Dual Functional Commitments for Arbitrary Circuits of Bounded Sizes

Abstract

A functional commitment (FC) commits to a value x, and can later generate a proof for a function value y = f (x) w.r.t. some function \text{f}\in \mathcal{F}. In contrast, the dual functional commitment (dual FC) allows a committer to commit to a function \text{f}\in \mathcal{F}, and later produces an opening proof π for the function value y = f(x) given an input x.

We propose a new construction of dual FC scheme from lattices. Our scheme is the first dual FC that can support arbitrary circuits of bounded sizes. Moreover, our dual FC scheme enjoys computational binding, and we prove the computational binding property of our dual FC based on the l-succinct H-SIS assumption, a falsifiable generalization of the l-succinct SIS assumption introduced by Wee (Crypto 2024), in the random oracle model. Moreover, our dual FC scheme is quasi-succinct with a succinct commitment and a quasi-succinct opening proof.

Keywords

Dual Functional Commitment / Arbitrary Circuits / Lattice

RIGHTS & PERMISSIONS

Higher Education Press 2026

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