ElGamal-type encryption for optimal dynamic quantizer in encrypted control systems

This study considers a quantizer design problem with controller encryption for minimizing performance degradation caused by encryption. It is difficult to design an optimal dynamic quantizer that converts real numbers to plaintexts for encrypted control systems with ElGamal encryption because the plaintext space of ElGamal encryption is intermittent and does not include zero and negative numbers. A variant of ElGamal encryption is proposed to apply a conventional optimal dynamic quantizer for encrypted control systems. The proposed multiplicative homomorphic cryptosystem, wherein the plaintext space is consecutive integers within a certain range, can handle zero and negative integers properly. Numerical simulations demonstrate that the optimal dynamic quantizer with the proposed cryptosystem improves the control performance of an encrypted regulator. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.