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.
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