集合交集元素和的保密计算

李顺东; 赵雪玲; 家珠亮

doi:10.12263/DZXB.20211444

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集合交集元素和的保密计算

学术论文 | 更新时间：2025-07-02

- 集合交集元素和的保密计算
- Private Intersection-Sum Computation
- 电子学报 2023年51卷第1期页码：86-92
- 作者机构：
  
  陕西师范大学计算机科学学院，陕西西安 710119
- 作者简介：
  
  [ "李顺东　男，1963年生，河南平顶山人.教授、博士生导师.现为陕西师范大学计算科学学院博士生导师.主要研究领域为密码学与信息安全." ]
  [ "赵雪玲　女，1996年生，陕西西安人.现为陕西师范大学计算机科学学院硕士研究生.主要研究领域为密码学、信息安全、有关集合的保密计算.E-mail： xueling@snnu.edu.cn" ]
  [ "家珠亮　女，1992年生，山西运城人.现为陕西师范大学计算机科学学院硕士研究生.主要研究领域为密码学、信息安全、有关统计量的保密计算.E-mail： zhuliang@snnu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(61272435)
- DOI：10.12263/DZXB.20211444
  中图分类号： TP309.2
- 收稿：2021-10-21，
  
  修回：2022-09-14，
  
  纸质出版：2023-01-25
- 稿件说明：
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李顺东,赵雪玲,家珠亮.集合交集元素和的保密计算[J].电子学报,2023,51(01):86-92.

LI Shun-dong,ZHAO Xue-ling,JIA Zhu-liang.Private Intersection-Sum Computation[J].ACTA ELECTRONICA SINICA,2023,51(01):86-92.
李顺东,赵雪玲,家珠亮.集合交集元素和的保密计算[J].电子学报,2023,51(01):86-92. DOI： 10.12263/DZXB.20211444.

LI Shun-dong,ZHAO Xue-ling,JIA Zhu-liang.Private Intersection-Sum Computation[J].ACTA ELECTRONICA SINICA,2023,51(01):86-92. DOI： 10.12263/DZXB.20211444.

摘要

安全多方计算作为密码学的重要分支，长期以来主要致力于解决两方或多方参与者隐私数据的联合计算.集合交集元素和的隐私计算作为安全多方计算中的科学计算问题，在保密计算广告转化率中具有重要作用.我们利用保密替换和加密选择求集合的交集，结合Lifted ElGamal加密算法，研究了不同限制下（数据范围较小和数据范围较大）集合交集元素和多方保密计算.本文方案解决两方计算时，Bob只需从Alice发送的数据中选择数据，避免了复杂的模指数运算，且双方不需多次交互，降低了计算成本和通信次数.多方参与计算时，根据加密选择和保密替换的性质，得到集合交集的密文，然后在密文上计算得到集合交集元素的和.通过理论分析和实验证明，本文协议是高效的.最后利用模拟范例证明本文协议是安全的.

Abstract

As an important branch of cryptography

secure multi-party computation has long been mainly dedicated to solving the joint computation on private data owned by two or more parties. As a scientific computation problem in secure multi-party computation

secure intersection-sum computation plays an important role in privately computing advertising conversion rate. We use private substitution

encryption selection and lifted ElGamal cryptosystem to design secure intersection-sum protocols for different scenarios

that is

small data range and large data range for multi-party. When the proposed scheme is used to solve the secure intersection-sum for two-party

Bob only needs to choose data from the data sent by Alice without performing expensive modular exponentiations

and the two parties do not need to interact multiple times. The computational cost and communication times are reduced. In the multi-party protocols

all parties use encryption selection and private substitution to obtain some ciphertexts and perform computation on the ciphertexts to obtain the ciphertext of the intersection-sum. Theoretical analysis and experimental results show that our protocol is efficient. Finally

we use the simulation paradigm to strictly prove that our protocol is secure.

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references

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