Speeding up the Multiplication Algorithm for Large Integers

Abstract

Multiplication is one of the basic operations that influence the performance of many computer applications such as cryptography. The main challenge of the multiplication operation is the cost of the operation as compared to other basic operations such as addition and subtraction, especially when the size of the numbers is large. In this work, we investigate the use of the window strategy for multiplying a sequence of large integers to design an efficient sequential algorithm in order to reduce the number of bit-multiplication operations involved in multiplying a sequence of large integers. In our implementation, several parameters are considered and measured for their effect on the proposed algorithm and the best-known sequential algorithm in the literature. These parameters are the size of the sequence of integers, the size of the integers, the size of the window, and the distribution of the data. The experimental results prove the effectiveness of the proposed algorithm are compared to the ones of the best-known sequential algorithm, and the proposed algorithm is able to achieve a reduction in computing time greater than 50% in most cases.

Building Applications and Developing Digital Signature Devices based on the Falcon Post-Quantum Digital Signature Scheme

“…[1]. In particular, the Falcon digital signature is one of the schemes that has many security advantages against quantum computer systems [6][7].…”