基于身份的整数矩阵全同态加密方案
Identity-Based Integer Matrix Fully Homomorphic Encryption Scheme
DOI: 10.12677/CSA.2023.139166, PDF,   
作者: 李明祥：河北金融学院，金融研究所，河北 保定
关键词: 全同态加密；基于身份；层次型；LWE 问题；Fully Homomorphic Encryption； Identity-Based； Leveled； LWE Problem
摘要: 全同态加密允许人们在不知晓解密密钥的情形下对密文进行任意计算。它在云计算等领域具有重 要的应用价值。本论文致力于基于身份的多比特全同态加密方案的设计与安全性分析。首先，基 于带误差学习问题 (learning with errors, LWE) 设计了一个层次型基于身份的多比特全同态加 密方案，该方案加密整数矩阵，支持整数矩阵加法和乘法同态运算；其次，在标准模型下证明了 所设计方案满足 INDr-sID-CPA 安全性；最后，给出了所设计方案有关参数的具体设置。迄今 为止，人们还没有提出支持整数矩阵同态运算的基于身份的多比特全同态加密方案。因此，所设 计的方案不仅具有理论意义，而且在云计算等领域还具有应用前景。
Abstract: Fully homomorphic encryption allows us to perform arbitrary computation on en- crypted data despite not having the secret decryption key. It has critical applications in fields such as cloud computing. This paper focuses on the design and security anal- ysis of identity-based multi-bit fully homomorphic encryption schemes. Firstly, based on the learning with errors (LWE) problem, this paper designs a leveled identity-based multi-bit fully homomorphic encryption scheme which encrypts integer matrices and supports homomorphic integer matrix addition and multiplication. Then, this paper proves that the proposed scheme satisfies INDr-sID-CPA security in the standard mod- el. Finally, this paper gives the specific parameter settings of the proposed scheme. To date, the identity-based multi-bit fully homomorphic encryption scheme for integer matrix messages has not been proposed. Hence, the proposed scheme in this paper not only has theoretical significance but also has application prospects in cloud computing and other fields.
文章引用：李明祥. 基于身份的整数矩阵全同态加密方案[J]. 计算机科学与应用, 2023, 13(9): 1675-1690. https://doi.org/10.12677/CSA.2023.139166

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