Speed-up of Data Analysis with Kernel Trick in Encrypted Domain

Fully Homomorphic Encryption (FHE) is a cryptographic method that guarantees the privacy and security of user data during computation. FHE algorithms can perform unlimited arithmetic computations directly on encrypted data without decrypting it. Thus, even when processed by untrusted systems, confidential data is never exposed. In this work, we develop new techniques for accelerated encrypted execution and demonstrate the significant performance advantages of our approach. Our current focus is the Fully Homomorphic Encryption over the Torus (CGGI) scheme, which is a current state-of-the-art method for evaluating arbitrary functions in the encrypted domain. CGGI represents a computation as a graph of homomorphic logic gates and each individual bit of the plaintext is transformed into a polynomial in the encrypted domain. Arithmetic on such data becomes very expensive: operations on bits become operations on entire polynomials. Therefore, evaluating even relatively simple nonlinear functions with the CGGI cryptosystem, such as a sigmoid, can take thousands of seconds on a single CPU thread. Using our novel framework for end-to-end accelerated encrypted execution called ArctyrEX, developers with no knowledge of complex FHE libraries can simply describe their computation as a C program that is evaluated 18x faster on average relative to the GPU-accelerated Concrete library for multiplication-intensive benchmarks.

Accelerating the development of a practical Fully Homomorphic Encryption (FHE) scheme is the goal of the DARPA PROCEED program. For the past year, this program has had as its focus the acceleration of various aspects of the FHE concept toward practical implementation and use. FHE would be a game-changing technology to enable secure, general computation on encrypted data, e.g., on untrusted off-site hardware. However, FHE will still require several orders of magnitude improvement in computation before it will be practical for widespread use. Recent theoretical breakthroughs demonstrated the existence of FHE schemes [1, 2], and to date much progress has been made in both algorithmic and implementation improvements. Specifically our contribution to the Proceed program has been the development of FPGA based hardware primitives to accelerate the computation on encrypted data using FHE based on lattice techniques [3]. Our project, SIPHER, has been using a state of the art tool-chain developed by Mathworks to implement VHDL code for FPGA circuits directly from Simulink models. Our baseline Homomorphic Encryption prototypes are developed directly in Matlab using the fixed point toolbox to perform the required integer arithmetic. Constant improvements in algorithms require us to be able to quickly implement them in a high level language such as Matlab. We reported on our initial results at HPEC 2011 [4]. In the past year, increases in algorithm complexity have introduced several new design requirements for our FPGA implementation. This report presents new Simulink primitives that had to be developed to deal with these new requirements.

With the wide adoption of cloud computing paradigm, it is important to develop appropriate techniques to protect client data privacy in the cloud. Encryption is one of the major techniques that could be used to achieve this goal. However, data encryption at the rest alone is insufficient for secure cloud computation environments. There is also the need for efficient techniques to carry out computation over encrypted data. Fully homomorphic encryption (FHE) and garbled circuits are naturally used to process encrypted data without leaking any information about the data. However, existing FHE schemes are inefficient for processing large amount of data in cloud and garbled circuits are one time programs and cannot be reused. Based on quaternion/octonion algebra and Jordan algebra over finite rings \(\mathbb {Z}_q\), this paper designs efficient fully homomorphic symmetric key encryption (FHE) schemes without bootstrapping (that is, noise-free FHE schemes) that are secure in the weak ciphertext-only security model assuming the hardness of solving multivariate quadratic equation systems and solving univariate high degree polynomial equation systems in \(\mathbb {Z}_q\). The FHE scheme designed in this paper is sufficient for privacy preserving computation in cloud.

With the emerging techniques of wireless communication and cloud computing, large volumes of multimedia data are outsourced from resource constrained users to the cloud with abundant resource for both delegated storage and computation. Unfortunately, there is a risk of users’ image privacy leakage in the process of outsourcing to untrusted cloud. Most of the existing work achieved privacy-preserving image feature extraction and matching by using public key (fully) homomorphic encryption (FHE), but the heavy computational overhead and communication overhead cannot adapt to resource-constrained mobile devices. Other works disabled to realize image denoising in the encrypted domain or only focused on the scale-invariant feature transform (SIFT) descriptor that is inappropriate for position-sensitive feature extraction. To address these issues, in this paper, a privacy-preserving shape context based image denoising and matching protocol PPOIM with efficient outsourcing is proposed. Firstly, to improve the accuracy of image matching, a privacy-preserving image denoising scheme PPID is proposed without exploiting public key FHE. Then, based on PPID, a privacy-preserving image matching protocol PPOIM adopting shape context descriptor is devised, where two secure and efficient comparison and counting protocols in the encrypted domain are presented. All the original image privacy, query image privacy and image matching result privacy are well protected. Finally, formal security proof and extensive simulations on real-world data sets demonstrate the efficiency and practicability of our proposed PPOIM.

