Download pdf
Efficiency of large integer multiplication algorithms: A comparative study of traditional methods and Karatsuba's algorithm
- 1 University of California
* Author to whom correspondence should be addressed.
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.
Keywords
Large integer multiplication, Efficiency, Algorithms, Traditional methods, Karatsuba's Algorithm
[1]. Thirumoorthi, M., Leigh, A. J., Heidarpur, M., Khalid, M., & Mirhassani, M. (2023). Novel Formulations of M-Term Overlap-Free Karatsuba Binary Polynomial Multipliers and Their Hardware Implementations. IEEE Transactions on Very Large Scale Integration (VLSI) Systems.
[2]. Zhu, Y., Zhu, M., Yang, B., Zhu, W., Deng, C., Chen, C., ... & Liu, L. (2020). A high-performance hardware implementation of saber based on the Karatsuba algorithm. Cryptology ePrint Archive.
[3]. Biswas, S., & Biswas, N. (2023). Comparative Analysis of Multi-digit Modular Multiplication Algorithms for public key Cryptosystem in Big Data Security. American Journal of Electronics & Communication, 3(3), 16-19.
[4]. Edamatsu, T., & Takahashi, D. (2020). We are accelerating large integer multiplication using Intel AVX-512IFMA. In Algorithms and Architectures for Parallel Processing: 19th International Conference, ICA3PP 2019, Melbourne, VIC, Australia, December 9–11, 2019, Proceedings, Part I 19 (pp. 60-74). Springer International Publishing.
[5]. Andre, W. (2020). Efficient adaptation of the Karatsuba algorithm for implementing large-scale multipliers for cryptographic algorithms on FPGA on FPGA. International Journal of Reconfigurable and Embedded Systems (IJRES), 9(3), 235–241.
[6]. Langhammer, M., & Pasca, B. (2021, February). Folded integer multiplication for FPGAs. In The 2021 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays (pp. 160–170).
[7]. Wong, Z. Y., Wong, D. C. K., Lee, W. K., & Mok, K. M. (2021). High-speed RLWE-oriented polynomial multiplier utilizing the Karatsuba algorithm. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(6), 2157-2161.
[8]. Huai, Z., Parhi, K. K., & Zhang, X. (2021, October). Efficient architecture for long integer modular multiplication over Solinas prime. In 2021 IEEE Workshop on Signal Processing Systems (SiPS) (pp. 146–151). IEEE.
[9]. Dervişağaoğlu, O. (2020). Determination of Multiplication Algorithm with Basis on Pascal Triangle. Cankaya University Journal of Science and Engineering, 17(1), 71-79.
[10]. Wang, X., Wu, N., Zhou, F., & Ge, F. (2022, November). Efficient, configurable digit-serial multiplier based on improved karatsuba algorithm over GF (2m). In 2022 IEEE 22nd International Conference on Communication Technology (ICCT) (pp. 1531–1535). IEEE.
[11]. Yamazaki, S. (2023). An Extension of the Karatsuba Algorithm in Case the Multiplicand and Multiplier Bit Widths are Different. IEICE Technical Report; IEICE Tech. Rep., 123(71), 58–61.
Cite this article
Zhang,J. (2024). Efficiency of large integer multiplication algorithms: A comparative study of traditional methods and Karatsuba's algorithm. Applied and Computational Engineering,69,30-36.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 6th International Conference on Computing and Data Science
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).