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Research

Equifficient Polynomial Commitments Enable Faster, Smaller zk-SNARKs

Research introduces Equifficient Polynomial Commitments, a new primitive that yields Pari, the smallest SNARK at 160 bytes, and Garuda, a prover three times faster than Groth16.
October 29, 20254 min

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Briefing

The core problem in verifiable computation is the asymptotic trade-off between proof size and prover efficiency in succinct non-interactive arguments of knowledge (SNARKs). This research proposes the Equifficient Polynomial Commitment (EPC) scheme, a novel cryptographic primitive that enforces committed polynomials share the same coefficient representation across different bases. This new foundation enables the construction of two distinct, highly optimized SNARKs ∞ Pari , which achieves the smallest known proof size at 160 bytes, and Garuda , which significantly accelerates proof generation by supporting both arbitrary custom gates and free linear gates. This breakthrough directly addresses the computational bottleneck in zk-Rollups and zk-EVMs, promising a future where verifiable computation is both universally fast and minimally burdensome on-chain.

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Context

The foundational challenge in constructing practical SNARKs has centered on minimizing the proof’s size for on-chain verification while simultaneously reducing the off-chain time required for the prover to generate it. Established pairing-based SNARKs, such as Groth16, achieve minimal proof size but are restricted to a single, circuit-specific trusted setup and lack the flexibility to efficiently handle complex, repetitive operations without substantial overhead. Conversely, newer systems that support custom gates or universal setups often sacrifice proof succinctness or increase prover complexity, maintaining a persistent trilemma in cryptographic proof systems. The prevailing theoretical limitation was the lack of a commitment scheme that could simultaneously optimize for both proof size and computational structure.

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Analysis

The paper’s core mechanism is the Equifficient Polynomial Commitment (EPC) , a new flavor of polynomial commitment scheme. Conceptually, a standard polynomial commitment allows a prover to commit to a polynomial and later prove its evaluation at a specific point. The EPC scheme introduces a new constraint ∞ it cryptographically enforces that multiple committed polynomials must share an identical representation (the same coefficients) in a particular basis. This is achieved by integrating the EPC scheme into a hybrid model, where it is specifically used to enforce linear constraints, while the underlying Polynomial Interactive Oracle Proof (IOP) handles the nonlinear constraints.

This architectural separation allows the resulting SNARK, Garuda , to treat all additive constraints as “free” and efficiently incorporate custom gates, drastically reducing the total circuit size and prover computation time. The sister construction, Pari , leverages the same EPC primitive to achieve an unprecedentedly small proof size by using a modified constraint system, optimizing for succinctness.

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Parameters

  • Pari Proof Size ∞ 160 bytes. This is the smallest known proof size for any zk-SNARK, instantiated on the BLS12-381 curve.
  • Garuda Prover Speedup ∞ 3 times faster than Groth16. This metric demonstrates the significant reduction in off-chain proof generation time.
  • Pari Proof Elements ∞ Two group elements and two field elements. This composition defines the minimal cryptographic overhead for the succinct proof.
  • Garuda Gate Support ∞ Free linear gates. This feature eliminates the cryptographic cost for all additive constraints in the circuit.

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Outlook

This research establishes a new frontier in SNARK design by introducing the Equifficient Polynomial Commitment as a powerful primitive. The immediate next step is the engineering and auditing of these constructions for production-grade zk-Rollups and zk-EVMs, where the prover speed of Garuda and the succinctness of Pari offer direct, substantial scaling benefits. In the 3-5 year horizon, the EPC concept is likely to unlock new research avenues in multi-prover and distributed proving systems, enabling highly efficient collaborative zero-knowledge proofs where different parties can contribute to a single, minimal proof over distributed data. The core principle of enforcing coefficient equality via a commitment scheme will be foundational for future compiler-based SNARK frameworks.

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Verdict

The introduction of Equifficient Polynomial Commitments represents a foundational advance in cryptographic efficiency, fundamentally redefining the practical limits of zk-SNARK succinctness and prover performance.

zero knowledge proofs, succinct non-interactive argument, polynomial commitment schemes, cryptographic primitive, prover efficiency, proof size, verifiable computation, circuit complexity, trusted setup, algebraic group model, random oracle model, pairing based cryptography, free linear gates, custom gates, zero knowledge scalability Signal Acquired from ∞ ZK Summit

Micro Crypto News Feeds

cryptographic primitive

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

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.

polynomial commitment

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

succinctness

Definition ∞ Succinctness refers to the quality of being brief but comprehensive in expression.

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.

proof generation

Definition ∞ Proof generation is the process by which participants in a blockchain network create cryptographic proofs to validate transactions or data.

zero-knowledge proofs

Definition ∞ Zero-knowledge proofs are cryptographic methods that allow one party to prove to another that a statement is true, without revealing any information beyond the validity of the statement itself.

polynomial commitments

Definition ∞ Polynomial commitments are cryptographic techniques that allow a party to commit to a polynomial function in a way that enables efficient verification of properties about that polynomial.

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