A More Accurate and Robust Binary Ring-LWE Decryption Scheme and Its Hardware Implementation for IoT Devices
Dongdong Xu, Xiang Wang, Yuanchao Hao, Zhun Zhang, Qiang Hao, Zhiyu Zhou
Abstract
Learning with error (LWE) over the ring based on binary distribution (ring-BinLWE) has become a potential Internet-of-Things (IoT) confidentiality solution with its anti-quantum attack properties and uncomplicated calculations. Compared with ring-LWE based on discrete Gaussian distribution, the decryption scheme of ring-LWE based on binary distribution needs to be re- determined due to the asymmetry of the error distribution. The direct application of the ring-LWE decryption function based on discrete Gaussian distribution can cause serious misjudgment. In this article, we propose a more accurate and robust decryption scheme for ring-BinLWE based on 2’s complement ring. Compared with the previous decryption function, the re- derived decryption function significantly improves the decoding rate by 50%. Furthermore, based on the proposed decryption function, high-performance, and lightweight hardware architectures for terminal devices in IoT are, respectively, proposed, which are scalable and can be easily adapted to ring-BinLWE hardware deployment with other parameter sets. When the parameter set is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n\,\,=$ </tex-math></inline-formula> 256, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q\,\,=$ </tex-math></inline-formula> 256, the high-performance implementation consumes 7.6k LUTs, 6.2k FFs, and 2.3k SLICEs on Spartan 6 field-programmable gate array (FPGA) platform. Compared with the previous implementation, our resource overhead increases by only 23% while the decryption accuracy is significantly improved by 50%. The lightweight implementation for parameter set <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n\,\,=$ </tex-math></inline-formula> 256, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q\,\,=$ </tex-math></inline-formula> 256 consumes only 230 LUTs, 338 FFs, and 84 SLICEs on the Spartan 6 FPGA platform. Compared with the previous work, the area <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> time (AT) is reduced by 47.8%, which is more suitable for deployment on resource-constrained IoT nodes.