Non-linear constraints are mathematical conditions that restrict variables using non-linear equations or inequalities. Unlike linear constraints, these relationships involve terms where variables are multiplied together, raised to powers other than one, or appear within non-linear functions. They define complex, non-convex feasible regions in optimization problems. Such constraints often arise in advanced computational and cryptographic contexts.
Context
In zero-knowledge proof systems, non-linear constraints are necessary to represent complex computations that go beyond simple arithmetic operations. Converting these into efficient circuit representations remains a significant challenge. Research endeavors focus on developing new techniques to handle non-linear constraints more efficiently, which can greatly expand the expressiveness and utility of ZKP applications.
Equifficient Polynomial Commitments introduce a new cryptographic primitive that separates linear and nonlinear constraints, setting the new frontier for zk-SNARK efficiency.
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