Simple Encrypted Arithmetic Library - SEAL v2.1

Achieving fully homomorphic encryption was a longstanding open problem in cryptography until it was resolved by Gentry in 2009. Soon after, several homomorphic encryption schemes were proposed. The early homomorphic encryption schemes were extremely impractical, but recently new implementations, new data encoding techniques, and a better understanding of the applications have started to change the situation. In this paper we introduce the most recent version (v2.1) of Simple Encrypted Arithmetic Library - SEAL, a homomorphic encryption library developed by Microsoft Research, and describe some of its core functionality

Approximation-based homomorphic encryption for secure and efficient blockchain-driven watermarking service

Homomorphic encryption has been widely used to preserve the privacy of watermarking process on blockchain-driven watermarking services. It offers transparent and traceable encrypted watermarking without revealing sensitive data such as original images or watermark data to the public. Nevertheless, the existing works suffer from enormous memory storage and extensive computing power. This study proposed an approximation-based homomorphic encryption for resource-efficient encrypted watermarking without sacrificing watermarking quality. We demonstrated the efficiency of the Cheon-Kim-Kim-Son (CKKS) encrypted watermarking process using discrete cosine transform-singular value decomposition (DCT-SVD) embedding. The evaluation results showed that it could preserve the watermarking quality similar to non-encrypted watermark embedding, even after geometrical and filtering attacks. Compared to existing homomorphic encryption, such as Brakerski-Gentry-Vaikuntanathan (BFV) encryption, it has superior performance regarding resource utilization and watermarking quality preservation

A Homomorphic Encryption Framework for Privacy-Preserving Spiking Neural Networks

Machine learning (ML) is widely used today, especially through deep neural networks (DNNs); however, increasing computational load and resource requirements have led to cloud-based solutions. To address this problem, a new generation of networks has emerged called spiking neural networks (SNNs), which mimic the behavior of the human brain to improve efficiency and reduce energy consumption. These networks often process large amounts of sensitive information, such as confidential data, and thus privacy issues arise. Homomorphic encryption (HE) offers a solution, allowing calculations to be performed on encrypted data without decrypting them. This research compares traditional DNNs and SNNs using the Brakerski/Fan-Vercauteren (BFV) encryption scheme. The LeNet-5 and AlexNet models, widely-used convolutional architectures, are used for both DNN and SNN models based on their respective architectures, and the networks are trained and compared using the FashionMNIST dataset. The results show that SNNs using HE achieve up to 40% higher accuracy than DNNs for low values of the plaintext modulus t, although their execution time is longer due to their time-coding nature with multiple time steps

Glyph: Fast and Accurately Training Deep Neural Networks on Encrypted Data

Big data is one of the cornerstones to enabling and training deep neural networks (DNNs). Because of the lack of expertise, to gain benefits from their data, average users have to rely on and upload their private data to big data companies they may not trust. Due to the compliance, legal, or privacy constraints, most users are willing to contribute only their encrypted data, and lack interests or resources to join the training of DNNs in cloud. To train a DNN on encrypted data in a completely non-interactive way, a recent work proposes a fully homomorphic encryption (FHE)-based technique implementing all activations in the neural network by \textit{Brakerski-Gentry-Vaikuntanathan (BGV)}-based lookup tables. However, such inefficient lookup-table-based activations significantly prolong the training latency of privacy-preserving DNNs. In this paper, we propose, Glyph, a FHE-based scheme to fast and accurately train DNNs on encrypted data by switching between TFHE (Fast Fully Homomorphic Encryption over the Torus) and BGV cryptosystems. Glyph uses logic-operation-friendly TFHE to implement nonlinear activations, while adopts vectorial-arithmetic-friendly BGV to perform multiply-accumulation (MAC) operations. Glyph further applies transfer learning on the training of DNNs to improve the test accuracy and reduce the number of MAC operations between ciphertext and ciphertext in convolutional layers. Our experimental results show Glyph obtains the state-of-the-art test accuracy, but reduces the training latency by $99\%$ over the prior FHE-based technique on various encrypted datasets.Comment: 10 pages, 8 figure

