基于LWE密码系统的动态反馈控制器的全同态加密全面介绍
Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-based Cryptosystem
AI总结：
本文介绍了基于LWE问题的密码系统，该系统通过在密文注入随机错误来保证安全性，尽管这会限制同态运算的递归操作，但在动态反馈控制器中可以克服这一限制，从而构建安全的反馈控制系统。
摘要：
基于学习误差（LWE）问题的密码系统被视为后量子密码系统，因为它不依赖于量子计算机容易解决的大素数分解问题。此外，基于LWE的密码系统允许完全同态运算，使得两个加密变量可以相加和相乘而无需解密。本章提供了基于LWE的密码系统的全面介绍，并通过示例说明。LWE基于密码系统的安全关键在于在密文中注入随机错误，然而这会由于误差的增长而阻碍对密文进行无限递归同态运算。我们展示当该密码系统用于保证闭环系统稳定性的动态反馈控制器时，可以克服这一限制。最后，通过MATLAB代码说明如何将LWE基于密码系统定制化以构建安全的反馈控制系统。本章为没有密码系统背景的控制工程师编写。
英文摘要：
The cryptosystem based on the Learning-with-Errors (LWE) problem is considered as a post-quantum cryptosystem, because it is not based on the factoring problem with large primes which is easily solved by a quantum computer. Moreover, the LWE-based cryptosystem allows fully homomorphic arithmetics so that two encrypted variables can be added and multiplied without decrypting them. This chapter provides a comprehensive introduction to the LWE-based cryptosystem with examples. A key to the security of the LWE-based cryptosystem is the injection of random errors in the ciphertexts, which however hinders unlimited recursive operation of homomorphic arithmetics on ciphertexts due to the growth of the error. We show that this limitation can be overcome when the cryptosystem is used for a dynamic feedback controller that guarantees stability of the closed-loop system. Finally, we illustrate through MATLAB codes how the LWE-based cryptosystem can be customized to build a secure feedback control system. This chapter is written for the control engineers who do not have background on cryptosystems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
