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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (11): 2409-2417    DOI: 10.3785/j.issn.1008-973X.2025.11.020
计算机技术     
基于紧凑零知识证明的海上位置共享方案
王沁雪1,2(),张文芳1,2,*()
1. 西南交通大学 信息科学与技术学院，四川 成都 610031
2. 西南交通大学 信息安全与国家计算网格实验室，四川 成都 610031
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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摘要：

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    
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
收稿日期: 2024-11-01 出版日期: 2025-10-30
:  TP 393  
基金资助: 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）.
通讯作者: 张文芳     E-mail: yukikiwa@163.com;wfzhang@swjtu.edu.cn
作者简介: 王沁雪（2000—），女，硕士生，从事区块链隐私保护的研究. orcid.org/0009-0001-9197-3865. E-mail：yukikiwa@163.com
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引用本文:

王沁雪,张文芳. 基于紧凑零知识证明的海上位置共享方案[J]. 浙江大学学报(工学版), 2025, 59(11): 2409-2417.

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.

链接本文:

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

图 1  CZKP-1t-MPS系统的架构
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.
  
图 2  不同匿名集大小下CZKP-1t的性能表现
方案Tp/msTv/ms
文献[13]方案2 096584
文献[16]方案384288
本文方案776536
表 1  零知识证明实测计算开销的对比（匿名集t = 256）
数据交易阶段T/ms
文献[12]方案本文方案
数据上传5 450324
数据购买19 000437
数据获取6 5503 692
取款18 2505 863
验证6273
表 2  与BP3-MTS的计算开销对比
交易类型交易输出输出大小/B
${\mathrm{Trans}} _{ {{\mathrm{create}} }}$$4|{G}|+3\left|{Z}_q\right|+|{\mathrm{s n}}|$260
${\mathrm{Trans}} _{ {{\mathrm{PubData}} }}$$4|{G}|+5\left|{Z}_q\right|+|V|$296
${\mathrm{Trans}} _{ {{\mathrm{PurData}} }}$$27|{G}|+22\left|{Z}_q\right|+|{\mathrm{s n}}|$1 600
${\mathrm{Trans}} _{ {{\mathrm{FetSata}} }}$$14|{G}|+34\left|{Z}_q\right|$1 550
${\mathrm{Trans}} _{ {{\mathrm{RefreData}} }}$$27|{G}|+38\left|{Z}_q\right|$2 107
${\mathrm{Trans}} _{ {{\mathrm{Deposit}} }}$$24|{G}|+21\left|{Z}_q\right|+|{\mathrm{s n}}|$1 496
表 3  CZKP-1t-MPS中交易的输出大小
数据共享阶段c/B
BP3-MP3[12]CZKP-1t-MPS
Setup481×106162
PublishData398468
PurchaseData3861927
FetchData1921648
RefreshPayment3202303
DepositPayment1691
表 4  CZKP-1t-MPS与其他方案的通信开销对比
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