Efficient Large Integers Arithmetic by Adopting Squaring and Complement Recoding Techniques

The efficient squaring algorithm plays an important role in large number arithmetic. All multiplication algorithms can be used for squaring large integers, but their performance can be greatly improved by using the standard squaring algorithm. Complement recoding method can be divided into two groups: 1’s complement recoding method and 2’s complement recoding method. In this paper, we propose an efficient squaring algorithm by combing 1’s complement recoding method with standard squaring algorithm to fast evaluate the squaring. The computational complexity of the proposed squaring method is