A Bitwise Design and Implementation for Privacy-Preserving Data Mining: From Atomic Operations to Advanced Algorithms

Abstract

Homomorphic encryption (HE) is considered as one of the most powerful solutions to securely protect clients' data from malicious users and even severs in the cloud computing. However, though it is known that HE can protect the data in theory, it has not been well utilized because many operations of HE are too slow, especially multiplication. In addition, existing data mining research studies using encrypted data focus on implementing only speci c algorithms without addressing the fundamental problem of HE. In this paper, we propose a fundamental design and implementation of data mining algorithm through logical gates. In order to do this, we design various logic of atomic operations in encrypted domain and nally apply these logic to wellknown data mining algorithms. We also analyze the execution time of atomic and advanced algorithms.

Fully Homomorphically Encrypted Deep Learning as a Service

“…The lack of division will undoubtedly cause issue with things such as activation functions if we were to use a sigmoid function ( 1 1+e −x ) meaning we should use a different function or approximate. One such possibility is a Taylor expansion series which closely approximates sigmoid, although there are a number of alternative methods proposed [14], [15]. FHE/RLWE has recently been paired with deep learning with success, causing some movement toward FHE in literature but primarily for convolutional neural networks (CNNs).…”

t-BMPNet: Trainable Bitwise Multilayer Perceptron Neural Network over Fully Homomorphic Encryption Scheme

“…In this section, we summarize concise details of some of the basic operations given in Table 1 to show insights into how we designed the basis of our system. For the full details of its construction, we recommend the readers to refer to [19,23]. Note that we use notations ⊕, ∧, ∨, and to denote logical gates XOR, AND, OR, and NOT that are homomorphically designed and provide bootstrapping after each operation.…”

“…where ct.s i and ct.c i represent the encrypted sum and carry at index i, respectively. Additionally, we improved and optimized the full-adder circuit considering the execution time for each homomorphic operation which is elaborated in [23].…”

“…Since we have only considered multiplication in positive cases, and also cannot determine whether the ct.a and ct.b are positive or negative values, the algorithm for "encrypted" multiplication has to follow both of the cases. is is just an outline of the bitwise homomorphic multiplication, and for the interested readers, check [23] for more specific details of the algorithm.…”

“…For the sake of the flow of this study, we suggest the readers to refer to [19,23,24] for a more insightful understanding of the above operations as well as other homomorphic operations given in Table 1. e Algorithm 1 illustrates the whole process of the training in plaintext, where lines (7-10) and lines (12,15,16) are the feedforward and the backpropagation algorithms, respectively.…”