| 摘要: |
| 向量承诺是对一组长度为d的有序元素(m_1,...,m_d)进行的承诺,后续可以打开特定位置的元素值。现有的功能性比较完备的向量承诺方案通常需要进行可信设置,不具备透明性,方案中陷门的泄露将会使恶意证明者能够随意生成证明,导致方案变得很不安全。除了透明性,零知识性与抗量子性在大部分向量承诺方案中也缺乏考虑,使得方案容易遭到敌手的攻击,也将面临量子计算机的挑战。本文基于Fast Reed-Solomon Interactive Oracle Proofs of Proximity(FRI),结合拉格朗日多项式插值法,设计了同时具备透明性、抗量子性以及诚实验证者零知识性质的向量承诺方案FRI-VC。除了具备向量承诺的基本功能外,FRI-VC还能够实现同一向量中多个位置元素的同时打开与验证以及不同向量多个位置元素的同时打开与验证,所需证明长度与打开单个向量某一个位置元素时的证明长度相同。本文对FRI-VC方案的安全性进行了详细的证明,同时与其他几个典型的向量承诺方案进行了对比。 |
| 关键词: 向量承诺 透明性 抗量子性 零知识性 |
| DOI：10.19363/J.cnki.cn10-1380/tn.2023.08.45 |
| 投稿时间：2021-09-15修订日期：2021-11-15 |
| 基金项目:国家自然科学基金项目(No.61932019、No.61772521和No.61772522)；中科院前沿学科重点研究项目(No.QYZDB-SSW-SYS035) |
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| FRI-VC: A Transparent and Zero-Knowledge Vector Commitment Scheme |
|
Yang Liuyu, Zhang Xinxuan, Deng Yi
|
| (1.State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences 2.School of Cyber Security, University of Chinese Academy of Sciences) |
| Abstract: |
| Vector commitment is a commitment to an ordered sequence of elements (m_1,...,m_d) of length d, and the elements at specific positions can be opened later. The existing vector commitment schemes with relatively complete functions usually need trusted setup and are not transparent. The disclosure of trapdoors in the scheme will enable malicious prover to generate proofs at will, resulting in the scheme becoming very unsafe. In addition to transparency, zero-knowledge and quantum-resistant properties are not considered in most schemes either, which makes the scheme vulnerable to be attacked by adversaries and will face the challenge of quantum computers. In this paper, we present a transparent, quantum-resistant and honest verifier zero-knowledge vector commitment scheme named FRI-VC based on Fast Reed Solomon Interactive Oracle Proofs of Proximity(FRI) and Lagrange Polynomial Interpolation. In addition to the basic function of vector commitment, FRI-VC can also open and verify at the same time of both elements at multiple locations in the same vector and elements at multiple locations across different vectors. The proof length required is the same as when opening an element at a certain location of a single vector. In this paper, the security of FRI-VC scheme is proved in detail, and the scheme is also compared with several other typical vector commitment schemes. |
| Key words: vector commitment transparency quantum resistance zero-knowledge property |
