Research

Equifficient Polynomial Commitments Enable Fastest, Smallest Zero-Knowledge SNARKs

New Equifficient Polynomial Commitments (EPCs) enforce polynomial basis consistency, yielding SNARKs with record-smallest proof size and fastest prover time.
November 2, 20254 min

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Briefing

The core problem in Zero-Knowledge SNARKs is the inherent trade-off between succinct proof size and efficient prover computation, with no single construction simultaneously achieving optimal performance in both. This research introduces the Equifficient Polynomial Commitment Scheme (EPC) , a novel cryptographic primitive that enforces a consistent representation (equal coefficients) of committed polynomials across different components of the SNARK. This foundational mechanism enables the construction of two new SNARKs, Pari and Garuda, which collectively set new performance frontiers → Pari achieves the smallest known proof size, while Garuda delivers the fastest prover time by supporting both free linear gates and custom gates. This theoretical breakthrough fundamentally re-architects the SNARK compiler paradigm, promising a new generation of verifiable computation systems with unprecedented efficiency for blockchain scaling and privacy.

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Context

Prior to this work, SNARK construction relied on polynomial commitment schemes (PCS) like KZG or FRI, which forced developers to choose between minimal proof size (e.g. Groth16’s three elements) and efficient prover time with features like custom gates (e.g. HyperPlonk).

No existing SNARK could leverage the speed of free linear gates and the circuit compression of custom gates while maintaining an optimally succinct proof size. The prevailing challenge was designing a single, unified commitment primitive that could satisfy the stringent consistency requirements of a fast prover without sacrificing the succintness of the final proof.

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Analysis

The Equifficient Polynomial Commitment Scheme (EPC) is a new cryptographic primitive that operates within the SNARK compiler framework. Conceptually, the EPC ensures that a committed polynomial has the same coefficient representation across the different encoding bases used by the SNARK’s underlying Polynomial Interactive Oracle Proof (IOP). This is achieved by using the EPC to enforce linear constraints, while the IOP handles the non-linear constraints. By enforcing this “equal coefficient” property, the EPC acts as a strategic drop-in replacement for a standard PCS, which allows the resulting SNARK constructions (Pari and Garuda) to simultaneously inherit the benefits of linear-time prover techniques (free addition gates) and circuit-specific optimization techniques (custom gates) without the typical increase in proof size or verification complexity.

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Parameters

  • Pari Proof Size → 160 bytes. (The smallest proof size among all known SNARKs, achieved using the BLS12-381 curve).
  • Garuda Prover Speed → 3x faster than Groth16. (The first SNARK to combine free addition gates and custom gates for a significant reduction in proof generation time).
  • New Primitive → Equifficient Polynomial Commitment Scheme (EPC). (A cryptographic primitive that enforces a consistent polynomial representation).

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Outlook

The introduction of the EPC primitive and the resulting SNARKs, Pari and Garuda, opens a new research avenue for hybrid SNARK construction, specifically in optimizing the compiler approach. Future work will focus on generalizing EPCs to a universal and updatable setting, moving beyond the current circuit-specific trusted setup. In 3-5 years, this technology will enable truly stateless clients and highly complex, verifiable computation → such as full-scale verifiable machine learning models → to be executed and verified on-chain with unprecedented speed and minimal data overhead, fundamentally shifting the cost structure of decentralized applications.

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Verdict

This research delivers a foundational cryptographic primitive that resolves the core efficiency trade-off in Zero-Knowledge SNARKs, defining the new performance standard for verifiable computation.

Zero-Knowledge Proofs, SNARK construction, Polynomial Commitment Scheme, Verifiable Computation, Cryptographic Primitive, Proof Size Optimization, Prover Time Efficiency, Equifficient Commitment, Succinct Argument, Trusted Setup, Custom Gates, Free Linear Gates, SNARK Compiler, Algebraic Group Model, Universal Setup, Stateless Clients, Blockchain Scaling, Proof Aggregation, Circuit Arithmetization, Polynomial IOP Signal Acquired from → youtube.com

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polynomial commitment scheme

Definition ∞ A polynomial commitment scheme is a cryptographic primitive that allows a prover to commit to a polynomial in a way that later permits opening the commitment at specific points, proving the polynomial's evaluation at those points without revealing the entire polynomial.

polynomial commitment

Definition ∞ Polynomial commitment is a cryptographic primitive that allows a prover to commit to a polynomial in a concise manner.

succinct proof size

Definition ∞ Succinct proof size refers to the property of a cryptographic proof system where the size of the proof generated is significantly smaller than the computation it verifies.

cryptographic primitive

Definition ∞ A cryptographic primitive is a fundamental building block of cryptographic systems, such as encryption algorithms or hash functions.

proof size

Definition ∞ This refers to the computational resources, typically measured in terms of data size or processing time, required to generate and verify a cryptographic proof.

custom gates

Definition ∞ Custom gates refer to specialized logical operations or functions defined within the algebraic circuits used for zero-knowledge proofs.

commitment scheme

Definition ∞ A commitment scheme is a cryptographic primitive allowing a party to commit to a chosen value while keeping it hidden, with the ability to reveal it later.

verifiable computation

Definition ∞ Verifiable computation is a cryptographic technique that allows a party to execute a computation and produce a proof that the computation was performed correctly.

zero-knowledge snarks

Definition ∞ Zero-Knowledge SNARKs, which stands for Succinct Non-interactive ARguments of Knowledge, are a cryptographic proof system allowing one party to prove they possess certain information without revealing the information itself.

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