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

Abstract

The large integer multiplication is the basis of many computer science algorithms, ranging from cryptography to complex calculations in various scientific fields. Contemporary society excessively depends on complex computing tasks. Hence, the need for good algorithms is becoming increasingly apparent as well. This text gives the reader an in-depth knowledge of the multiplication algorithms of large integers by contrasting traditional algorithms with the new Algorithm developed by Karatsuba. This research methodology involves a comparative analysis of the components using an advanced analysis framework that primarily focuses on execution times, efficiency metrics, and resource utilization. Incontrovertibly, the experimental results confirm the Karatsuba algorithm's undoubted hastiness compared to the conventional approaches. This study extends our grasp of the evolution of algorithms in computational optimization, enabling people to get unique and relevant findings that will benefit numerous areas where large integer multiplications are involved. In addition to these findings, the study also highlights the importance of algorithm selection in ensuring computational efficiency and accuracy in large integer multiplications across various applications.