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On the Size of Pairing-based Non-interactive Arguments of Knowledge

This paper presents a highly efficient construction for a non-interactive argument of knowledge (NIZK), commonly known as a Zero-Knowledge Succinct Non-Interact

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Abstract

This paper presents a highly efficient construction for a non-interactive argument of knowledge (NIZK), commonly known as a Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (ZK-SNARK), which has become known as Groth16. The work focuses on optimizing the size of the proof and the speed of verification, critical factors for the practical deployment of zero-knowledge proofs in various applications, particularly in blockchain and privacy-preserving technologies. Utilizing pairing-based cryptography, the author constructs a SNARK scheme that achieves the shortest possible proof size, consisting of only three group elements, regardless of the complexity of the statement being proven. Furthermore, the verification time is exceptionally fast, involving a constant number of pairing computations. The methodology involves an intricate design of the cryptographic primitives and argument structure to minimize overhead while maintaining strong security guarantees. This research has been profoundly influential, with Groth16 becoming one of the most widely adopted and fundamental SNARK constructions due to its unparalleled efficiency in proof size and verification. Authors: Jens Groth Publication: IACR ePrint Archive Publication date: 2016-01-01

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Key findings

  • The paper introduces Groth16, a construction for Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (SNARKs).
  • Groth16 achieves the shortest possible proof size, consisting of only three group elements.
  • Verification time is constant and very fast, making it highly practical.
  • The construction utilizes pairing-based cryptography to achieve its efficiency.
  • Groth16 has become a foundational scheme for privacy and scalability solutions in blockchain.

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Citation

Jens Groth (2016). On the Size of Pairing-based Non-interactive Arguments of Knowledge. IACR ePrint Archive. https://eprint.iacr.org/2016/260.pdf
Canonical knowledge ID: research:on-the-size-of-pairing-based-non-interactive-arguments-of-knowledge