Improving the Efficiency of Homomorphic Encryption Schemes

In this dissertation, we explore different approaches to practical homomorphic encryption schemes. For partial homomorphic encryption schemes, we observe that the versatility is the main bottleneck. To solve this problem, we propose general approaches to improve versatility of them by either extending the range of supported circuits or extending the message space. These general approaches can be applied to a wide range of partial HE schemes and greatly increase the number of applications that they support. For fully homomorphic encryption schemes, the slow running speed and the large ciphertext are the main challenges. Therefore, we propose efficient implementations as well as methods to compress the ciphertext. In detail, the Gentry Halevi FHE scheme and the LTV FHE scheme are implemented and the resulting performance shows significant improvement over previous works. For ciphertext compression, the concept of scheme conversion is proposed. Given a scheme converter, we can convert between schemes with compact ciphertext for communication and homomorphic schemes for computation

Implementing Homomorphic Encryption Based Secure Feedback Control for Physical Systems

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast

cuXCMP: CUDA-Accelerated Private Comparison Based on Homomorphic Encryption

Private comparison schemes constructed on homomorphic encryption offer the noninteractive, output expressive and parallelizable features, and have advantages in communication bandwidth and performance. In this paper, we propose cuXCMP, which allows negative and float inputs, offers fully output expressive feature, and is more extensible and practical compared to XCMP (AsiaCCS 2018). Meanwhile, we introduce several memory-centric optimizations of the constant term extraction kernel tailored for CUDA-enabled GPUs. Firstly, we fully utilize the shared memory and present compact GPU implementations of NTT and INTT using a single block; Secondly, we fuse multiple kernels into one AKS kernel, which conducts the automorphism and key switching operation, and reduce the grid dimension for better resource usage, data access rate and synchronization. Thirdly, we precisely measure the IO latency and choose an appropriate number of CUDA streams to enable concurrent execution of independent operations, yielding a constant term extraction kernel with perfect latency hide, i.e., CTX. Combining these approaches, we boost the overall execution time to optimum level and the speedup ratio increases with the comparison scales. For one comparison, we speedup the AKS by 23.71×, CTX by 15.58×, and scheme by 1.83× (resp., 18.29×, 11.75×, and 1.42×) compared to C (resp., AVX512) baselines, respectively. For 32 comparisons, our CTX and scheme implementations outperform the C (resp., AVX512) baselines by 112.00× and 1.99× (resp., 81.53× and 1.51×)

GPS: Integration of Graphene, PALISADE, and SGX for Large-scale Aggregations of Distributed Data

Secure computing methods such as fully homomorphic encryption and hardware solutions such as Intel Software Guard Extension (SGX) have been applied to provide security for user input in privacy-oriented computation outsourcing. Fully homomorphic encryption is amenable to parallelization and hardware acceleration to improve its scalability and latency, but is limited in the complexity of functions it can efficiently evaluate. SGX is capable of arbitrarily complex calculations, but due to expensive memory paging and context switches, computations in SGX are bound by practical limits. These limitations make either of fully homomorphic encryption or SGX alone unsuitable for large-scale multi-user computations with complex intermediate calculations. In this paper, we present GPS, a novel framework integrating the Graphene, PALISADE, and SGX technologies. GPS combines the scalability of homomorphic encryption with the arbitrary computational abilities of SGX, forming a more functional and efficient system for outsourced secure computations with large numbers of users. We implement GPS using linear regression training as an instantiation, and our experimental results indicate a base speedup of 1.03x to 8.69x (depending on computation parameters) over an SGX-only linear regression training without multithreading or hardware acceleration. Experiments and projections show improvements over the SGX-only training of 3.28x to 10.43x using multithreading and 4.99x to 12.67 with GPU acceleration

Design of a Flexible Schoenhage-Strassen FFT Polynomial Multiplier with High-Level Synthesis

Homomorphic Encryption (HE) is a promising field because it allows for encrypted data to be sent to and operated on by untrusted parties without the risk of privacy compromise. The benefits and applications of HE are far reaching, especially in regard to cloud computing. However, current HE solutions require resource intensive arithmetic operations such as high precision, high degree polynomial multiplication resulting in a minimum computational complexity of O(n log(n)) on standard CPUs though application of the Fast Fourier Transform (FFT). These operations result in poor overall performance for HE schemes in software and would benefit greatly from hardware acceleration. This work aims to accelerate the multi-precision arithmetic operations used in HE with specific focus on an implementation of the Schönhage-Strassen FFT based multiplication algorithm. It is to be incorporated into a larger HE library of arithmetic functions tuned for High Level Synthesis (HLS) that enables flexible solutions for hardware/software systems on reconfigurable cloud resources. Although this project was inspired by HE, it could be incorporated within a generic mathematical library and support other domains. The developed FFT based polynomial multiplier exhibits flexibility in the selection of security parameters facilitating its use in a wide range of HE schemes and applications. The design also displayed substantial speedup over the polynomial multiplication functions implemented in the Number Theory Library (NTL) utilized by software based HE solutions

Cryptoleq: A Heterogeneous Abstract Machine for Encrypted and Unencrypted Computation

The rapid expansion and increased popularity of cloud computing comes with no shortage of privacy concerns about outsourcing computation to semi-trusted parties. Leveraging the power of encryption, in this paper we introduce Cryptoleq: an abstract machine based on the concept of One Instruction Set Computer, capable of performing general-purpose computation on encrypted programs. The program operands are protected using the Paillier partially homomorphic cryptosystem, which supports addition on the encrypted domain. Full homomorphism over addition and multiplication, which is necessary for enabling general-purpose computation, is achieved by inventing a heuristically obfuscated software re-encryption module written using Cryptoleq instructions and blended into the executing program. Cryptoleq is heterogeneous, allowing mixing encrypted and unencrypted instruction operands in the same program memory space. Programming with Cryptoleq is facilitated using an enhanced assembly language that allows development of any advanced algorithm on encrypted datasets. In our evaluation, we compare Cryptoleq\u27s performance against a popular fully homomorphic encryption library, and demonstrate correctness using a typical Private Information Retrieval problem