KaratSaber: New Speed Records for Saber Polynomial Multiplication using Efficient Karatsuba FPGA Architecture

Wong, Zheng-Yan; Wong, Denis C. K.; Lee, Wai-Kong; Mok, Kai-Ming; Yap, Wun‐She; Khalid, Ayesha

doi:10.1109/tc.2023.3238129

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…The most expensive operation of the butterfly unit in NTT, in terms of resources and time, is the modular multiplication of the coefficient with the root of unities. The first approach we propose utilizes the fact that with parameter q = 3329 < 2 12 , which means the coefficient is up to 12 − bit long, we can split it to sum of multiples precomputed product with the roots of unity and can eliminate the full multiplication and as well as the need for dedicated storage for the root of unities completely. 3.…”

Section: Related Workmentioning

confidence: 99%

“…3. The second butterfly unit we propose will utilize the quarter square multiplication to perform modular multiplication xy = (x + y) 2 /4 − (x − y) 2 /4, by realizing the fact that although a 12 × 12 multiplication typically requires a 2 24 depth look-up table while a 12 − bit squares only requires 2 12 . Therefore, by replacing multiplication by squares with additional processing, we can fit the quarter squares on a single dual-port ROM that fits neatly on one BRAM.…”

Section: Related Workmentioning

confidence: 99%

“…This holds true not only for the Kyber cryptography algorithm but also for other cryptographic algorithms. Polynomial multiplication can be computed using several algorithms, including the schoolbook algorithm [8][9][10], Karatsuba algorithm [11,12], Toom-Cook algorithm [13,14], and NTT algorithm [15][16][17]. Out of these algorithms, the schoolbook algorithm is the most basic and straightforward.…”

Section: Introductionmentioning

confidence: 99%

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Compact and Low-latency FPGA-based NTT Architecture for CRYSTALS Kyber Post-Quantum Cryptography Scheme

Kieu-Do-Nguyen,

The Binh,

Pham-Quoc

et al. 2024

Preprint

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In the era of the post-quantum Internet of Things (IoT), the implementation of anti-quantum cryptographic algorithms in numerous terminals can successfully defend against prospective quantum computing assaults. Lattice-based cryptography can withstand quantum computing attacks, making it a viable substitute for the currently prevalent classical public-key cryptographic technique. Nevertheless, the algorithm’s significant time complexity will result in a substantial computational burden on the edge computing chip in the IoT terminal. The computation of polynomial multiplication is the most demanding task in lattice-based cryptographic algorithms. Therefore, the investigation into efficient methods for calculating polynomial multiplication is highly important. Quick number theory transformations (NTT) are a widely employed technique to accelerate polynomial multiplication. This study presents a hardware implementation of an efficient number theory transformation. We utilize a multi-level pipeline architecture in the design to accomplish parallel calculations and execute it on a low-profile Artix7-XC7A100T FPGA device. The performance evaluation results demonstrate that our implementation significantly enhances performance and reduces resource usage compared to other existing proposals on the same platform. We suggested NTT core can be implemented in edge computing chips to enhance computational speed due to its small and low-latency design. The experimental results show that the proposed design, which supports both NTT and inverse NTT, achieves 417-Megahertz and consumes only 541-LUTs on Artix-7 XC7A100T.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%