Many new systems have been proposed which hide an easily invertible multivariate quadratic map in a larger structure by adding more variables and introducing some mixing of a random component to the structured system. While many systems which have been formed by attempting to hide the hidden... See full abstract

Many new systems have been proposed which hide an easily invertible multivariate quadratic map in a larger structure by adding more variables and introducing some mixing of a random component to the structured system. While many systems which have been formed by attempting to hide the hidden structure of equations have been broken by observing symmetric properties of the differential of the public key, the dichotomy between the roles of the different types of variables, or even the different types of monomials in the systems, have given rise to differential invariant attacks which distinguish between subspaces corresponding to one type of variable or the other. In this monologue, we take a general approach, and describe a basic construction, TriTon, of which several of the above types of systems are special cases. We analyse this system, and conclude that such constructions are weak with naive choices of parameters.
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