The aim of this project was to develop a new Reservoir Computer
implementation, based on a chaotic Chua circuit. In addition to suitable
classification and regression benchmarks, the Reservoir Computer was applied to
Post-Quantum Cryptography, with its suitability for this application
investigated and assessed. The cryptographic algorithm utilised was the
Learning with Errors problem, for both encryption and decryption. To achieve
this, the Chua circuit was characterised, in simulation, and by physical
circuit testing. The Reservoir Computer was designed and implemented using the
results of the characterisation. As part of this development, noise was
considered and mitigated.
The benchmarks demonstrate that the Reservoir Computer can achieve current
literature benchmarks with low error. However, the results with Learning with
Errors suggest that a Chua-based Reservoir Computer is not sufficiently complex
to tackle the high non-linearity in Post-Quantum Cryptography. Future work
would involve researching the use of different combinations of multiple Chua
Reservoir Computers in larger neural network architectures. Such architectures
may produce the required high-dimensional behaviour to achieve the Learning
with Errors problem.
This project is believed to be only the second instance of a Chua-based
Reservoir Computer in academia, and it is the first to be applied to
challenging real-world tasks such as Post-Quantum Cryptography. It is also
original by its investigation of hitherto unexplored parameters, and their
impact on performance. It demonstrates a proof-of-concept for a
mass-producible, inexpensive, low-power consumption hardware neural network. It
also enables the next stages in research to occur, paving the road for using
Chua-based Reservoir Computers across various applications.

本研究旨在基于混沌 Chua 电路开发一种新的储层计算机实现。该实现被应用于后量子密码学，研究并评估了其适用性。研究结果表明，Chua 基础的储层计算机在当前文献基准下具有低误差，但在解决后量子密码学中高非线性问题方面不足够复杂。未来的研究将探索在更大的神经网络结构中使用多个 Chua 储层计算机的不同组合，以实现所需的高维行为来解决学习中的错误问题。该研究为 Chua 基础的储层计算机在学术界的应用提供了第二个案例，并首次应用于后量子密码学等具有挑战性的实际任务。研究还通过调查迄今为止未探索的参数及其对性能的影响展示了创新性，并证明了一种可批量生产、廉价且低功耗的硬件神经网络的概念验证，为后续研究奠定了基础，为 Chua 基础的储层计算机在各种应用中的使用铺平了道路。

基于混沌 Chua 电路的新型储备计算核心及其在后量子密码学中的应用研究

New Reservoir Computing Kernel Based on Chaotic Chua Circuit and  Investigating Application to Post-Quantum Cryptography

In recent years, quantum computers and Shor quantum algorithm have posed a
threat to current mainstream asymmetric cryptography methods (e.g. RSA and
Elliptic Curve Cryptography (ECC)). Therefore, it is necessary to construct a
Post-Quantum Cryptography (PQC) method to resist quantum computing attacks.
Therefore, this study proposes a PQC-based neural network that maps a
code-based PQC method to a neural network structure and enhances the security
of ciphertexts with non-linear activation functions, random perturbation of
ciphertexts, and uniform distribution of ciphertexts. In practical experiments,
this study uses cellular network signals as a case study to demonstrate that
encryption and decryption can be performed by the proposed PQC-based neural
network with the uniform distribution of ciphertexts. In the future, the
proposed PQC-based neural network could be applied to various applications.

该研究提出了一种基于 PQC 的神经网络，通过非线性激活函数、密文的随机扰动和均匀分布来增强密文的安全性，并以蜂窝网络信号为案例研究，证明了该方法可以实现加密和解密。未来，该基于 PQC 的神经网络可以应用于各种应用领域。

后量子密码神经网络

Post-Quantum Cryptography Neural Network

Learning with Errors (LWE) is a hard math problem underlying recently
standardized post-quantum cryptography (PQC) systems for key exchange and
digital signatures. Prior work proposed new machine learning (ML)-based attacks
on LWE problems with small, sparse secrets, but these attacks require millions
of LWE samples to train on and take days to recover secrets. We propose three
key methods -- better preprocessing, angular embeddings and model pre-training
-- to improve these attacks, speeding up preprocessing by $25\times$ and
improving model sample efficiency by $10\times$. We demonstrate for the first
time that pre-training improves and reduces the cost of ML attacks on LWE. Our
architecture improvements enable scaling to larger-dimension LWE problems: this
work is the first instance of ML attacks recovering sparse binary secrets in
dimension $n=1024$, the smallest dimension used in practice for homomorphic
encryption applications of LWE where sparse binary secrets are proposed.

使用三种关键方法：更好的预处理、角度嵌入和模型预训练，以提高对 LWE 的机器学习攻击，加速预处理 25 倍，提高模型样本效率 10 倍，并首次证明预训练改进和降低了对 LWE 的机器学习攻击的成本。