In this work, we present $\texttt{Volley Revolver}$, a novel matrix-encoding method that is particularly convenient for privacy-preserving neural networks to make predictions, and use it to implement a CNN for handwritten image classification. Based on this encoding method, we develop several additional operations for putting into practice the secure matrix multiplication over encrypted data matrices. For two matrices $A$ and $B$ to perform multiplication $A \times B$, the main idea is, in a simple version, to encrypt matrix $A$ and the transposition of the matrix $B$ into two ciphertexts respectively. Along with the additional operations, the homomorphic matrix multiplication $A \times B$ can be calculated over encrypted data matrices efficiently. For the convolution operation in CNN, on the basis of the $\texttt{Volley Revolver}$ encoding method, we develop a feasible and efficient evaluation strategy for performing the convolution operation. We in advance span each convolution kernel of CNN to a matrix space of the same size as the input image so as to generate several ciphertexts, each of which is later used together with the input image for calculating some part of the final convolution result. We accumulate all these part results of convolution operation and thus obtain the final convolution result.
翻译:在这项工作中,我们提出了美元(textt{Volley Celver)美元,这是一种新颖的矩阵编码方法,它特别便于隐私保护神经网络进行预测,并用来实施CNN手写图像分类。根据这种编码方法,我们开发了几项额外操作,以将加密数据矩阵的安全矩阵乘法化为实践。对于两个矩阵,用美元和美元(B)来执行乘法B$(乘法),主要的想法是,在一个简单版本中,分别将美元(A)和美元(B)的矩阵转换成两个密码。除了其他操作外,单态矩阵乘法也可用于手写图像分类。根据这个编码方法,我们可以在加密数据矩阵中高效地计算到安全矩阵乘法。对于两个矩阵,用美元(A)和美元(B)来进行乘法乘法(B)进行乘法(B),主要的想法是用一个简单版本,将CNN的每一个变式矩阵都加密到一个矩阵空间($B$B$$)。除了额外的操作外,单质矩阵的乘数倍的乘数乘数乘数乘数(我们这些变数的进图)的计算结果,我们用这些变相图的计算结果都用来计算。