FPGA Implementation of Comparative Analysis and Performance Evaluation for Different LFSR Techniques

Abstract

We explore the FPGA-based implementation and comparative performance evaluation of various Linear Feedback Shift Register (LFSR) techniques used for pseudorandom sequence generation in digital systems. Five architectures—Fibonacci LFSR, Galois LFSR, Non-Linear Feedback Shift Register (NLFSR), Modular LFSR, and Masked LFSR—are designed using Verilog HDL and synthesized on an FPGA platform. The evaluation is carried out based on key performance metrics, including hardware resource utilization, power consumption, propagation delay, throughput, and randomness quality. The results show that Fibonacci and Galois LFSRs offer simple, low-area, and high-speed implementations, making them suitable for resource-constrained applications. In contrast, NLFSR and Masked LFSR provide enhanced security and improved randomness at the cost of higher complexity and resource usage. The study provides a clear comparison of LFSR techniques and helps in selecting appropriate architectures based on application-specific requirements in FPGA-based designs.

Introduction

The text describes the design, implementation, and evaluation of different Linear Feedback Shift Register (LFSR) architectures on FPGA platforms for generating pseudorandom sequences used in cryptography, testing, and secure communication systems.

LFSRs are chosen because they are simple, fast, and hardware-efficient, making them suitable for FPGA-based systems. The study implements multiple LFSR types—Fibonacci, Galois, Non-Linear (NLFSR), Modular, and Masked LFSRs—using Verilog HDL and deploys them on a Xilinx Artix-7 FPGA for analysis.

The methodology includes theoretical study of LFSR structures, hardware design in Verilog, FPGA synthesis and testing using Vivado, and performance evaluation based on hardware usage, power consumption, speed, randomness quality, and security. Randomness is validated using NIST statistical tests, while security is assessed particularly for nonlinear and masked designs.

The architecture is modular and scalable, allowing easy modification of feedback logic and register size for different applications. Each clock cycle shifts data, computes feedback, and generates pseudorandom output, ensuring continuous sequence generation.

Results show that all LFSRs function correctly and generate pseudorandom sequences. Fibonacci and Galois LFSRs produce stable linear sequences, while NLFSR generates more complex and less predictable outputs. Masked LFSR improves security by increasing output complexity, and Modular LFSR demonstrates flexibility and scalability.

Conclusion

Implementing a 64-bit Fibonacci LFSR on FPGA provides a reliable and efficient method for generating long pseudo-random sequences essential in applications like cryptography and error detection. While the Fibonacci LFSR architecture is straightforward and moderate in resource usage, its feedback XOR logic can introduce longer critical path delays compared to alternative designs. Comparative analysis reveals that the Galois LFSR technique often outperforms Fibonacci LFSRs in terms of maximum operating frequency and power efficiency, due to its distributed feedback structure that reduces combinational logic delay. However, both techniques can achieve maximal sequence lengths when using appropriate primitive polynomials. Ultimately, the choice between Fibonacci, Galois, or other LFSR architectures depends on the specific requirements of the FPGA application, including speed, resource constraints, power consumption, and ease of implementation. Careful evaluation using synthesis and simulation tools on the target FPGA platform is recommended to select the most suitable LFSR design for your needs.

References

[1] M. Rahman, A. Hossain, S. Karim, and F. Anwar, “FPGA-Based Secure Non-Linear LFSR Architecture for Cryptographic Applications,” IEEE Access, vol. 13, pp. 1–12, 2025. [2] K. Sharma and P. Verma, “Performance Evaluation of Fibonacci and Galois LFSRs on FPGA Platforms,” International Journal of Reconfigurable Computing, vol. 2024, Article ID 4587321, pp. 1–10, 2024. [3] S. R. Kumar and L. Devi, “Power and Area Optimization of LFSR Designs Using Verilog HDL,” Microprocessors and Microsystems, vol. 102, pp. 104–112, 2024. [4] A. Mohammed and T. Lee, “Comparative Study of Linear and Non-Linear Feedback Shift Registers,” in Proceedings of the IEEE International Conference on VLSI Systems, 2023, pp. 215–220. [5] J. Patel and R. Singh, “Modular LFSR Design for High-Speed Pseudo-Random Number Generation,” International Journal of Electronics and Communications, vol. 147, pp. 154–162, 2022. [6] H. Chen, Y. Liu, X. Zhang, and Q. Wang, “Masked LFSR Architecture for Side-Channel Attack Resistance,” IEEE Transactions on Circuits and Systems—I: Regular Papers, vol. 68, no. 9, pp. 3721–3732, 2021. [7] P. Gupta and M. Rao, “FPGA Implementation of Pseudo-Random Sequence Generators Using LFSR,” International Journal of Engineering Research & Technology (IJERT), vol. 9, no. 6, pp. 1123–1128, 2020. [8] R. K. Das and S. Mehta, “Hardware Efficient Galois LFSR for Cryptographic Applications,” International Journal of Computer Applications, vol. 177, no. 23, pp. 15–20, 2019. [9] L. Wang and Y. Zhao, “Design and Analysis of LFSR-Based Random Number Generator on FPGA,” in Proceedings of the IEEE International Conference on Communication Systems, 2018, pp. 310–314. [10] T. Narayanan and V. Subramani, “Area Optimized LFSR Architecture Using HDL for FPGA,” International Journal of Advanced Research in Electronics, vol. 6, no. 4, pp. 45–51, 2017.

Copyright

Copyright © 2026 G. Krishnaveni, M. Kavya, M. Kavya , B. Kavya Sree. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.