What Cost Savings Should I Expect When Migrating From Single-Proof Verification to High-Throughput Batching on Polygon?

Short description: Moving from single-proof verification to high-throughput batching on Polygon routinely cuts on-chain verification gas by 70–95% per proof, while also unlocking higher throughput and simpler UX. This guide quantifies those savings with current gas math, live network parameters, and concrete implementation patterns you can ship.

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TL;DR for decision‑makers

• Today, verifying one Groth16 proof on an EVM chain costs about 200k–250k gas plus ~7k per public input; STARK verifications often exceed 1M gas. On Polygon PoS, that translates to roughly $0.05–$0.10 per Groth16 verify at current gas and POL prices. (medium.com)
• Switching to batching typically drops per‑proof gas into the 15k–50k band (70–95% savings), with constant‑cost “O(1)” verification possible via recursive aggregation (~350k gas per batch), and signature aggregation (BLS) for attestation‑heavy flows (~113k gas flat). (blog.nebra.one)

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Why this matters now on Polygon

• Polygon PoS uses POL as gas since Sept 4, 2024; the MATIC→POL migration is effectively complete. All fees you pay and optimize against are in POL. (polygon.technology)
• The network has been raising capacity and lowering confirmation times (PIPs to lift block gas ceiling, Heimdall v2 for faster finality). Capacity uptrends mean bigger batches fit per block; faster finality reduces UX latency penalties when you wait for a batch to land. (forum.polygon.technology)
• Current Polygon gas tracker: sub‑cent base fees for simple transfers; blocks routinely under 50% utilization—i.e., batch room exists most of the time. (polygonscan.com)

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Baseline: what a “single-proof” costs on EVM today

For Groth16 on BN254 (alt_bn128), post‑Istanbul/EIP‑1108 gas math is well-characterized:

• Pairing check precompile = 45,000 base + 34,000 per pairing. Typical Groth16 verifiers use 3–4 pairings → 147k–181k gas just for pairings. Add calldata and scaffolding and you land ~200k–250k gas (+~7,160 per public input). (eips.ethereum.org)
• Calldata cost baseline: 4 gas/zero byte, 16 gas/non‑zero byte (EIP‑2028). Proof payloads are dominated by non‑zero bytes; expect ~4,096 calldata gas for a 256‑byte Groth16 proof (before public inputs). (eips.ethereum.org)

Reality check on Polygon PoS at today’s prices (January 2026):

• Polygonscan base gas around 2,300–2,400 gwei; POL ≈ $0.128. A 220k‑gas verify costs ≈ 0.517 POL ≈ $0.066. Adjust linearly with your observed gas. (polygonscan.com)

Throughput ceiling with one‑by‑one verification: at ~250k gas per verify and a ~45M per‑block gas budget (representative at the chain level), you’re capped near 180–200 proofs per block; even on a fast chain, that bottlenecks high‑volume apps. (docs.alignedlayer.com)

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Batching primitives you can adopt (and when)

Batching isn’t one thing; pick the mechanism that matches your constraints.

1) On‑chain Groth16 batch verification (random linear combination)

• Replace “3 pairings per proof” with “n + 2 pairings total” by combining n proofs via random scalars and checking one equation. Pairings drop from 3n to ~n+2; MSM/ECMUL work increases modestly but is cheap relative to pairings. (fractalyze.gitbook.io)
• Gas model (rough):
  • Pairings: 45k + 34k·(n+2) gas.
  • ECADD/ECMUL: 150/6,000 gas apiece where used (EIP‑1108).
  • Calldata: linear in number of proofs + public inputs. (eips.ethereum.org)

Rule of thumb: at n=100, pairings ≈ 3.51M gas (≈35.1k/proof) plus a few thousand per proof for MSM/calldata, so you often land ~40k–50k gas per proof—an 80%+ reduction vs single‑proof 220k. On Polygon PoS that’s ≈ $0.01/proof at today’s gas. (eips.ethereum.org)

When to use: You need “on‑chain math” with no extra trust and can tolerate proof payload growth and some coder effort in safe batching logic.

Caveats and guardrails:

• Soundness relies on binding randomizers to the batch context; include domain separators and nonces to avoid malleability. (fractalyze.gitbook.io)
• Gas spikes from calldata can dominate for huge n; keep an eye on calldata pricing changes (EIPs 7623/7976 discussions tighten floors for data‑heavy txs over time). (eips-wg.github.io)

2) Off‑chain recursive aggregation → O(1) on‑chain verification

• Aggregate many proofs into one recursive proof verified once on‑chain, e.g., Halo2‑KZG stack. Common deployments measure ~350k gas per aggregated verify, largely independent of batch size. (blog.nebra.one)
• Example: NEBRA’s UPA measured per‑proof on‑chain submission ≈ 20k gas plus ~100k/batch overhead, then a ~350k gas final verify. At batch=32, total ~0.73M gas → ~23k per proof; at batch=100, ~2.35M gas → ~23.5k per proof. (blog.nebra.one)

When to use: You want maximal on‑chain savings and can amortize seconds of off‑chain proving latency. Good for oracle/state attestations, batched mints/claims, and periodic settlement.

