimizing modular squaring based on generalized Chinese remainder theorem is introduced.The several algorithms are compared in the different surroundings.