Towards zero knowledge argument for double discrete logarithm with constant cost

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2024-08-26 DOI:10.1016/j.tcs.2024.114799

Diya Krishnan , Xiang Fu

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Abstract

Given that the Schnorr's protocol for Discrete Logarithm (DLOG) exchanges three messages, it is an interesting problem whether a constant round zero-knowledge protocol exists for the Double Discrete Logarithm problem (DDLOG), i.e., to demonstrate the knowledge of a secret witness x in $g^{h^{x}}$ . In this paper, we show that it exists for a fragment of DDLOG with two restrictions: (1) The outer group of DDLOG supports bilinear pairing, and it needs a trusted set-up for common reference string (CRS). (2) $x < t$ where t is the size of KZG commitment key in CRS. The protocol is zero knowledge and constant round, with $O (1)$ complexity for prover and verifier, regardless of the desired security strength. The contributions of the work are mainly theoretical due to its restrictions and concrete performance.

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以恒定成本实现双离散对数的零知识论证

鉴于离散对数（DLOG）的施诺尔协议（Schnorr's protocol）需要交换三条信息，那么对于双离散对数问题（DDLOG），即在ghx中证明秘密证人x的知识，是否存在恒定轮零知识协议，这是一个有趣的问题。本文证明，DDLOG 的一个片段存在零知识协议，但有两个限制条件：(1) DDLOG 的外群支持双线性配对，并且需要一个可信的共同参考字符串（CRS）设置。(2) x<t 其中 t 是 CRS 中 KZG 承诺密钥的大小。该协议是零知识和恒定回合协议，无论所需的安全强度如何，证明者和验证者的复杂度均为 O(1)。由于其限制和具体性能，这项工作的贡献主要在于理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.