Overview
Verifying complex off-chain computations efficiently remains one of the main bottlenecks in blockchain scaling solutions. Dispute resolution protocols based on garbled circuit constructions rely heavily on boolean circuit representations, which leads to massive communication and storage requirements.
This research introduces OHMG (One Hot Modular Garbling), a novel garbling scheme designed to address this inefficiency by switching how arithmetic computation is represented inside garbled circuits. Instead of decomposing arithmetic into Boolean gates, OHMG operates natively over small integers using one-hot encodings. The result is a garbling framework where each arithmetic gate requires at most a single ciphertext, regardless of wire size.
OHMG is explicitly designed for privacy-free authenticity-preserving applications. While the evaluator learns all cleartext wires, the protocol guarantees that outputs cannot be forged without possessing valid garblings for the corresponding inputs. This trade-off enables aggressive optimizations that are particularly well suited for verifiable computation, blockchain dispute games, and zero-knowledge proof verification, where correctness and soundness matter more than input privacy.
A key feature of OHMG is its unified wire model, supporting Boolean, arithmetic, and one-hot representations, with efficient translations between them. Many of these operations, such as binary-to-arithmetic conversions, are either free or require only one ciphertext. For multi-input arithmetic functions, OHMG leverages tensor products of one-hot encodings, allowing complex gates to be evaluated with constant single-ciphertext communication cost while shifting complexity to local computation.
The paper formally proves the security of OHMG in the Universal Composability (UC) framework, ensuring that its authenticity guarantees hold even under adaptive corruption and when composed with other protocols. It also presents a concrete blockchain application, showing how OHMG can be integrated with Bitcoin-style UTXOs to enforce correct computation in trustless environments.
Overall, OHMG represents a significant step forward in making arithmetic-heavy verifiable computation practical at scale: reducing circuit size by orders of magnitude while maintaining strong cryptographic guarantees.
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