Fully homomorphic encryption (FHE) allows us to perform computations directly over encrypted data and can be widely used in some highly regulated industries. Gentry’s bootstrapping procedure is used to refresh noisy ciphertexts and is the only way to achieve the goal of FHE up to now. In this paper, we optimize the LWE-based GSW-type bootstrapping procedure. Our optimization decreases the lattice approximation factor for the underlying worst-case lattice assumption from \(\tilde{O}(N^{2.5})\) to \(\tilde{O}(N^{2})\), and is time-efficient by a \(O(\lambda )\) factor. Our scheme can also achieve the best factor in prior works on bootstrapping of standard lattice-based FHE by taking a larger lattice dimension, which makes our scheme as secure as the standard lattice-based PKE. Furthermore, in this work we present a technique to perform more operations per bootstrapping in the LWE-based FHE scheme. Although there have been studies to evaluate large FHE gates using schemes over ideal lattices, (i.e. using FHEW or TFHE), we are the first to study how to perform complex functions homomorphically over standard lattices.

Evaluating arbitrary functions on encrypted data is one of the holy grails of cryptography, with Fully Homomorphic Encryption (FHE) being probably the most prominent and powerful example. FHE, in its current state is, however, not efficient enough for practical applications. On the other hand, simple homomorphic and somewhat homomorphic approaches are not powerful enough to support arbitrary computations.We propose a new approach towards a practicable system for evaluating functions on encrypted data. Our approach allows to chain an arbitrary number of computations, which makes it more powerful than existing efficient schemes. As with basic FHE we do not encrypt or in any way hide the function, that is evaluated on the encrypted data. It is, however, sufficient that the function description is known only to the evaluator. This situation arises in practice for software as a Software as a Service (SaaS)-scenarios, where an evaluator provides a function only known to him and the user wants to protect his data. Another application might be the analysis of sensitive data, such as medical records.In this paper we restrict ourselves to functions with only one input parameter, which allow arbitrary transformations on encrypted data.

Fully Homomorphic Encryption (FHE) is the holy grail of encrypted communications. It opens the door to several advanced functionalities to overcome the security and trust issues of the IT world. After 2009, once Craig Gentry had shown that FHE could be achieved, a study in this field boomed, and significant improvement was made in identifying more efficient and realistic programs. FHE is primitive cryptography that enables arbitrary functions to be calculated via encrypted data. These systems are applicable in different ways since they permit users to encrypt their private information securely while still outsourcing the processing of protected data without fearing disclosing the real data. In 2012, LTV12 presented the first multi-key FHE system and demonstrated the possibility of using multi-key systems in somewhat homomorphic encryption (SHE). Like in the one key context, there have been many advances in the field, but no effort has been made to develop the multi-key methods. This paper presents a discussion of FHE and MKFHE with a specific focus on the current techniques and three implementations, comprising the first in the multi-key setups, to the extent of our understanding.

Garbled computation in cloud

In this paper we report on our work to design, implement and evaluate a Fully Homomorphic Encryption (FHE) scheme. Our FHE scheme is an NTRU-like cryptosystem, with additional support for efficient key switching and modulus reduction operations to reduce the frequency of bootstrapping operations. Ciphertexts in our scheme are represented as matrices of 64-bit integers. The basis of our design is a layered software services stack to provide high-level FHE operations supported by lower-level lattice-based primitive implementations running on a computing substrate. We implement and evaluate our FHE scheme to run on a commodity CPU-based computing environment. We implemented our FHE scheme to run in a compiled C environment and use parallelism to take advantage of multi-core processors. We provide experimental results which show that our FHE implementation provides at least an order of magnitude improvement in runtime as compared to recent publicly known evaluation results of other FHE software implementations.

A KPU is a replacement for a standard RISC processor that natively runs encrypted machine code on encrypted data in registers and memory — a 'general-purpose crypto-processor', in other words. It works because the processor's arithmetic is customised to make the chosen encryption into a mathematical homomorphism, resulting in what is called a 'fully-homomorphic encryption' design. This paper discusses the problems and solutions associated with implementing a KPU in hardware.

