Performance Analysis of the Quantum Safe Multivariate Polynomial Public Key Algorithm

Abstract

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.