Implementation of Number Theoretic Transform Unit for Polynomial Multiplication of Lattice-based Cryptography

Xin, Mingyong; Xu, Changbao; Huang, Kai; Yu, Hongzhou; Yao, Hao; Jiang, Xiaowen; Liu, Dehong

doi:10.1109/iccece54139.2022.9712707

Cited by 4 publications

(1 citation statement)

References 8 publications

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“…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%

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: Introductionmentioning

confidence: 99%

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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show abstract

Quantum Computing

Agrawal,

Jain,

Thorat

et al. 2023

Quantum Computing in Cybersecurity

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Research on blockchain smart contract technology based on resistance to quantum computing attacks

Zheng

2024

PLoS ONE

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In recent years, blockchain technology has developed rapidly and has been widely used in medical, financial, energy and other fields. However, in the process of practical application, each blockchain is a small independent ecosystem, with all transactions and operations limited to the chain, resulting in a large number of mutually heterogeneous to independent blockchains. It presents challenges for cross-chain interactions, cross-organization data sharing, and cross-blockchain expansion, and hinders the wider application of blockchain technology. In addition, the traditional digital signature method based on elliptic curve cipher faces the threat of being cracked by quantum computing attacks. To solve the aforementioned problems, this paper proposed a blockchain smart contract technique based on quantum computing attack resistance(BSCTQCAT). The technique first introduces the digital signature of the lattice cipher into the blockchain to resist the quantum search algorithm attack. Then, based on the smart contract authentication scheme, the nodes on multiple heterogeneous chains are organized into an identity agent layer P2P network, through which transactions on the chain will establish a credible identity management and message authentication mechanism between different chains, solving the current problem that each chain is difficult to communicate with each other. In this paper, the performance of the algorithm is evaluated by simulating the Bitcoin transaction scenario and analyzing the experimental data.

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Implementation of Number Theoretic Transform Unit for Polynomial Multiplication of Lattice-based Cryptography

Cited by 4 publications

References 8 publications

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

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

Quantum Computing

Research on blockchain smart contract technology based on resistance to quantum computing attacks

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