Caveats: Proving latency grows with n; parallelize workers and bound batch windows to meet SLOs.

3) Signature aggregation for attestations (BLS)

• If your “proofs” are attestations (oracles, bridge votes, validator signatures), aggregate BLS signatures and verify a single signature. Two pairings (~113k gas) check an arbitrarily large committee signature; this is often the cheapest path for feeds/bridges. (eips.ethereum.org)

When to use: Data availability/attestation heavy flows where the ZK is off‑chain or not needed at all times.

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Worked examples with current Polygon numbers

Assumptions for all examples below: 2,350 gwei gas, POL=$0.128, block gas budget ~45M. Adjust with your ops figures; savings percentages are robust across prices. (polygonscan.com)

Example A — 500 user proofs per minute (Groth16, 2 public inputs)

• Single‑proof: 500 × (220k + 2×7.16k) ≈ 131M gas. That’s 3 blocks worth; per‑proof ≈ $0.066–$0.072. (medium.com)
• On‑chain batch verify (n=100, done 5×/min): ~3.5M gas pairings + ~0.3M gas MSM/calldata ≈ 3.8M per batch → 19M gas/min; ≈ 40k–45k per proof → $0.009–$0.011. ~85% cheaper. (eips.ethereum.org)
• Recursive aggregation (five 100‑proof batches): (5 × 2.35M) ≈ 11.75M gas total/min (including ~350k verify each) → ~23.5k per proof → ~$0.006. ~90%+ cheaper, plus you free blockspace. (blog.nebra.one)

Operational impact:

• Blocks used drop from ~3 to <1 per minute for the same throughput. Your queueing delay goes from “wait 2–3 blocks” to “fits in one block with headroom,” making UX steadier during spikes.

Example B — 50 oracle feeds each second, committee‑signed (BLS)

• Naïve ECDSA per feed: 50 sig verifications + storage writes → hundreds of thousands of gas/second.
• BLS aggregate per second: ~113k gas to check the whole set; even with per‑feed bookkeeping your steady‑state is typically <250k gas/second—an order of magnitude improvement on verification overhead. (eips.ethereum.org)

Example C — Cross‑rollup settlement with a zkEVM proof

• If you verify or settle state to Ethereum L1, post‑Dencun EIP‑4844 blob pricing cut L2 DA costs by an order of magnitude and continues to evolve with higher blob targets. Your L1 leg gets cheaper, and batching on Polygon for the L2‑side verification compounds those savings. (eip4844.com)

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How EIP‑4844 and evolving calldata pricing interact with batching

• Dencun (Mar 13, 2024) introduced blobs for rollup DA on L1, dramatically lowering L2s’ L1 posting costs; future upgrades are raising blob capacity. If your Polygon architecture touches Ethereum for settlement, you get this tailwind “for free.” (eip4844.com)
• Meanwhile, calldata on the EVM keeps getting re‑examined (EIP‑7623 live discussions; EIP‑7976 draft), mostly to discourage extremely data‑heavy transactions. Batching that minimizes calldata per proof (or avoids calldata via recursion) is naturally more future‑proof against such repricings. (eips-wg.github.io)

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Best emerging practices we see working in production

Contract-level

• Hardcode the verification key (VK) in immutable storage/bytecode to avoid SLOAD costs and reduce calldata size; pack points tightly and avoid redundant limbs. Pairing precompile calls dominate, so keep what’s around them minimal. (eips.ethereum.org)
• For batch Groth16, implement the random linear combination technique with domain‑separated challenges (e.g., keccak of batch id, block hash, and commitment to all proofs) to prevent mix‑and‑match malleability. (fractalyze.gitbook.io)
• Prefer event logs over persistent SSTORE for per‑proof receipts unless you truly need on‑chain state for gating. First‑write SSTORE still costs 20k gas; events are cheaper and indexable off‑chain. (ethereum.org)
• If your flow is signature‑heavy, switch to BLS aggregation on BN254 today (two pairings). Keep an eye on BLS12‑381 precompile efforts (EIP‑2537) if/when they land to raise security margins. (eips.ethereum.org)

Batch scheduler and ops

• Derive batch size from a simple model: per_proof_gas ≈ per_proof_overhead + batch_fixed_gas / batch_size. Solve for your target per_proof_gas under block gas and latency SLOs; cap batches at a percentage of current block gas (e.g., ≤40%) to avoid reverts in spikes. (blog.nebra.one)
• Parallelize proving/aggregation workers; keep a “flush on timeout” path so latecomer proofs don’t stall. For multi‑tenant aggregators, shard queues by customer to keep tail latency bounds tight. (blog.nebra.one)
• Monitor: batch fill rate, prove time p50/p95, per‑proof gas, revert rate, calldata bytes per proof, blocks‑to‑finality. Polygon’s recent upgrades target ~2–5s deterministic finality; confirm against the finalized tag in your RPC before releasing funds. (docs.polygon.technology)