Biometrics offers higher accuracy for personal recognition as well as provides greater security than traditional methods because of its properties. However, ironically, these properties are also weaknesses because biometric data is permanently linked with an individual and cannot be revoked or cancelled, especially when biometric data is compromised, which can lead to a serious privacy issue. By reviewing current approaches, fully homomorphic encryption (FHE) is considered as a promising solution for this privacy issue because of its ability to perform computations in the encrypted domain. We studied the effectiveness of FHE when it is used in biometric systems. The main contributions of this paper are the implementation of a privacy-preserving iris biometric authentication protocol adapted to lattice-based FHE and a sound security analysis of authentication and privacy. This work is concluded with some factors to be addressed to enhance privacy as well as some considerations to improve the performance of this implementation.

Credit scoring plays a crucial role in financial decision-making but inherently relies on highly sensitive personal and financial data, raising significant privacy concerns. Conventional credit scoring systems expose raw data to centralized servers, creating vulnerabilities to misuse, unauthorized access, or data breaches. To address this gap, we propose a privacypreserving credit scoring framework based on the CKKS scheme of Fully Homomorphic Encryption (FHE), which enables arithmetic operations to be performed directly on encrypted data without decryption. Our approach allows clients to encrypt their financial attributes before submission, while the credit scoring model executes inference entirely in the encrypted domain, ensuring that sensitive inputs remain confidential throughout the process. The results demonstrate that encrypted inference achieves accuracy comparable to plaintext computation, with negligible loss due to CKKS approximation, while incurring overhead in terms of latency, ciphertext expansion, and memory usage. We further analyze the trade-offs between performance and security levels to identify practical parameter settings. This work represents a novel demonstration of end-to-end encrypted credit scoring using CKKS-based FHE, highlighting its potential for deployment in privacy-sensitive financial applications.

We present new constructions of multi-party homomorphic secret sharing (HSS) based on a new primitive that we call homomorphic encryption with decryption to shares (HEDS). Our first construction, which we call \(\mathsf {Scooby} \), is based on many popular fully homomorphic encryption (FHE) schemes with a linear decryption property. \(\mathsf {Scooby} \) achieves an n-party HSS for general circuits with complexity \(O(|F| + \log n)\), as opposed to \(O(n^2 \cdot |F|)\) for the prior best construction based on multi-key FHE. \(\mathsf {Scooby} \) can be based on (ring)-LWE with a super-polynomial modulus-to-noise ratio. In our second construction, \(\mathsf {Scrappy} \), assuming any generic FHE plus HSS for NC1-circuits, we obtain a HEDS scheme which does not require a super-polynomial modulus. While these schemes all require FHE, in another instantiation, \(\mathsf {Shaggy} \), we show how in some cases it is possible to obtain multi-party HSS without FHE, for a small number of parties and constant-degree polynomials. Finally, we show that our \(\mathsf {Scooby} \) scheme can be adapted to use multi-key fully homomorphic encryption, giving more efficient spooky encryption and setup-free HSS. This latter scheme, \(\mathsf {Casper} \), if concretely instantiated with a B/FV-style multi-key FHE scheme, for functions F which do not require bootstrapping, gives an HSS complexity of \(O(n \cdot |F| + n^2 \cdot \log n)\).

Fully Homomorphic Encryption (FHE) is a cryptosystem supporting arbitrary computations over encrypted data. Gentry is one of the foregoers to put forward the concept of full homomorphism who developed the first version of efficient FHE schemes. FHE provides important ideas and directions for the study of privacy-preserving. In my paper, we present a multi-key FHE scheme in virtue of NTRU (Number Theory Research Unit) to implement a neural network, which is capable of preventing the training data from revealing. Compared with the traditional schemes, the neural network of our system works over ciphertexts with semantic security. Meanwhile, the cryptosystem scheme is in the form of multi-keys, thus the data owned by different providers, model trainers, or servers can be independently encrypted but jointly computed. Thereafter, in contrast to federated learning, our scheme does not require any local training. To testify our method, we finally selected a set of commonly used parameters and designed a neural network based on NTRU encryption. And used the physical machine to make encryption predictions for encoding the MNIST dataset, the prediction accuracy of our privacy model is 80%.

Fully Homomorphic Encryption (FHE) is an advanced cryptographic technique that enables computation on encrypted data without requiring decryption. This capability eliminates the need to expose sensitive data during processing, making FHE particularly suitable for cloud computing, healthcare analytics, financial systems, and privacypreserving artificial intelligence. Despite its strong theoretical foundation, FHE faces practical challenges including high computational complexity, large ciphertext expansion, and bootstrapping overhead. This paper presents a comprehensive study of FHE, including its theoretical background, working mechanism, security properties, real-world applications, limitations, and emerging research trends.