Comparative Analysis of Multi-digit Modular Multiplication Algorithms for public key Crypto system in Big Data Security

Abstract

Big data security is a significant concern today due to rapidly growing data volume, velocity, and varieties of data in nature. Data security is a major concern because during transmission through insecure channels. From its recognition, the Montgomery multi-digit multiplication algorithms are still well-accepted approaches in the numerical calculation, chaos arithmetic, and highperformance implementation of public key cryptosystems such as RSA, Diffie-Hellman, and the Elliptic curve cryptosystems. We have presented the comparative study of multi-digit integer multiplication algorithms, and their performance is evaluated in terms of CPU execution time. Montgomery modular multiplication is a good practice, among others.

Efficiency of large integer multiplication algorithms: A comparative study of traditional methods and Karatsuba's algorithm

“…In the sense of classical multiplication, the problem degrades down to several simpler sub-problems that are, in turn, recursively solved to the final result [2] The systems exploit simple mathematical operations like addition and multiplication through these means, relying upon the facts and theorems from number theory and algebra to perform complex calculations. Although these traditional methods may be conceptually simple, their theoretical Background only sometimes inherently results in computational efficiency, more than all when approached with big integers [3]. However, despite the accord of their operations with well-known mathematical rules, classical algorithms may need help when faced with calculations involving a vast number of numerical digits.…”