FPGA Based Accelerator for Implementation of Large Integer Polynomials


Authors : Dr. J. Kamala; M. V. Tejendra Prasad

Volume/Issue : Volume 9 - 2024, Issue 5 - May

Google Scholar : https://tinyurl.com/c9tdvsax

Scribd : https://tinyurl.com/3fvzkdnx

DOI : https://doi.org/10.38124/ijisrt/IJISRT24MAY261

Abstract : A 13-bit multiplier is implemented on the Artix- 7 100T FPGA using a divide-and-conquer algorithm. The designis coded in SystemVerilog, leveraging its powerful features for hardware description and synthesis. The divide-and-conquer approach breaks down the multiplication task into smaller sub- tasks, enhancing efficiency and reducing complexity. The FPGA’s high- performance capabilities, particularly on the Artix-7 100T board, make it well-suited for accelerating the computations involved. Additionally, Area Delay Product (ADP) tools are employed to evaluate the algorithm’s efficiency. This project aims to showcase the synergy between algorithmic design, hardware implementation, and FPGA capabilities, emphasizing the versa- tility of the Artix-7 100T FPGA in handling complex arithmetic operations.

Keywords : Multiplier, Verilog, FPGA, Areadelayprod- UCT(ADP).

References :

  1. J. Xie, P. K. Meher, M. Sun, Y. Li, B. Zeng, and Z.-H. Mao, ”Efficient FPGA Implementation of Low-Complexity Systolic Karatsuba Multi- plier Over GF(2m) Based on NIST Polynomials,” in IEEE Transactions on Circuits and Systems–I: Regular Papers, vol. 64, no. 7, pp. 1815, July 2017. DOI: 10.1109/TCSI.2017.2667164
  2. S. Khan, W.-K. Lee, A. Khalid, A. Majeed, and S. O. Hwang, ’Area- Optimized Constant-Time Hardware Implementation for Polynomial Multiplication,’ in IEEE Embedded Systems Letters, vol. 15, no. 1, pp. 5, March 2023. DOI: 10.1109/LES.2023
  3. Lu, Y. Cui, A. Khalid, C. Gu, C. Wang, and W. Liu, ”A Novel Combined Correlation Power Analysis (CPA) Attack on Schoolbook Polynomial Multiplication in Lattice-based Cryptosystems,” in 2022 IEEE 35th International System-on-Chip Conference (SOCC), Nanjing, China, 2022, pp. 1-6, DOI: 10.1109/SOCC56010.2022.9908076.
  4. Y. Cui, Y. Zhang, Z. Ni, S. Yu, C. Wang, and W. Liu, ”High-Throughput Polynomial Multiplier for Accelerating Saber on FPGA,” in IEEE Transactions on Circuits and Systems—II: Express Briefs, vol. 70, no. 9, September 2023.
  5. Z.-Y. Wong, D. C.-K. Wong, W.-K. Lee, K.-M. Mok, W.-S. Yap, and A. Khalid, ”KaratSaber: New Speed Records for Saber Polynomial Multiplication Using Efficient Karatsuba FPGA Architecture,” in IEEE Transactions on Computers, vol. 72, no. 7,July 2023
  6. P.   He,   Y.   Tu,   C¸ .   K.   Koc¸,   and   J.   Xie,   ”Hardware-Implemented Lightweight Accelerator for Large Integer Polynomial Multiplication,” in IEEE Computer Architecture Letters, vol. 22, no. 1, pp. 1-1, January- June 2023.
  7. Y. Cui et al., ”High-Throughput Polynomial Multiplier for Accelerating Saber on FPGA,” in IEEE Transactions on Circuits and Systems—II: Express Briefs, vol. 70, no. 9, pp. 1465-1469, September 2023.
  8. Zoni, A. Galimberti, and W. Fornaciari, ”Flexible and Scalable FPGA-Oriented Design of Multipliers for Large Binary Polynomials,” in IEEE Access, DOI: 10.1109/ACCESS.2022.3084732.

A 13-bit multiplier is implemented on the Artix- 7 100T FPGA using a divide-and-conquer algorithm. The designis coded in SystemVerilog, leveraging its powerful features for hardware description and synthesis. The divide-and-conquer approach breaks down the multiplication task into smaller sub- tasks, enhancing efficiency and reducing complexity. The FPGA’s high- performance capabilities, particularly on the Artix-7 100T board, make it well-suited for accelerating the computations involved. Additionally, Area Delay Product (ADP) tools are employed to evaluate the algorithm’s efficiency. This project aims to showcase the synergy between algorithmic design, hardware implementation, and FPGA capabilities, emphasizing the versa- tility of the Artix-7 100T FPGA in handling complex arithmetic operations.

Keywords : Multiplier, Verilog, FPGA, Areadelayprod- UCT(ADP).

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