TY - GEN
T1 - Method for Running Dynamic Systems over Encrypted Data for Infinite Time Horizon without Bootstrapping and Re-encryption
AU - Kim, Junsoo
AU - Shim, Hyungbo
AU - Sandberg, Henrik
AU - Johansson, Karl H.
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - In this paper, we propose a method for dynamic systems to operate over homomorphically encrypted data for an infinite time horizon, where we do not make use of reset, re-encryption, or bootstrapping for the encrypted messages. The given system is first decomposed into the stable part and the anti-stable part. Then, the stable part is approximated to have finite impulse response, and by a novel conversion scheme, the eigenvalues of the state matrix of the anti-stable part are approximated to algebraic integers. This allows that the given system can be implemented to operate for an infinite time horizon using only addition and multiplication over encrypted data, without re-encrypting any portion of data. The performance error caused by the approximation and quantization can be made arbitrarily small, with appropriate choice of parameters.
AB - In this paper, we propose a method for dynamic systems to operate over homomorphically encrypted data for an infinite time horizon, where we do not make use of reset, re-encryption, or bootstrapping for the encrypted messages. The given system is first decomposed into the stable part and the anti-stable part. Then, the stable part is approximated to have finite impulse response, and by a novel conversion scheme, the eigenvalues of the state matrix of the anti-stable part are approximated to algebraic integers. This allows that the given system can be implemented to operate for an infinite time horizon using only addition and multiplication over encrypted data, without re-encrypting any portion of data. The performance error caused by the approximation and quantization can be made arbitrarily small, with appropriate choice of parameters.
UR - https://www.scopus.com/pages/publications/85126065970
U2 - 10.1109/CDC45484.2021.9682828
DO - 10.1109/CDC45484.2021.9682828
M3 - Conference contribution
AN - SCOPUS:85126065970
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5614
EP - 5619
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -