Zinc+: SNARKs for Polynomial Rings

Nearly all succinct proof systems express computations as algebraic constraints over a finite field. Operations not native to this field, such as bitwise manipulation, modular arithmetic, and lattice-ring operations, require an arithmetization step that can inflate the witness size by one or more orders of magnitude. We introduce Universal Constraint Systems (UCS) and Zinc$+$. The first is a relation that can express the above constraints with minimal overhead. The second is a framework for bui