📘 Scalable Collaborative zk-SNARK and Its Application to Fully Distributed Proof Delegation

(High-level explanation)

🎯 Problem Motivation

Traditional zk-SNARK proof generation is:

computationally heavy, especially for large circuits, and
typically done by a single prover.

In many real-world systems (blockchains, decentralized protocols, collaborative computations), no single party wants or is able to generate the entire proof alone.

Goal:
Build a protocol where multiple provers can collaboratively (and securely) generate a single zk-SNARK proof without trusting one another and with sublinear communication overhead.

⭐ Main Contributions

1. A general construction of a Collaborative zk-SNARK

This allows N provers to jointly produce a SNARK proof for a computation without sharing private witnesses.

Key properties:

Scales to many provers (scalable MPC-like structure).
Maintains zero-knowledge and soundness even if all but one provers are malicious.
Works with Groth16-style and Plonkish SNARKs depending on instantiation.

2. Introduction of a new primitive: “Collaborative Multi-Exponentiation (CME)”

SNARK proof generation relies heavily on multi-scalar multiplications (MSMs) such as:

\sum_i a_i G_i

In collaborative settings, the vectors $a_i$ (derived from secret witnesses) may be additively shared among provers.

The paper introduces CME, a protocol where:

inputs to the MSM are secret-shared among many provers,
yet the final MSM result is produced without revealing the shares.

CME is the technical core enabling distributed proof generation to be efficient.

3. A fully distributed system for proof delegation

The authors apply their scalable collaborative zk-SNARK construction to create a fully decentralized proving pool.

Use case:
A user wants a proof (e.g., for an L2 rollup, ZK-ML, or verification task), but offloads the computation to a network of distributed provers.

Properties:

User never reveals their secret witness.
No trusted coordinator.
Provers work collectively and are rewarded for their computation.
Robust even under adversarial provers.

This is different from traditional “proof outsourcing” because no single prover computes the whole proof, and no special trust assumptions are needed.

⚙️ How the Collaborative zk-SNARK Works (Intuition)

Step 1 — Secret-sharing the witness

The client splits their witness $w$ into additive shares:

w = w_1 + w_2 + \cdots + w_N

Each prover only gets $w_i$ .

Step 2 — Local computation

Each prover computes:

their share of intermediate polynomial evaluations,
their contribution to constraint polynomials,
shares of randomizers to preserve zero-knowledge.

Step 3 — Collaborative Multi-Exponentiation (CME)

The provers collectively compute large MSMs required for SNARK setup:

No single prover sees the full scalars.
Output is the correct MSM needed by the SNARK prover.

This step replaces the most expensive part of proof generation.

Step 4 — Aggregation into a single SNARK proof

Using CME outputs and local shares, the protocol merges everything into a classical zk-SNARK proof format (e.g., Groth16).

The verifier sees a standard SNARK proof — they cannot tell it was produced collaboratively.

📈 Performance & Scalability

The paper demonstrates:

Near-linear scaling as number of provers increases.
Dramatically reduced per-prover load.
Low communication relative to circuit size (sublinear, dominated by aggregated MSM communication).
Practical performance competitive with centralized provers for large circuits.

🔐 Security Model

The construction gives:

Zero-knowledge: No prover learns anything about the witness.
Soundness: Even if all but one provers are malicious, they cannot fabricate a false proof.
Robustness: System continues functioning despite adversarial dropout (threshold variants supported).

🧭 Applications

✔ Decentralized proving pools

For rollups (e.g., zk-rollup networks) where proof generation must be continuous and expensive.

✔ Distributed ML inference with ZK

Large neural-network proofs can be broken across many GPUs.

✔ On-chain proof markets

Users submit jobs; provers cooperatively generate proofs and get rewarded.

✔ Trust-minimized outsourced proof generation

A user can outsource proof generation without trusting a single prover.

📄 If you want…

I can provide:

✅ A 1-paragraph summary
✅ A whiteboard-style conceptual explanation
✅ A point-by-point explanation of the math (CME, MSM, polynomial commitments)
✅ A slide-ready summary
✅ A comparison with Boojum, Plonky2, multi-prover Halo2, GKR-based MPC, etc.
✅ Pseudocode or diagrams for CME

Adhyayan

Saturday, December 06, 2025