Paper 2026/1561

DeepBrake: Efficient Row-Wise Reed-Solomon Commitments for Arbitrary Points

Abstract

Brakedown (CRYPTO 2023) is a transparent polynomial commitment scheme with fast proving. Its reliance on codes with small minimum distance forces the protocol to sample more columns to achieve soundness, resulting in larger proof sizes. Replacing the underlying code with Reed-Solomon codes yields better distance properties and should reduce the number of required queries. However, the standard row-wise RS protocol cannot exploit proximity results beyond the unique-decoding radius, such as the Johnson bound (JACM 2023). The bottleneck is structural: the protocol performs two independent checks—proximity testing and evaluation binding. Increasing the proximity radius reduces queries for the first check but increases queries for the second, leaving the overall proof size unchanged. Diamond and Posen (CIC 2024) consolidate these checks when the evaluation point is chosen randomly by the verifier. For predetermined or application-specified points, existing approaches introduce a sumcheck reduction that adds logarithmic rounds and prover overhead. We present DeepBrake, a Reed-Solomon polynomial commitment that consolidates the two checks for arbitrary evaluation points without sumcheck. By fixing row evaluations before the verifier samples the random fold, the protocol uses a single proximity test to verify both properties simultaneously. This enables DeepBrake to exploit stronger proximity bounds and reduce the number of queries. At $n=2^{20}$ and rate $1/2$ over Ft255, DeepBrake's opening phase is $3.5\times$ faster than the Diamond-Posen baseline with sumcheck, with $16.5\%$ lower total prover time and $2.7\%$ larger proof size. We further introduce BrakeWHIR, which replaces the explicit proof elements with succinct polynomial commitment openings using WHIR (EUROCRYPT 2025). BrakeWHIR achieves $2.6\times$ faster verification and $1.9\times$ smaller proofs than DeepBrake.