保护隐私的有理数科学计算

刘旭红; 孙晨

doi:10.11959/j.issn.2096-109x.2022038

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保护隐私的有理数科学计算

学术论文 | 更新时间：2024-06-03

- 保护隐私的有理数科学计算
- Private-preserving scientific computation of the rational numbers
- 网络与信息安全学报 2022年8卷第3期页码：97-110
- 作者机构：
- 作者简介：
  
  [ "刘旭红（1992− ），女，山西吕梁人，上海体育学院助教，主要研究方向为应用数学、密码学理论、安全多方计算、密码学原理与算法" ]
  [ "孙晨（1985− ），女，山东菏泽人，上海体育学院副教授，主要研究方向为控制科学与工程、动作识别、健康数据挖掘" ]
- 基金信息：
- DOI：10.11959/j.issn.2096-109x.2022038
  中图分类号： TP309
- 网络首发：2022-06，
  
  纸质出版：2022-06-15
- 稿件说明：
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刘旭红, 孙晨. 保护隐私的有理数科学计算[J]. 网络与信息安全学报, 2022,8(3):97-110.

Xuhong LIU, Chen SUN. Private-preserving scientific computation of the rational numbers[J]. Chinese Journal of Network and Information Security, 2022, 8(3): 97-110.
刘旭红, 孙晨. 保护隐私的有理数科学计算[J]. 网络与信息安全学报, 2022,8(3):97-110. DOI： 10.11959/j.issn.2096-109x.2022038.

Xuhong LIU, Chen SUN. Private-preserving scientific computation of the rational numbers[J]. Chinese Journal of Network and Information Security, 2022, 8(3): 97-110. DOI： 10.11959/j.issn.2096-109x.2022038.

摘要

安全多方计算作为密码学的基本组成部分，是各种密码协议的基础，是国际密码学界的研究热点。近年来，许多学者研究了各种各样的安全多方计算问题，包括保密的信息比较、保密的集合问题和保密的计算几何等，并提出相应的解决方案。而在许多实际应用场景中，安全多方计算问题需要应用有理数进行描述，因此研究有理数域上的安全多方计算问题具有重要的理论与实际意义。但现有的安全多方计算问题的研究成果大多数局限于整数范围，且研究的数据主要是单维度数据。关于有理数域上多维度数据安全多方计算问题的研究较少且无法推广应用。基于有理数的分数表示形式，设计了新的编码方案（有理数编码方案和有理向量编码方案），可将有理数域上任意维数的数据进行编码，为研究有理数域上其他安全多方计算问题提供了新的解决思路。以该编码方案和单向哈希函数为基础，分别设计了有理数相等、有理向量相等和集合问题的保密判定协议。所设计的协议仅采用基本算术运算和单向哈希函数进行计算，不需要使用公钥加密算法，使得协议的计算效率较高；且协议对研究问题中的数据范围没有限制，适用范围更广。进一步应用模拟范例严格证明了协议在半诚实模型下的安全性；并通过理论分析和模拟实验验证了协议的高效性和适用性。通过具体实例说明协议具有广泛适用性，可以推广应用于其他有理数域的安全多方计算几何问题。

Abstract

As a fundamental part of cryptography

secure multiparty computation (SMC) is a building block of various cryptographic protocols

and it is also a hot topic in the international cryptographic community.In recent years

many SMC problems

such as secret information comparison

secret set problems and secure multiparty computational geometry

have been widely studied.As many practical problems need to be described by rational numbers

it is both theoretically and practically important to study the SMC problems in the rational number field.However

most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field

but they can’t be generalized.Based on the fractional representation of rational numbers

the new encoding schemes about rational numbers and rational number vectors were proposed

which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function

some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm

and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile

and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.

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