Analysis of Multivariate Encryption Schemes: Application to Dob

In this paper, we study the effect of two modifications to multivariate public key encryption schemes: internal perturbation (ip), and \(Q_+\). Focusing on the Dob encryption scheme, a construction utilising these modifications, we accurately predict the number of degree fall polynomials produced in a Gröbner basis attack, up to and including degree five. The predictions remain accurate even when fixing variables. Based on this new theory we design a novel attack on the Dob encryption scheme, which breaks Dob using the parameters suggested by its designers.