Welcome to the resource topic for 2024/688
Title:
Succinct Functional Commitments for Circuits from k-Lin
Authors: Hoeteck Wee, David J. Wu
Abstract:A functional commitment allows a user to commit to an input \mathbf{x} and later, open the commitment to an arbitrary function \mathbf{y} = f(\mathbf{x}). The size of the commitment and the opening should be sublinear in |\mathbf{x}| and |f|.
In this work, we give the first pairing-based functional commitment for arbitrary circuits where the size of the commitment and the size of the opening consist of a constant number of group elements. Security relies on the standard bilateral k-\mathsf{Lin} assumption. This is the first scheme with this level of succinctness from falsifiable bilinear map assumptions (previous approaches required SNARKs for \mathsf{NP}). This is also the first functional commitment scheme for general circuits with \mathsf{poly}(\lambda)-size commitments and openings from any assumption that makes fully black-box use of cryptographic primitives and algorithms. As an immediate consequence, we also obtain a succinct non-interactive argument for arithmetic circuits (i.e., a SNARG for \mathsf{P}/\mathsf{poly}) with a universal setup and where the proofs consist of a constant number of group elements. In particular, the CRS in our SNARG only depends on the size of the arithmetic circuit |C| rather than the circuit C itself; the same CRS can be used to verify computations with respect to different circuits. Our construction relies on a new notion of projective chainable commitments which may be of independent interest.
ePrint: https://eprint.iacr.org/2024/688
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