Paper 2026/487 Original: eprint.iacr.org/2026/487 ↗

Linear-Time, Constant-Depth Blind Polynomial Commitments from Generalized RAA Codes, with an End-to-End Blind SNARK Implementation

Abstract

In this work, we construct a new and highly efficient blind polynomial commitment scheme (PCS) over non-binary fields. Our scheme is specifically designed to handle encrypted coefficients without requiring expensive bootstrapping operations, achieving a breakthrough in the "complexity-depth" trade-off. The proposed scheme features an extremely efficient prover both asymptotically and concretely. The commitment and evaluation phases are dominated by a strictly linear $O(n)$ number of field operations. Furthermore, the construction maintains a constant multiplicative depth, which is a critical requirement for efficiency in homomorphic encryption settings. Concretely, for large-scale circuit sizes, our prover is significantly faster than prior state-of-the-art schemes such as phalanx and laminate. Our underlying technique is the Generalized RAA code, an extremely efficient error-correcting code that extends the binary RAA code structure to arbitrary non-binary prime fields $\mathbb{F}_{p}$. We analyze the bounds over non-binary fields, which demonstrate that this code maintains a linear minimum distance property with high probability. By combining Ligero’s IOPP framework, we obtain the first asymptotically and concretely good blind PCS that achieves strictly linear $O(n)$ encoding complexity for the prover while avoiding the expensive bootstrapping operations.