Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.Comment: Improved numerical exampl

Key schedule algorithm based on coordinate geometry of a three-dimensional hybrid cube

Cryptographic algorithms play an important role in information security where it ensures the security of data across the network or storage. A key schedule algorithm is the mechanism that generates and schedules all session-keys for the encryption process. The 2-dimensional hybrid cube is generated based on permutation and combination of integer numbers that are utilized in the construction of encryption and decryption key in the non-binary block cipher. The generation of key space by using the 2-dimensional hybrid cubes are not sufficient to resist attacks and could easily be exploited. Therefore, the large key space is more desirable to resist any attack on the secret key. This research proposed a new Key Schedule Algorithm based on the coordinate geometry of a Hybrid Cube (KSAHC) for the non-binary block cipher. By using the three-dimensional hybrid cube in KSAHC transformation, encryption keys are represented as n × n × n matrix of integer numbers and used in the development of the permutation and substitution of order 4 square matrix. Triangular Coordinate Extraction (TCE) technique has also been introduced to extract the coordinates during the rotation of Hybrid Cube surface (HCs) and plays an important role in the development of KSAHC algorithm. The Hybrid Cube Encryption Algorithm (HiSea) has been implemented to validate the encryption keys that are generated from the proposed algorithm. The strength of the keys and ciphertext are compared with the Advanced Encryption Standard (AES), HiSea, and Dynamic Key Schedule Algorithm (DKSA). The proposed KSAHC algorithm has been validated using the randomness test proposed and recommended by NIST, the average result of avalanche test is 93%, entropy is 0.9968, correlation assessment test is -0.000601 and having large key space 2.70 × 1067 keys that makes the Brute Force attack difficult and time-consuming. Therefore, it can be concluded that the strength and validity of KSAHC algorithm have been enhanced as compared to other algorithms and can serve as the alternative algorithm in designing security systems