$\textsf{Sluice}$: Prove-Phase Bounded-Memory Groth16 via Read-Write Streaming

We present $\textsf{Sluice}$, a read-write streaming Groth16 prover that reduces $\textit{prove-phase}$ random-access working memory from $\mathcal{O}(N)$ to $\mathcal{O}(\log N)$ once the CRS, QAP, and witness are materialized as private streams. It preserves the standard Groth16 interface: a proof of 3 group elements, 3-pairing verification, and unchanged verifier contracts.

Our key technical contribution is $\textit{Split-Butterfly-Merge}$ ($\mathsf{SBM}$), an NTT algorithm in the read-write streaming model with $\mathcal{O}(\log N)$ memory, $\mathcal{O}(N \log N)$ total I/O, and $\mathcal{O}(\log N)$ sequential passes over external storage.

Combining SBM with streaming sparse R1CS evaluation and chunked Pippenger MSM yields a verifier-compatible Groth16 proving path that exchanges RAM for sequential storage I/O and wall-clock time. Our prototype uses a fixed-window MSM engineering point; the measurements validate memory reduction and proof compatibility, while the theorem states the asymptotically tuned MSM schedule.

We implement $\textsf{Sluice}$ over BN-254. Direct prove-only runs produce valid 128-byte proofs through $N=2^{25}$. The same-size bounded-memory comparison is at $N=2^{23}$: $\textsf{Sluice}$ succeeds under an 8GB Linux cgroup cap, whereas the standard prover is killed under 8GB and 12GB caps and succeeds only at 16GB. These results position $\textsf{Sluice}$ as a storage-rich, RAM-limited proving option rather than a replacement for optimized in-memory provers.