安全高效的隐私保护公共可验证矩阵乘法外包计算方案

doi:10.11959/j.issn.1000-0801.2023251

电信科学 ›› 2023, Vol. 39 ›› Issue (12): 110-121.doi: 10.11959/j.issn.1000-0801.2023251

• 研究与开发 • 上一篇

安全高效的隐私保护公共可验证矩阵乘法外包计算方案

孙守道¹, 杨沈¹, 陈一恒¹, 王强²

¹ 国网辽宁省电力有限公司沈阳供电公司，辽宁沈阳 110002
² 沈阳新龙源电表仪器有限公司，辽宁沈阳 110111

修回日期:2023-12-10 出版日期:2023-12-01 发布日期:2023-12-01
作者简介:孙守道（1990- ），男，国网辽宁省电力有限公司沈阳供电公司工程师，主要从事网络安全、信息系统运维等工作
杨沈（1990- ），男，国网辽宁省电力有限公司沈阳供电公司副高级工程师，主要从事网络安全、信息系统运维等工作
陈一恒（1999- ），男，沈阳新龙源电表仪器有限公司工程师，主要研究方向为安全外包计算
王强（1991- ），男，博士，沈阳新龙源电表仪器有限公司副高级工程师，主要研究方向为网络与信息安全、应用密码学、隐私计算、区块链、联邦学习等
基金资助:
国家电网有限公司辽宁省科技项目(5222SY230004)

Secure efficient privacy-preserving publicly verifiable outsourced computation scheme for matrix multiplication

Shoudao SUN¹, Shen YANG¹, Yiheng CHEN¹, Qiang WANG²

¹ State Grid Liaoning Electric Power Co., Ltd.Shenyang Power Supply Company, Shenyang 110002, China
² Shenyang Xinlongyuan Electric Meter Instrument Co., Ltd., Shenyang 110111, China

Revised:2023-12-10 Online:2023-12-01 Published:2023-12-01
Supported by:
State Grid Co., Ltd.Liaoning Science and Technology Project(5222SY230004)

摘要/Abstract

摘要：

外包计算允许那些资源有限的数据拥有者将复杂的计算外包给资源丰富的云服务器。矩阵乘法在科学计算和密码学领域都有着重要的应用。可验证矩阵乘法外包计算允许数据拥有者将外包矩阵 $M$ 和请求向量 $x$ 外包给不可信的云服务器进行乘法计算，并且验证云服务器返回计算结果的正确性及完整性。但是，现有方案无法同时解决如下问题：外包矩阵 $M$ 的隐私性、请求向量 $x$ 的隐私性、不支持公共验证、效率低下难以应用。为解决上述问题，提出了一种安全高效的隐私保护公共可验证矩阵乘法外包计算方案，并给出了该模型的形式化定义及安全性定义。采用矩阵盲化技术保证外包矩阵 $M$ 和请求向量 $x$ 的隐私性，采用闭型效率的伪随机函数实现计算结果的公共可验证及方案整体的高效性。理论与实验结果表明，与现有方案相比，所提方案在保证外包矩阵 $M$ 和请求向量 $x$ 隐私性的同时还支持公共验证，具有更全面的功能。同时，所提方案整体计算效率更高，与现有方案相比至少能提升14%的效率，具有较高的实用价值。

关键词: 可验证计算, 隐私保护, 公共验证, 云计算

Abstract:

Outsourced computation allows data owners with limited resources to delegate complex computations to resource-rich cloud servers.Matrix multiplication has important applications in scientific computing and cryptography.Verifiable outsourced computation for matrix multiplication enables data owners to outsource the matrix $M$ and the request vector $x$ to untrusted cloud servers for multiplication computation, while verifying the correctness and integrity of the computation results returned by the cloud server.However, existing solutions fail to simultaneously address the following issues: privacy of the outsourced matrix $M$ , privacy of the request vector $x$ , lack of support for public verification, and inefficiency for practical applications.To tackle these problems, proposes a secure efficient privacy-preserving publicly verifiable outsourced computation scheme for matrix multiplication was proposed, and formal definitions and security definitions for the model were provided.Matrix blinding techniques were used to preserve the privacy of the outsourced matrix $M$ and the request vector $x$ , while algebraic pseudorandom functions were employed to achieve public verification of the computation results and overall efficiency of the scheme.Theoretical and experimental results demonstrate that compared with the existing schemes, the proposed scheme not only guarantees the privacy of outsourced matrix $M$ and request vector $x$ , but also supports public verification, which offers more comprehensive functionality.At the same time, the overall computation efficiency of the proposed scheme is higher, which can improve at least 14% compared with existing schemes, and has higher practical value.

Key words: verifiable computation, privacy-preserving, public verification, cloud computing

中图分类号:

TP309

孙守道, 杨沈, 陈一恒, 王强. 安全高效的隐私保护公共可验证矩阵乘法外包计算方案[J]. 电信科学, 2023, 39(12): 110-121.

Shoudao SUN, Shen YANG, Yiheng CHEN, Qiang WANG. Secure efficient privacy-preserving publicly verifiable outsourced computation scheme for matrix multiplication[J]. Telecommunications Science, 2023, 39(12): 110-121.

图/表 10

图1

表1

方案的功能对比"

功能	PVDC^[19]	BVC^[21]	PVDM^[15]	ESVOM^[20]	本文方案
外包可验证	√	√	√	√	√
公共验证	√	×	√	√	√
对 $M$ 的隐私性	×	×	×	×	√
对 $x$ 的隐私性	×	×	×	×	√

表1

表2

表3

图2

图3

图4

图5

图6

图7

参考文献 17

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算法	PVDC^[19]	BVC^[21]	PVDM^[15]	ESVOM^[20]	本文方案
KeyGen	O(mn)	O(mn)	O(mn)	O(1)	O(mn)
ProbGen	O(n)	O(m+n)	O(m+n)	O(mn)	O(m+n)
Comp	O(mn)	O(mn)	O(mn)	O(mn)	O(mn)
Verify	O(m)	O(m)	O(m)	O(m)	O(m)
Solve	—	—	—	—	O(δmn)

算法	PVDC^[19]	BVC^[21]	PVDM^[15]	ESVOM^[20]	本文方案
KeyGen	O(mn)	O(mn)	O(mn)	—	O(mn)
ProbGen	O(m+n)	O(m+n)	O(m+n)	O(m)	O(m+n)
Comp	O(m)	O(m)	O(m)	O(m)	O(m)
Verify	O(m)	O(m)	O(m)	O(m)	O(m)
Solve	—	—	—	—	—

安全高效的隐私保护公共可验证矩阵乘法外包计算方案

Secure efficient privacy-preserving publicly verifiable outsourced computation scheme for matrix multiplication

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