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Title:
A Lattice-based Designated Verifier zkSNARK from Standard Assumptions
Authors: Mohammad Sadegh Ahmadi, Taraneh Eghlidos, Behzad Abdolmaleki, Ngoc Khanh Nguyen
Abstract:Designated Verifier zero-knowledge Succinct Non-Interactive Arguments of Knowledge (DV-zkSNARKs) are cryptographic argument systems in which the ability to verify proofs is restricted to a designated verifier. Unlike publicly verifiable zkSNARKs, these constructions ensure that only an authorized party can validate the correctness of the proof. Existing lattice-based DV-zkSNARK constructions typically rely on either linear-only encryption (LOE) or linear targeted malleability (LTM). The former does not guarantee security against quantum adversaries, while the latter restricts knowledge soundness to the non-adaptive setting. To address these limitations, we propose an inner product argument system that relies solely on the hardness of the Module Short Integer Solution (MSIS) assumption and achieves knowledge soundness in the random oracle model. This construction enables a designated verifier, holding a secret key, to succinctly verify inner product of a committed witness with an arbitrary vector. By combining our argument system with a linear probabilistic checkable proof (LPCP) compiler, to the best of our knowledge, we obtain the first DV-zkSNARK construction based on standard assumptions. Our implementation achieves prover and verification times comparable to the state of the art, while reducing public parameter size by a factor of 10, at the cost of a 2.5× increase in proof size.
ePrint: https://eprint.iacr.org/2025/2099
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