基于三重扰动和线性组合的批量矩阵乘法可验证计算方案

Verifiable computation scheme of batch matrix multiplication based on triple perturbation and linear combination

随着云计算、物联网技术的发展,可验证计算作为一种新兴的计算技术得到了广泛的应用。可验证计算在为用户带来便利的同时也存在着安全挑战:数据隐私性、结果可验证性和高效性。目前,矩阵乘法可验证计算方案基本采用稀疏矩阵相乘的加密方法来保护数据的隐私性。分析稀疏矩阵加密算法后,发现存在两个挑战:一是行或列公因子泄露原始矩阵行或列数据,二是零元素泄露原始矩阵零元素统计信息。同时,现有方案对云服务器计算结果的验证效率也不理想。针对数据隐私保护挑战,设计的批量矩阵乘法可验证计算方案利用三重扰动加密算法在不增加加解密计算复杂度的同时达到更强的隐私保护效果,其中,通过构造特殊的上或下三角稀疏矩阵加入双重扰动(乘法扰动和加法扰动)来保护行或列数据,通过构造特殊的加法稀疏矩阵加入单重扰动(加法扰动)来保护零元素信息。针对云服务器计算结果验证效率挑战,所提方案利用矩阵线性组合技术实现计算结果的批量验证,验证效率提高了约50倍,并随着矩阵数量的增多而提升。性能分析表明,所提方案基本没有增加客户端加解密开销,并提高了结果验证效率。

With the development of cloud computing and internet of things technology,verifiable computing has been widely used as a new computing technology.While verifiable computing brings convenience to users,there are also security challenges:data privacy,verifiability of results,and efficiency.At present,the sparse matrix multiplication encryption method is used to protect the privacy of data in the matrix multiplication verifiable calculation scheme.After analyzing the sparse matrix encryption algorithm,it is found that there are two challenges.The one is that the row or column common factor leaks the row or column data of the original matrix.The other is that the zero element leaks the statistic information of the zero element of the original matrix.Meanwhile,the existing scheme is also not ideal for the verification efficiency of cloud server computing results.Aiming at the challenge of data privacy protection,the designed batch matrix multiplication verifiable computation scheme uses triple perturbation encryption algorithm to achieve stronger privacy protection without increasing the computational complexity of encryption and decryption.Specifically,a special upper or lower triangular sparse matrix is constructed to add double perturbation(multiplicative perturbation and additive perturbation)to protect row or column data,and a special additive sparse matrix is constructed to add a single perturbation(additive perturbation)to protect zero element information.Aiming at the challenge of verification efficiency of cloud server computing results,the scheme uses matrix linear combination technology to realize batch verification of calculation results.The verification efficiency is increased by about 50 times and increases with the increase of the number of matrices.Performance analysis shows that this scheme does not increase the client encryption and decryption overhead and improves the efficiency of result verification.