Block-Accumulate Codes: Accelerated Linear Codes for PCGs and ZK

Linear error-correcting codes with fast encoding and high minimum distance are a central primitive across modern cryptography. They appear prominently in at least two domains: (1) pseudorandom correlation generators (PCGs), which enable sublinear-communication generation of correlations such as oblivious transfer and vector oblivious linear evaluation, and (2) zero-knowledge proof systems, where linear-time encoders underpin proof soundness and scalability. In both settings, the prover or sender must multiply by a large generator matrix $\mathbf{G}$, often with dimensions in the millions, making computational efficiency the dominant bottleneck.

We propose a generalized paradigm for building crypto-friendly binary codes with provable minimum distance. Roughly speaking, these codes are based on randomized turbo codes such as repeat-accumulate codes. We prove linear asymptotic minimum distance and compute the exact expected weight spectrum for concrete sizes. We observe that our codes approach the Gilbert-Varshamov distance bound and outperform prior constructions.

We construct several novel codes, the most promising of which we call Block-Accumulate codes. Among codes with provable distance, our code is $8\times$ faster than the state of the art on a CPU and $50\times$ faster on a GPU; even against aggressive parameters with conjectured distance, it is $3\times$ and $20\times$ faster, respectively. Under these parameters, this yields overall PCG speedups of $2.5\times$ on the CPU and $15\times$ on the GPU, achieving a projected 200$+$ million OTs per second, or about 100 million binary Beaver triples per second, on the GPU (excluding the one-time 10 ms GGM seed expansion). We also observe a $2\times$ encoding speedup and half the peak memory consumption in the Blaze zero-knowledge (PCS) scheme of Brehm et al. (EUROCRYPT '25).