Design of a Lightweight Fast Fourier Transformation for FALCON using Hardware-Software Co-Design
Pages 228 - 232
Abstract
Lattice-based post-quantum cryptographic algorithm FALCON needs to execute the time-critical Fast-Fourier Transformation (FFT). Existing works in the literature have explored hardware for FFT of FALCON using Cooley-Tukey. In this work, we have designed an efficient hardware-software co-design of FFT for FALCON using Winograd’s FFT method. Winograd’s FFT is a widely adopted technique for FFT and reduces the multiplication counts for higher-radix FFT than the Cooley-Tukey, with a penalty of some extra addition/subtraction. Our Winograd radix-8 framework for FFT outperforms the traditional Cooley-Tukey method. Moreover,our proposed architecture is flexible in adopting different instruction sets and can also be configured for any type of FFT method with specific instruction sets.
References
[1]
Janice S Agnello. 1979. An Introduction to the Winograd Discrete Fourier Transform. (1979).
[2]
Ghada Alsuhli, Hani Saleh, Mahmoud Al-Qutayri, Baker Mohammad, and Thanos Stouraitis. 2024. Area and Power Efficient FFT/IFFT Processor for FALCON Post-Quantum Cryptography. arXiv preprint arXiv:2401.10591 (2024).
[3]
Luke Beckwith, Duc Tri Nguyen, and Kris Gaj. 2023. Hardware Accelerators for Digital Signature Algorithms Dilithium and FALCON. IEEE Design & Test (2023).
[4]
AJAA Bekele. 2016. Cooley-tukey fft algorithms. Advanced algorithms (2016).
[5]
Nikhilesh Bhagat, Daniel Valencia, Amirhossein Alimohammad, and Fred Harris. 2018. High-throughput and compact FFT architectures using the Good–Thomas and Winograd algorithms. IET Communications 12, 8 (2018), 1011–1018.
[6]
Nikhilesh Vinayak Bhagat. 2016. A novel high-throughput FFT architecture for wireless communication systems. Ph. D. Dissertation. San Diego State University.
[7]
Richard E Blahut. 2010. Fast algorithms for signal processing. Cambridge University Press.
[8]
Xiangren Chen, Bohan Yang, Shouyi Yin, Shaojun Wei, and Leibo Liu. 2022. CFNTT: Scalable radix-2/4 NTT multiplication architecture with an efficient conflict-free memory mapping scheme. IACR Transactions on Cryptographic Hardware and Embedded Systems (2022), 94–126.
[9]
Emre Karabulut and Aydin Aysu. 2023. A hardware-software co-design for the discrete gaussian sampling of falcon digital signature. Cryptology ePrint Archive (2023).
[10]
Youngbeom Kim, Jingyo Song, and Seog Chung Seo. 2022. Accelerating falcon on ARMv8. IEEE Access 10 (2022), 44446–44460.
[11]
Kevin Kiningham, Philip Levis, Mark Anderson, Dan Boneh, Mark Horowitz, and Maurice Shih. 2019. Falcon—A flexible architecture for accelerating cryptography. In 2019 IEEE 16th International Conference on Mobile Ad Hoc and Sensor Systems (MASS). IEEE, 136–144.
[12]
Georg Land, Pascal Sasdrich, and Tim Güneysu. 2021. A hard crystal-implementing dilithium on reconfigurable hardware. In International Conference on Smart Card Research and Advanced Applications. Springer, 210–230.
[13]
Suraj Mandal and Debapriya Basu Roy. 2024. KiD: A Hardware Design Framework Targeting Unified NTT Multiplication for CRYSTALS-Kyber and CRYSTALS-Dilithium on FPGA. In 2024 37th International Conference on VLSI Design and 2024 23rd International Conference on Embedded Systems (VLSID). IEEE, 455–460.
[14]
Stavros Paschalakis and Peter Lee. 2003. Double precision floating-point arithmetic on FPGAs. In Proceedings. 2003 IEEE International Conference on Field-Programmable Technology (FPT)(IEEE Cat. No. 03EX798). IEEE, 352–358.
[15]
Thomas Pornin. 2019. New efficient, constant-time implementations of falcon. Cryptology ePrint Archive (2019).
[16]
Mateusz Raciborski and Aleksandr Cariow. 2022. On the derivation of Winograd-type DFT algorithms for input sequences whose length is a power of two. Electronics 11, 9 (2022), 1342.
[17]
Michael Schmid, Dorian Amiet, Jan Wendler, Paul Zbinden, and Tao Wei. 2023. Falcon Takes Off-A Hardware Implementation of the Falcon Signature Scheme. Cryptology ePrint Archive (2023).
[18]
Shmuel Winograd. 1978. On computing the discrete Fourier transform. Mathematics of computation 32, 141 (1978), 175–199.
Index Terms
- Design of a Lightweight Fast Fourier Transformation for FALCON using Hardware-Software Co-Design
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June 2024
797 pages
ISBN:9798400706059
DOI:10.1145/3649476
Copyright © 2024 Owner/Author.
This work is licensed under a Creative Commons Attribution International 4.0 License.
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Published: 12 June 2024
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