Biblio

The Multivariate Polynomial Public Key (MPPK) algorithm, over a prime Galois field, takes a multiplier multivariate polynomial and two multiplicand univariate solvable polynomials to create two product multivariate polynomials. One of variables is for secret message and all others are for noises. The public key consists of all coefficients of the product multivariate polynomials, except the two constant terms for the message variable. The private key is made of both multiplicands. Encryption takes a list of random numbers, over the prime Galois field. The first number is the secret to exchange. The other random numbers generate noise automatically cancelled by decryption. The secret is easily extracted from the evaluation of a solvable equation. The level of security provided by MPPK is adaptable. The algorithm can be used in several different ways. In this paper, we review the performance achieved by MPPK for several combinations of polynomial configurations and Galois field sizes. For every combination, we calculated key generation time, encryption time and decryption time. We also compare the effectiveness of MPPK with the performance of all four NIST PQC finalists. For MPPK, the data has been collected from the execution of an implementation in Java. In comparison to the NIST PQC finalists, MPPK key generation, encryption and decryption performance is excellent.

This paper is about the estimation of the cyber-resilience of CPS. We define two new resilience estimation metrics: k-steerability and l-monitorability. They aim at assisting designers to evaluate and increase the cyber-resilience of CPS when facing stealthy attacks. The k-steerability metric reflects the ability of a controller to act on individual plant state variables when, at least, k different groups of functionally diverse input signals may be processed. The l-monitorability metric indicates the ability of a controller to monitor individual plant state variables with l different groups of functionally diverse outputs. Paired together, the metrics lead to CPS reaching (k,l)-resilience. When k and l are both greater than one, a CPS can absorb and adapt to control-theoretic attacks manipulating input and output signals. We also relate the parameters k and l to the recoverability of a system. We define recoverability strategies to mitigate the impact of perpetrated attacks. We show that the values of k and l can be augmented by combining redundancy and diversity in hardware and software, in order to apply the moving target paradigm. We validate the approach via simulation and numeric results.

We focus on resilience towards covert attacks on Cyber-Physical Systems (CPS). We define the new k-steerability and l-monitorability control-theoretic concepts. k-steerability reflects the ability to act on every individual plant state variable with at least k different groups of functionally diverse input signals. l-monitorability indicates the ability to monitor every individual plant state variable with £ different groups of functionally diverse output signals. A CPS with k-steerability and l-monitorability is said to be (k, l)-resilient. k and l, when both greater than one, provide the capability to mitigate the impact of covert attacks when some signals, but not all, are compromised. We analyze the influence of k and l on the resilience of a system and the ability to recover its state when attacks are perpetrated. We argue that the values of k and l can be augmented by combining redundancy and diversity in hardware and software techniques that apply the moving target paradigm.