Digital Implementation of Homomorphically Encrypted Feedback Control - PowerPoint PPT Presentation

Digital Implementation of Homomorphically Encrypted Feedback Control for Cyber-Physical Systems J. Tran, F. Farokhi, M. Cantoni, I. Shames MIDAS LAB (Melbourne Information, Decision, and Autonomous Systems Lab) University of Melbourne 1 / 23

A (Somehow) Familiar Problem Decryption System Encryption Actuator Sensor Network Network Encryption Controller Decryption A classical networked control system (NCS) over secure networks: • A cyber-attacker cannot access network data for • Constructing the model of the system; • Driving the states of the system to an unsafe state. 2 / 23

A (Somehow) Familiar Problem with One Glaring Shortcoming “Just because you’re paranoid doesn’t mean they aren’t after you.” – Catch-22 Decryption System Encryption Actuator Sensor Network Network Encryption Decryption Controller The cyber-attacker can hack the control centre and access all information that s/he needs or the cloud provider is dodgy. 3 / 23

In the pursuit of a solution. . . In the proposed solution all exter- nal system-related signals must be encrypted while the performance (stability) of the closed-loop is not compromised. The computations need to be completed in a ‘timely’ fashion. Travis agree: “…There's no obvious solution to this plight Keep it locked, out of sight” “Good” Decryption System Actuator Sensor Encryption Network Controller Network 4 / 23

In the pursuit of a solution. . . Sun Tzu Agrees: “Be extremely subtle, even to the point of formlessness. Be extremely mysterious, even to the point of soundlessness. Thereby you can be the director of the opponent’s fate.” In the proposed solution all exter- nal system-related signals must be encrypted while the performance (stability) of the closed-loop is not compromised. The computations need to be completed in a ‘timely’ fashion. “Good” Decryption Actuator System Sensor Encryption Network Controller Network 5 / 23

Outline Semi-homomorphic Encryption: Implementing the Pallier Method Secure Control Architecture Secure Control Digital Implementation Experiment 6 / 23

Outline Semi-homomorphic Encryption: Implementing the Pallier Method Secure Control Architecture Secure Control Digital Implementation Experiment 7 / 23

Semi-homomorphic Encryption: Implementing the Pallier Method “Ford!” he said, “there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out.” – Douglas Adams, The Hitchhiker’s Guide to the Galaxy • A semi-homomorphic encryption scheme comes with public key κ P , private key κ S , and a group operator ◦ . • In Pallier the group operator is modulo multiplication: • D ( E ( a, κ P ) ◦ E ( b, κ P ) , κ S ) = a + b (ciphertext + ciphertext) • a and b are integers. • Encryption and Decryption require exponentation and multiplication of large numbers. • Large random numbers need to be generated. • ◦ operator the align is modulo multiplication. 8 / 23