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Research

Transparent Constant-Size Zero-Knowledge Proofs Eliminate Trusted Setup

This breakthrough cryptographic primitive, based on Groups of Unknown Order, yields a truly succinct zk-SNARK without a trusted setup, unlocking scalable, trustless computation.
November 22, 20253 min

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Briefing

The core research problem is the foundational trade-off in zk-SNARKs between succinctness (constant proof size) and transparency (no trusted setup). The paper proposes a new Polynomial Commitment Scheme, Dew-PC, which leverages Groups of Unknown Order (GUO) and an inner-product argument structure to achieve both properties simultaneously. This new mechanism enables Dew , a zk-SNARK that is both constant-sized and transparent, fundamentally resolving a major challenge in cryptographic design and paving the way for truly trustless, highly scalable layer-two architectures.

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Context

Before this research, zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) were broadly categorized into two types ∞ those with constant-sized proofs and fast verification (like KZG-based schemes) that required a trusted setup (SRS) , and those with a transparent setup (like STARKs) that had quasi-linear proof sizes and slower verification. This established dichotomy forced developers to choose between trust assumptions and proof efficiency, representing a critical limitation in scaling decentralized systems where universal trustlessness is paramount.

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Analysis

The core idea is the construction of Dew-PC , a new polynomial commitment scheme. It fundamentally differs from KZG by relying on Groups of Unknown Order (GUO) instead of bilinear pairings and a trusted setup. Dew-PC uses a transparent, public-coin inner-product argument to commit to a polynomial.

This commitment scheme is then compiled into the full Dew zk-SNARK. The use of GUO allows the system’s security to be rooted in a standard cryptographic assumption (the hardness of factoring or finding the order of the group), thereby eliminating the need for any secret randomness generation ceremony while maintaining the highly desirable property of constant-sized proofs.

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Parameters

  • Proof Size ∞ O(1) (Constant Size) ∞ The proof size remains constant, regardless of the size (N) of the computation being proven, which is the key measure of succinctness.
  • Setup Requirement ∞ Transparent (Public-Coin) ∞ The system’s public parameters are generated without any secret trapdoor, eliminating the need for a trusted setup ceremony.
  • Underlying Cryptography ∞ Groups of Unknown Order ∞ Security is based on the hardness of computing discrete logarithms in groups where the order is unknown, a standard cryptographic assumption.

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Outlook

This research unlocks the next generation of zero-knowledge rollups and decentralized state verification. In the next 3-5 years, this primitive could become the foundational proof system for Layer 2 scaling solutions, eliminating the single largest point of trust in current zk-rollups that rely on a trusted setup. It opens new research avenues in optimizing prover time for GUO-based schemes and exploring post-quantum security for this new class of transparent, succinct arguments.

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Verdict

The creation of a constant-sized, transparent zk-SNARK resolves the most critical trade-off in cryptographic succinctness, establishing a new, more secure foundation for all verifiable computation.

Zero-knowledge proofs, Transparent setup, Constant-size proofs, Polynomial commitment, Groups of unknown order, Succinct argument, Inner product argument, Cryptographic primitive, Verifiable computation, Trustless setup, Asymptotic security, Public-coin protocol, Cryptographic assumption, Non-interactive argument, Proof system design Signal Acquired from ∞ arxiv.org

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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.

constant-sized proofs

Definition ∞ Constant-sized proofs are cryptographic proofs whose size remains fixed regardless of the computation's complexity.

groups of unknown order

Definition ∞ Groups of unknown order refer to a mathematical concept used in advanced cryptography, particularly in constructions like RSA accumulators and verifiable delay functions.

cryptographic assumption

Definition ∞ A cryptographic assumption is a fundamental premise about the computational difficulty of solving certain mathematical problems, forming the basis for the security of cryptographic systems.

succinctness

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

trusted setup

Definition ∞ A trusted setup is a preliminary phase in certain cryptographic protocols, particularly those employing zero-knowledge proofs, where specific cryptographic parameters are generated.

unknown order

Definition ∞ Unknown order in cryptography refers to a mathematical group whose order, or the number of elements it contains, is not publicly known.

zero-knowledge

Definition ∞ Zero-knowledge refers to a cryptographic method that allows one party to prove the truth of a statement to another party without revealing any information beyond the validity of the statement itself.

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.

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