CryptoPIM: In-memory Acceleration for Lattice-based Cryptographic Hardware

Quantum computers promise to solve hard mathematical problems such as integer factorization and discrete logarithms in polynomial time, making standardized public-key cryptography (such as digital signature and key agreement) insecure. Lattice-Based Cryptography (LBC) is a promising post-quantum public-key cryptographic protocol that could replace standardized public-key cryptography, thanks to the inherent post-quantum resistant properties, efficiency, and versatility. A key mathematical tool in LBC is the Number Theoretic Transform (NTT), a common method to compute polynomial multiplication that is the most compute-intensive routine, and which requires acceleration for practical deployment of LBC protocols. In this paper, we propose, a high-throughput Processing In-Memory (PIM) accelerator for NTT-based polynomial multiplier with the support of polynomials with degrees up to 32k. Compared to the fastest FPGA implementation of an NTT-based multiplier, achieves on average 31x throughput improvement with the same energy and only 28% performance reduction, thereby showing promise for practical deployment of LBC

Efficiently processing complex-valued data in homomorphic encryption

We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan–Vercauteren scheme by replacing the integral plaintext modulus t by a linear polynomial X − b. Our generalization studies plaintext moduli of the form Xm + b. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed

Accelerating Number Theoretic Transformations for Bootstrappable Homomorphic Encryption on GPUs

Homomorphic encryption (HE) draws huge attention as it provides a way of privacy-preserving computations on encrypted messages. Number Theoretic Transform (NTT), a specialized form of Discrete Fourier Transform (DFT) in the finite field of integers, is the key algorithm that enables fast computation on encrypted ciphertexts in HE. Prior works have accelerated NTT and its inverse transformation on a popular parallel processing platform, GPU, by leveraging DFT optimization techniques. However, these GPU-based studies lack a comprehensive analysis of the primary differences between NTT and DFT or only consider small HE parameters that have tight constraints in the number of arithmetic operations that can be performed without decryption. In this paper, we analyze the algorithmic characteristics of NTT and DFT and assess the performance of NTT when we apply the optimizations that are commonly applicable to both DFT and NTT on modern GPUs. From the analysis, we identify that NTT suffers from severe main-memory bandwidth bottleneck on large HE parameter sets. To tackle the main-memory bandwidth issue, we propose a novel NTT-specific on-the-fly root generation scheme dubbed on-the-fly twiddling (OT). Compared to the baseline radix-2 NTT implementation, after applying all the optimizations, including OT, we achieve 4.2x speedup on a modern GPU.Comment: 12 pages, 13 figures, to appear in IISWC 202

PaReNTT: Low-Latency Parallel Residue Number System and NTT-Based Long Polynomial Modular Multiplication for Homomorphic Encryption

High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using the number-theoretic transform (NTT) and inverse NTT (iNTT). Chinese remainder theorem (CRT) is used to decompose the modulus into multiple smaller moduli. Our proposed architecture, namely PaReNTT, makes four novel contributions. First, parallel NTT and iNTT architectures are proposed to reduce the number of clock cycles to process the polynomials. This can enable real-time processing for HE applications, as the number of clock cycles to process the polynomial is inversely proportional to the level of parallelism. Second, the proposed architecture eliminates the need for permuting the NTT outputs before their product is input to the iNTT. This reduces latency by n/4 clock cycles, where n is the length of the polynomial, and reduces buffer requirement by one delay-switch-delay circuit of size n. Third, an approach to select special moduli is presented where the moduli can be expressed in terms of a few signed power-of-two terms. Fourth, novel architectures for pre-processing for computing residual polynomials using the CRT and post-processing for combining the residual polynomials are proposed. These architectures significantly reduce the area consumption of the pre-processing and post-processing steps. The proposed long modular polynomial multiplications are ideal for applications that require low latency and high sample rate as these feed-forward architectures can be pipelined at arbitrary levels