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This paper conducts an analysis of algorithms within Polaris, a plausibly post-quantum zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) protocol, by decomposing it into its construction components for detailed investigation. Recognizing the need for fast implementation in real-world applications, we introduce the Ursa Minor, an implementation framework tailored to evaluate Polaris’s efficiency. Our contribution in this framework are twofold: Firstly, we proposed a concrete GKR arithmetic circuit to be integrated in Polaris. Secondly, we optimized the efficiency of FRI protocol employed in Polaris, by eliminating the field inversion operations.

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Ursa Minor: The Implementation Framework for Polaris

  • 会议论文

  • 发表日期：

    2025年

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  • Mohammadtaghi Badakhshan,
  • Guiwen Luo,
  • Tanmayi Jandhyala,
  • Guang Gong

摘要

This paper conducts an analysis of algorithms within Polaris, a plausibly post-quantum zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) protocol, by decomposing it into its construction components for detailed investigation. Recognizing the need for fast implementation in real-world applications, we introduce the Ursa Minor, an implementation framework tailored to evaluate Polaris’s efficiency. Our contribution in this framework are twofold: Firstly, we proposed a concrete GKR arithmetic circuit to be integrated in Polaris. Secondly, we optimized the efficiency of FRI protocol employed in Polaris, by eliminating the field inversion operations.