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同态明文-密文矩阵运算及其应用

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支持单指令多数据操作的同态加密方案能有效提高密文计算的均摊效率,但密文结构导致矩阵运算复杂度高.在许多应用中,采用明文-密文矩阵操作可以在确保安全的同时实现隐私计算.基于此,提出一个适用于任意维数的明文-密文矩阵乘法方案.该方案通过明文矩阵编码和密文矩阵维数变换等步骤计算得到密文结果.与已知最好的 Jiang 等所提的密文方阵乘法算法相比,所提方案支持任意维数的矩阵乘法,并支持矩阵连乘;理论分析和实验结果均表明,所提方案具有更低的密文旋转复杂度和更高的计算效率.将所提方案应用在隐私保护的贝叶斯分类器中,能以更高安全参数和更少计算时间完成分类任务.
Matrix computation over homomorphic plaintext-ciphertext and its application
Those homomorphic encryption schemes supporting single instruction multiple data(SIMD)operations effec-tively enhance the amortized efficiency of ciphertext computations,yet the structure of ciphertexts leads to high complex-ity in matrix operations.In many applications,employing plaintext-ciphertext matrix operations can achieve priva-cy-preserving computing.Based on this,a plaintext-ciphertext matrix multiplication scheme for matrices of arbitrary dimen-sion was proposed.The resulting ciphertext was computed through steps such as encoding the plaintext matrix,transforming the dimensions of the encrypted matrix,etc.Compared to the best-known encrypted matrix multiplication algorithm for square matrices proposed by Jiang et al.,the proposed scheme supported matrix multiplication of arbitrary dimension,and consecutive matrix multiplications.Both theoretical analysis and experimental results show that the proposed scheme re-quires less rotations on ciphertexts and hence features higher efficiency.When applied to a privacy-preserving Bayesian clas-sifier,the proposed scheme can complete classification tasks with higher security parameters and reduced running time.

homomorphic encryptionmatrix computationmachine learningBayesian classifier

刘洋、杨林翰、陈经纬、吴文渊、冯勇

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重庆交通大学信息科学与工程学院,重庆 400074

中国科学院重庆绿色智能技术研究院生物计算安全重庆市重点实验室,重庆 400714

中国科学院大学重庆学院,重庆 400714

同态加密 矩阵运算 机器学习 贝叶斯分类器

国家重点研发计划基金资助项目重庆市自然科学基金资助项目重庆市自然科学基金资助项目重庆市自然科学基金资助项目重庆市自然科学基金资助项目重庆市自然科学基金资助项目

2020YFA0712303CSTB2023NSCQ-MSX0441cstc2021jcyjmsxmX0821cstc2021yszxjcyjX00042022YSZX-JCX0011CSTBCSTB2023YSZX-J

2024

10.11959/j.issn.1000-436x.2024024

通信学报
中国通信学会

通信学报

CSTPCD北大核心
影响因子：1.265
ISSN：1000-436X
年,卷(期)：2024.45(2)
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