On Karatsuba Multiplication Algorithm

Algorithms in cryptosystem such as RSA and Diffie-Hellman require the large integer multiplication. This paper introduces classical Knuth multiplication, Karatsuba multiplication and their time complexity, on the basis of which a new Karatsuba trick is presented and proved to be available in theory and in practice. The experiment result reveals that the improved Karatsuba multiplication is more efficient for implementation of large integer multiplication.