Abstract |
The residue number system (RNS) can be applied to cryptography, image processing, digital filtering, parallel computation, and cloud computing. It represents a large integer using a set of smaller integers, so it has property of carry-free and parallel, and high-speed in addition, subtraction, and multiplication. However, the other RNS operations, such as number comparison, division, overflow detection, and sign detection is very difficult and needs significant amounts of time. With the parity detection technique, we can improve these operations to be efficiently. In this paper, we provide a parity detection method basic on residue number system using three-moduli set {2p-1,2p+1,2p^2-1}, where p is a positive integer. Given RNS representation of X = (x_1,x_2,x_3 ) based on the three-moduli set where x_1= X mod 2p-1, x_2= X mod 2p+1, x_3= X mod 2p^2-1. The parity of X is equals to the result of (x_1 + x_2 + x_3 + G(d)) mod 2 (0 means even, 1 means odd) where d=2p(x_2-x_1)+(2x_3-x_1-x_2), G(d)=1, if d < 2m_3 or d < 0; otherwise, G(d)=0. |