# On the Size of Pairing-based Non-interactive Arguments of Knowledge Content type: Research Paper Summary: 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 Key concepts: Jens Groth, zero-knowledge proof, snarks, cryptography, privacy, scalability, pairing-based cryptography, verifiable computation
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On the Size of Pairing-based Non-interactive Arguments of Knowledge

Jens Groth

IACR ePrint ArchiveJanuary 2016

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.

Key Findings

  • 1The paper introduces Groth16, a construction for Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (SNARKs).
  • 2Groth16 achieves the shortest possible proof size, consisting of only three group elements.
  • 3Verification time is constant and very fast, making it highly practical.
  • 4The construction utilizes pairing-based cryptography to achieve its efficiency.
  • 5Groth16 has become a foundational scheme for privacy and scalability solutions in blockchain.

Topics

zero-knowledge proofsnarkscryptographyprivacyscalabilitypairing-based cryptographyverifiable computation
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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

BibTeX

@misc{onthe2016,
  title = {On the Size of Pairing-based Non-interactive Arguments of Knowledge},
  author = {Jens Groth},
  year = {2016},
  howpublished = {\url{https://eprint.iacr.org/2016/260.pdf}},
}

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