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. While our work primarily focuses on the Dob encryption scheme, we also believe that the presented techniques will be of particular interest to the analysis of other big–field schemes.

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