Maritime positioning sharing scheme based on compressing zero-knowledge proof

doi:10.3785/j.issn.1008-973X.2025.11.020

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (11): 2409-2417 DOI: 10.3785/j.issn.1008-973X.2025.11.020

Maritime positioning sharing scheme based on compressing zero-knowledge proof

Qinxue WANG1,2(

),Wenfang ZHANG1,2,*(

)

1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
2. Information Security andNational Computing Grid Laboratory, Southwest Jiaotong University, Chengdu 610031, China

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Abstract

A compact and lightweight zero-knowledge proof algorithm named CZKP-1t was constructed in order to address the issue of insufficient positioning reliability in traditional global navigation satellite systems (GNSS) under atmospheric variation and intentional signal interference. A maritime position data-sharing scheme called CZKP-1t-MPS was proposed by integrating with blockchain technology. This scheme enables position data sharing between conventionally positioned vessels and dynamically positioned vessels equipped with high-precision sensors, effectively enhancing the overall positioning accuracy of the maritime vessel network. The designed position-sharing method severs the connection between the two sharing parties and disassociates the position data from its requester, thereby ensuring strong privacy protection during the sharing process. CZKP-1t-MPS reduces the computational overhead by approximately 78% in the data-sharing process compared with existing maritime position-sharing methods, which guarantees real-time performance in heterogeneous maritime environment.

Key words： zero-knowledge proof blockchain privacy-preserving positioning sharing maritime transportation system

Received: 01 November 2024 Published: 30 October 2025

CLC:

TP 393

Fund: 国家自然科学基金资助项目（U2468201）；四川省科技计划资助项目（2024ZHCG0001）；四川省国际科技创新合作项目（2025YFHZ0161）.

Corresponding Authors: Wenfang ZHANG E-mail: yukikiwa@163.com;wfzhang@swjtu.edu.cn

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Cite this article:

Qinxue WANG,Wenfang ZHANG. Maritime positioning sharing scheme based on compressing zero-knowledge proof. Journal of ZheJiang University (Engineering Science), 2025, 59(11): 2409-2417.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.11.020 OR https://www.zjujournals.com/eng/Y2025/V59/I11/2409

基于紧凑零知识证明的海上位置共享方案

为了解决传统全球导航卫星系统在应对大气变化和故意信号干扰时定位可靠性不足的问题，构造紧凑的轻量级零知识证明算法CZKP-1t，结合区块链技术，提出海上位置数据共享方案CZKP-1t-MPS. 该方案实现了传统定位船舶与配置高精度传感器的动态定位船舶之间的位置数据共享，有效提高了海运船舶网络的整体定位精度. 利用构造的位置共享方法，可以断开位置共享双方，并断开位置数据与其请求者的链接关系，保证了位置共享过程中的强隐私保护. 与现有的海上位置共享方法相比，CZKP-1t-MPS降低了数据共享过程中约78%的计算开销，保证了船舶配备异质环境下海上位置共享的实时性.

关键词： 零知识证明, 区块链, 隐私保护, 位置共享, 海上交通系统

Fig.1 Architecture of CZKP-1t-MPS


PublishData 1）将${\text{Tran}}{{\text{s}}_{{\text{PubData}}}}$解析为 $({\mathrm{pk}}_R,{\mathrm{ED}}_j,\;\delta _i^{{\mathrm{ED}}_j},\;{v_j},\;{\pi _{{\text{pubdata}}}},\;{\sigma _{{R}}})$. 2）若${\mathrm{ED}}_j$在${\text{EDSET}}$中, 则返回0. 3）验证${\pi _{{\text{pubdata}}}}$和${\sigma _R}$是否有效. 若有效, 将${\mathrm{ED}}_j$存入EDSET, 将$\delta _i^{{\mathrm{ED}}_j}$存入, 否则返回0.
PurchaseData 1）将$ {\text{Tran}}{{\text{s}}_{{\text{PurData}}}} $解析为（$ {\mathrm{pk}}_{{U}},{\mathrm{sn}},{C_v},C_{{v_{{U}}}}^*,{\mathrm{au}}{{\mathrm{x}}_R},{\pi _{{\text{purdata}}}},{\sigma _{{U}}}) $ 2）若${\mathrm{sn}} \in {\text{SNSet}}({\mathrm{pk}}_{{U}})$, 则返回0. 3）验证$ {\pi _{{\text{purdata}}}} $和$ {\sigma _{{U}}} $是否有效. 若有效, 则将sn存入${\text{SNSet}}({\mathrm{pk}}_{{U}})$, ${C_v}$存入${\text{PaymentSet}}$, 否则返回0.
FetchData 1）将${\text{Tran}}{{\text{s}}_{{\text{FetData}}}}$解析为$({\mathrm{pk}}_{{U}},{\pi _{{\text{fetdata}}}},{\sigma _{{U}}})$. 2）验证${\pi _{{\text{fetdata}}}}$和${\sigma _{{U}}}$是否有效.若有效, 则将位置数据${D_j}$返回给${\mathrm{pk}}_{{U}}$, 否则返回0.
RefreshPayment 1）将${\text{Tran}}{{\text{s}}_{{\text{Refresh}}}}$解析为$ ({\mathrm{pk}}_{{R}},{\mathrm{tag}},C_{{R}}^{\text{*}},{\pi _{{\text{refresh}}}},{\sigma _{{R}}}) $. 2）若${\mathrm{tag}} \in {\text{TAGSet}}$, 则返回0. 3）验证${\pi _{{\text{refresh}}}}$和$ {\sigma _{{R}}} $是否有效. 若有效, 则返回1, 否则返回0.
DepositPayment 1）解析$ {\text{Tran}}{{\text{s}}_{{\text{Deposit}}}} $为$ ({\mathrm{pk}}_{{R}},{\mathrm{sn}},C_{{v_{{R}}}}^*,{\pi _{{\text{deposit}}}},{\sigma _{{R}}}) $. 2）若${\mathrm{sn}} \in {\text{SNSet}}({\mathrm{pk}}_{{R}})$, 则返回0. 3）验证$ {\pi _{{\text{deposit}}}} $和$ {\sigma _{{R}}} $是否有效. 若有效, 则返回1, 并将sn存入${\text{SNSet}}({\mathrm{pk}}_{{R}})$, 否则返回0.

Fig.2 Performance of CZKP-1t with different anonymity set size

Tab.1 Measured computational cost comparison of zero-knowledge proofs (anonymity set t = 256)

Tab.2 Comparison of computational cost with BP3-MTS

Tab.3 Output size of transactions in CZKP-1t-MPS

Tab.4 Comparison of communication cost of CZKP-1t-MPS with other schemes


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