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Efficient Number Theoretic Transform Architecture for CRYSTALS-Kyber
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DOI：10.1109/TCSII.2024.3465273.png)
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Abstract
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The Number Theoretic Transform (NTT) is a central primitive to compute polynomial multiplication in a finite ring for both post-quantum cryptography (PQC) and fully homomorphic encryption (FHE) schemes. This brief presents a novel, efficient NTT hardware architecture suitable for CRYSTALS-Kyber, one of the NIST PQC standards. It is based on a new novel unified butterfly unit (UBU) developed by combining interleaved multiplication, radix-4, and resource-sharing strategies. This unit computes all butterfly operations for any generic prime modulus value and is re-configurable to any modulus length. In the proposed NTT architecture, multiple UBUs are deployed, demonstrating an area-time tradeoff. UBU and NTT architectures are synthesized and implemented over the Xilinix Artix-7 FPGA platform and results are shown for different performance evaluation metrics. The implementation results show our lightweight and high-speed designs achieve up to 5.6x and 7x improvements in resource consumption and efficiency, respectively. To the authors' knowledge, it is the first generic NTT architecture based on interleaved multiplication approaches.
Keywords:
Computer architecture
Polynomials
Cryptography
Transforms
Field programmable gate arrays
Standards
Fast Fourier transforms
Number theoretic transform
FPGA
interleaved multiplication
post-quantum cryptography
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