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arXiv:2604.21410 · SICE Annual Conference (SICE)

Encrypted Visual Feedback Control Using RLWE-Based Cryptosystem

Taichi IKEZAKI, Kaoru Teranishi

Published Sep 1, 2026• 0 citations
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Abstract

This study proposes an encrypted visual feedback control algorithm for regulating a one-dimensional stage using Ring Learning With Errors (RLWE) encryption. The proposed algorithm performs both feature extraction and controller computations directly on encrypted images, ensuring that sensitive visual data remain protected throughout the entire control process. Furthermore, an image captured by the camera is encrypted into a single ciphertext leveraging the message packing technique of RLWE encryption, thereby reducing computational cost. The effectiveness of the proposed framework is demonstrated through numerical simulations.

DOI
10.23919/sicefes71276.2026.11739272

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This study proposes an encrypted visual feedback control algorithm for regulating a one-dimensional stage using Ring Learning With Errors (RLWE) encryption. The proposed algorithm performs both feature extraction and controller computations directly on encrypted images, ensuring that sensitive visual data remain protected throughout the entire control process. Furthermore, an image captured by the camera is encrypted into a single ciphertext leveraging the message packing technique of RLWE encryption, thereby reducing computational cost. The effectiveness of the proposed framework is demonstrated through numerical simulations.
In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller exhibits lower computational complexity compared to existing encrypted controllers implemented on LWE based schemes due to the polynomial structure of Ring-LWE. However, the structural difference introduces additional difficulties in analyzing the effect of error growth; Ring-LWE based schemes inject multiple error coefficients when encrypting a single message, which accumulate under recursive homomorphic multiplications. We show that their effect on the control performance can be arbitrarily bounded by the closed-loop stability, thus recovering the performance of the unencrypted controller. Furthermore, a novel method to “pack” a vector into a polynomial is presented, which enhances computational and memory efficiency when applied to the proposed encrypted controller. The effectiveness of the proposed design is demonstrated through numerical simulations.
Multimedia contents are inherently sensitive signals that must be protected when processed in untrusted environments. The field of Secure Signal Processing addresses this challenge by developing methods which enable operating with sensitive signals in a privacy-conscious way. Recently, we introduced a hard lattice problem called m-RLWE (multivariate Ring Learning with Errors) which gives support to efficient encrypted processing of multidimensional signals. Afterwards, Bootland et al. presented an attack to m-RLWE that reduces the security of the underlying scheme from a lattice with dimension \prod_in_i to \max\n_i\ _i . Our work introduces a new pre-/post-coding block that addresses this attack and achieves the efficient results of our initial approach while basing its security directly on RLWE with dimension \prod_in_i, hence preserving the security and efficiency originally claimed. Additionally, this work provides a detailed comparison between a conventional use of RLWE, m-RLWE and our new pre-/post-coding procedure, which we denote "packed''-RLWE. Finally, we discuss a set of encrypted signal processing applications which clearly benefit from the proposed framework, either alone or in a combination of baseline RLWE, m-RLWE and "packed''-RLWE.
Quantum-secure cryptography is a dynamic field due to its crucial role in various domains. This field aligns with the ongoing efforts in data security. Post-quantum encryption (PQE) aims to counter the threats posed by future quantum computers, highlighting the need for further improvement. Based on the learning with error (LWE) system, this paper introduces a novel asymmetric encryption technique that encrypts entire messages of n bits rather than just 1 bit. This technique offers several advantages including an additive homomorphic cryptosystem. The robustness of the proposed lightweight public key encryption method, which is based on a new version of LWE, ensures that private keys remain secure and that original data cannot be recovered by an attacker from the ciphertext. By improving encryption and decryption execution time—which achieve speeds of 0.0427 ms and 0.0320 ms, respectively—and decreasing ciphertext size to 708 bits for 128-bit security, the obtained results are very promising.
Ring-LWE (Ring Learning With Errors) is a post-quantum cryptography algorithm based on mathematical problems in number theory and algebra. It is an extension of LWE (Learning With Errors) first introduced by Oded Regev and is used for secure data encryption from quantum computer attacks. The process consists of three main steps: key generation, encryption, and decryption. Key generation uses random polynomials and noise to create public and private keys. While encryption produces ciphertext in the form of polynomial pairs, decryption uses the private key to return the ciphertext to the original message. To conduct the experiment, the modulus value q = 17, the modulus polynomial f(x) = x2 + 1, and the private key and random polynomial have been determined. The results of the experiment show that the message can be accurately decrypted using the private key, thus proving the success of this algorithm in maintaining data security. With its security properties that are resistant to quantum attacks, Ring-LWE is a promising alternative for future cryptography.
The design of encrypted controllers, which perform control operation directly over encrypted signals via homomorphic cryptosystems, should consider both security of the control data and performance of the controller. Considering the use of Learning With Errors (LWE) based cryptosystem, in this paper, we present a design procedure for encrypted linear dynamic controllers. Providing a guideline for choosing the parameters of the cryptosystem as well as quantization, the procedure guarantees both the desired level of security and performance. Receiving the encrypted signals of the plant input as well as the output, the proposed controller is able to perform the dynamic operation over encrypted data for infinite time horizon, without the use of decryption or reset of the state. Thanks to additively and multiplicatively homomorphic property of the LWE-based cryptosystem, information of both control signals and gain matrices is protected by encryption.
Ring Learning With Errors (Ring-LWE) is one of the basic schemes used to develop cryptographic algorithms that are resistant to quantum attacks, offering better computational efficiency compared to standard Learning With Errors (LWE). Ring-LWE uses the algebraic characteristics of polynomial rings to create a robust and fast encryption system. This study implements and evaluates the Ring-LWE algorithm in the context of public key exchange and encryption. Simulations are performed with various security parameters, including modulus size and error rate, to test the resistance to brute force attacks and lattice-based attacks. The experimental results show that the Ring-LWE algorithm can achieve a balance between security and computational efficiency, with shorter processing time than conventional LWE while maintaining a high level of security even in the face of quantum computers. From this study, it can be concluded that Ring-LWE is an excellent choice for application in post-quantum security systems, especially in encrypted communication and digital authentication applications. The next step can be directed at optimizing resource utilization and testing against various types of attacks.