# Overview of Multi-Variate Function Based Public-Key Cryptography and Cryptanalysis

In this talk, we will first give an introduction on multivariate public key cryptography with the emphasis on the fundamental cryptanalysis tools. We will then discuss a new quantum attack algorithm developed by Gao etc against the multivariate schemes using the HHL quantum algorithm. The complexity of this algorithm depends on the so-called condition numbers.

The work of Gao etc claims that there is a possibility such an algorithm is polynomial asymptotically. If it is indeed true, then we will have a quantum algorithm to solve a NP-complete problem in polynomial time. We will present a proof we developed recently that in general this new algorithm is actually exponential in terms of its complexity in solving a set of quadratic equations over a finite field. This second part of the talk is a joint work with Vlad Gheorghiu from University of Waterloo.

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mpkc-hhl-1.pdf | 731.87 KB |