Security and correctness

• Bind proofs to application context (chain id, contract address, batch id) inside the statement or via transcript so proofs cannot be replayed across batches or chains. (fractalyze.gitbook.io)
• For any non‑EVM verification path (e.g., off‑chain verification networks or AVSs), document the trust/latency trade‑offs; some stacks offer millisecond verification with BLS‑aggregated attestations on L1 for ~350k gas/batch and ~40k gas/proof at batch=20. Use this when time‑to‑finality matters more than cryptographic minimality. (blog.alignedlayer.com)

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Cost tables you can budget against (Polygon PoS, Jan 2026 snapshot)

• Single Groth16 verify (2 public inputs): ~220k–234k gas → ~0.52–0.55 POL ≈ $0.066–$0.070. (medium.com)
• Batch Groth16 (n=100, on‑chain combine): ~3.8M gas per batch → ~38k/proof → ~0.089 POL/proof ≈ $0.011. Savings ≈ 83–85%. (eips.ethereum.org)
• Recursive aggregation (Halo2‑KZG‑style): ~2.35M gas per 100‑proof batch → ~23.5k/proof → ~0.055 POL/proof ≈ $0.007. Savings ≈ 90–92%. (blog.nebra.one)
• BLS aggregate (committee attestation for any N): ~113k gas flat for the signature verify (+ bookkeeping) → often <250k gas total even for dozens of feeds. Savings grows with N. (eips.ethereum.org)

Note: your absolute $ costs will move with gas and POL price; the percentage savings persist because they’re structural.

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Migration blueprint we recommend

1. Map your proof inventory

• What fraction are zk‑SNARKs vs attestations? What are per‑proof payload sizes and public inputs? Identify “fast path” flows that cannot wait for batch windows.

1. Pick your batching lane per flow

• zk‑proof heavy and tolerant to seconds of latency? Use recursive aggregation.
• High‑frequency attestations/feeds? Switch to BLS aggregation.
• Need cryptographic minimality entirely in‑EVM? Implement random linear combination batching for Groth16.

1. Right‑size batch windows

• Start with 250–500ms windows for feeds (BLS), 2–6s windows for recursive aggregation, and a hard cap at 35–40% of current block gas for each batch submission. Use dynamic windows that shorten in congestion.

1. Minimize calldata and storage

• Pack proofs/inputs; avoid duplicate limbs; emit events instead of SSTORE receipts where feasible. Keep VKs immutable and in bytecode to reduce SLOAD.

1. Prove and verify safely

• Challenge derivation: domain‑separate batches; commit to proof list before deriving randomizers.
• Reorg/finality: write flows against finalized blocks (“finalized” tag) on Polygon PoS to avoid rare finality anomalies. (docs.polygon.technology)

1. Measure and iterate

• Track per‑proof gas, latency p95, revert causes (out‑of‑gas due to gas spikes, calldata underestimates), and batch fill rate. Raise/trim batch windows to hit SLOs.

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Frequently asked objections

• “Polygon is already cheap—why batch?”
  Because you want headroom and predictable UX as you scale. Single‑proof flows hit the same pairings ceiling and block gas ceiling; batching multiplies your effective throughput and makes fees robust to short‑term gas spikes. (docs.alignedlayer.com)

• “Will batching make our system less secure?”
  Not if you implement it correctly. Batch Groth16 uses standard randomness tricks; recursive aggregation has been battle‑tested in rollups. If you use an external verification layer, document its security model (e.g., restaked BLS quorum) and pick it for the right flows. (fractalyze.gitbook.io)

• “What about future EIP changes?”
  Trends favor lower L1 DA via blobs and tighter calldata floors. Batching that reduces calldata per result (or moves it into blobs/recursion) will age well under both. (eip4844.com)

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Bottom line

• On Polygon PoS today, moving from single‑proof verification to high‑throughput batching typically saves 70–95% gas per proof and collapses your verification throughput bottleneck by 5–10×, with no loss of cryptographic assurances when you choose the right mechanism. (medium.com)
• If your architecture settles to Ethereum L1 (zkEVM/appchains), EIP‑4844’s blob market further compounds savings on the settlement leg—so you get “cheaper L1, cheaper L2” when you adopt batching. (eip4844.com)

If you want our team to size your exact savings, we’ll run your trace data through these models and hand back a batch plan with concrete gas and latency SLOs, plus ready‑to‑deploy contracts and a proving/aggregation pipeline.