동적제어계 제어신호의 인증된 계산

학위논문 (석사) -- 서울대학교 대학원 : 자연과학대학 수리과학부, 2020. 8. 천정희.Significant concerns on networked control system are security problems caused by the network or the controller, since a compromise on them can cause a devastating behavior or entire failure of the system. In this paper, we first propose a fundamental solution to this problem by exploiting the verifiable computation to prevent malicious behavior of controller. First, we propose a new authenticated computation to check the matrix-vector multiplications---the main arithmetic of a controller---and to check the updates on the states of the controller. It enables a plant-side not only to check computations of a controller with much less computational cost than that required for the computations itself, but also to detect any compromise on the network or the controller. In addition, the proposed authenticated computation can be applied to linear dynamic systems without any additional asymptotic computational overhead on the actuator and the controller, since the verification cost of the actuator is independent from the dimension of the states. To further reduce the cost of the actuator, we also propose a batch verification and multi-exponentiation method. These methods dramatically reduce the constant overhead of the controller so that the performance estimation of the proposed scheme demonstrates its applicability in practice.제어기나 네트워크에 대한 위조는 위험한 상태나 체계의 정지를 야기할 수 있기에, 제어기 및 네트워크에 대한 보안 문제는 네트워크화된 제어체계가 가진 큰 우려라 할 수 있다.\\ 본 학위 논문에서는 이런 악의적인 제어기 문제를 근본적으로 해결하기 위해 검증가능한 계산을 처음으로 도입한다. 우선, 제어기의 주 연산인 행렬-벡터간 곱셈을 확인하고 제어기의 상태 갱신을 확인하기 위해 인증된 계산을 새로이 제시한다. 이는 플랜트 측으로 하여금 제어기의 계산을 제어기가 행하는 계산량보다 더 적은 계산량으로 확인하게 할 뿐만 아니라, 제어기나 네트워크에 위조가 있는지도 확인 가능하게 해 준다.\\ 또한 제어기 상태의 차원과 액츄에이터의 검증 시 계산량은 독립적이기에, 인증된 계산은 액츄에이터나 제어기에 점근적으로 계산량을 추가하지 않은 채 선형동적제어계에 도입할 수 있다.\\ 이와 더불어 액츄에이터의 계산량을 줄이기 위해 본 논문에서는 묶음 검증과 다중 곱연산을 도입하였다. 이런 개념들은 제어기의 일정한 계산량을 크게 줄여주어서, 이 체계가 실제에 반영할 수 있을 정도로 성능 예측이 가능해지도록 하였다.1 Introduction 1 2 Problem Formulation and Preliminaries 5 2.1 Notation 5 2.2 Problem Formulation 6 2.3 Conversion of Real-valued Parameters to Integers 7 2.4 Verifiable Computation 9 2.5 Freivalds Algorithm: Verifying Matrix Multiplication 10 2.6 Discrete Logarithm Assumption on Finite Group 11 3 Verification of Controller Computation 13 3.1 Four points of proposed VC Scheme 14 3.1.1 Randomized Verification 14 3.1.2 Compressed Commitments 15 3.1.3 Knowledge of Exponent 15 3.1.4 Proof of Equality 16 3.2 VC schemes for linear dynamic system 17 3.3 Security of the proposed VC 19 3.4 Efficiency of the proposed VC 21 3.5 Improving Efficiency 23 3.6 Performance Estimation of proposed scheme 25 4 Conclusions 27 Appendix 32 4.1 Proof of Lemma 2 32 4.2 Necessity of Alternative Random Vector 33 4.3 Algorithms: Batch Verification 34 4.4 Algorithms: Multi-exponentiation 35 Abstract (in Korean) 37 Acknowledgement (in Korean) 38Maste

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