Homomorphic Encryption (HE) is a set of powerful properties of certain cryptosystems that allow for privacy-preserving operation over the encrypted text. Still, HE is not widespread due to limitations in terms of efficiency and usability. Among the challenges of HE, scheme parametrization (i.e., the selection of appropriate parameters within the algorithms) is a relevant multi-faced problem. First, the parametrization needs to comply with a set of properties to guarantee the security of the underlying scheme. Second, parametrization requires a deep understanding of the low-level primitives since the parameters have a confronting impact on the precision, performance, and security of the scheme. Finally, the circuit to be executed influences, and it is influenced by, the parametrization. Thus, there is no general optimal selection of parameters, and this selection depends on the circuit and the scenario of the application. Currently, most of the existing HE frameworks require cryptographers to address these considerations manually. It requires a minimum of expertise acquired through a steep learning curve. In this paper, we propose a unified solution for the aforementioned challenges. Concretely, we present an expert system combining Fuzzy Logic and Linear Programming. The Fuzzy Logic Modules receive a user selection of high-level priorities for the security, efficiency, and performance of the cryptosystem. Based on these preferences, the expert system generates a Linear Programming Model that obtains optimal combinations of parameters by considering those priorities while preserving a minimum level of security for the cryptosystem. We conduct an extended evaluation where we show that an expert system generates optimal parameter selections that maintain user preferences without undergoing the inherent complexity of analyzing the circuit.
School of Computer Science and Statistics（计算机科学与统计学院）
Credit card fraud is a problem continuously faced by financial institutions and their customers, which is mitigated by fraud detection systems. However, these systems require the use of sensitive customer transaction data, which introduces both a lack of privacy for the customer and a data breach vulnerability to the card provider. This paper proposes a system for private fraud detection on encrypted transactions using homomorphic encryption. Two models, XGBoost and a feedforward classifier neural network, are trained as fraud detectors on plaintext data. They are then converted to models whic…
Recently, Lu et al. have proposed two image search schemes based on additive homomorphic encryption [IEEE Access, 2 (2014), 125-141]. We remark that both two schemes are flawed because: (1) the first scheme does not make use of the additive homomorphic property at all; (2) the additive homomorphic encryption in the second scheme is unnecessary and can be replaced by a more efficient symmetric key encryption.
Fully homomorphic encryption is a promising crypto primitive to encrypt your data while allowing others to compute on the encrypted data. But there are many well-known problems with fully homomorphic encryption such as CCA security and circuit privacy problem. Despite these problems, there are still many companies are currently using or preparing to use fully homomorphic encryption to build data security applications. It seems that the full homomorphic encryption is very close to practicality and these problems can be easily mitigated in implementation. Although the those problems are well kno…
This article presents the application of homomorphic authenticators, replication encodings to be precise, to multigroup fully homomorphic encryption schemes. Following the works of Gennaro and Wichs on homomorphic authenticators in combination with the work of multigroup schemes by Kwak et al. we present a verifiable solution for a fully homomorphic primitive that includes the multikey, multiparty and single-user cases. Furthermore, we propose a line of prospective research in constrained-resource scenarios.
Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation capabilities. The operations are matrix based, that is the scheme consists of mapping the operations on integers to operations on matrix. We also include a protocol which uses the proposed scheme for private data processing in clouds.
We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the scheme uses a polynomial based technique that does not require relinearization (and key switching). The noise associated with the ciphertext increases only linearly with every multiplication.
This paper presents a heuristic attack on the fully homomorphic encryption over the integers by using lattice reduction algorithm. Our result shows that the FHE in [DGHV10] is not secure for some parameter settings. We also present an improvement scheme to avoid the lattice attack in this paper.
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The fundamental theories of homomorphic encryption are then discussed with suitable examples. The chapter then provides a survey of some of the classical homomorphic encryption schemes existing in the current literature. Various applications and salient properties of homomorphic encryption schemes are then discussed in detail. The chapter then introduces the mos…
In this paper we provide a survey of various libraries for homomorphic encryption. We describe key features and trade-offs that should be considered while choosing the right approach for secure computation. We then present a comparison of six commonly available Homomorphic Encryption libraries - SEAL, HElib, TFHE, Paillier, ELGamal and RSA across these identified features. Support for different languages and real-life applications are also elucidated.
Recently Homomorphic Encryption (HE) is used to implement Privacy-Preserving Neural Networks (PPNNs) that perform inferences directly on encrypted data without decryption. Prior PPNNs adopt mobile network architectures such as SqueezeNet for smaller computing overhead, but we find naïvely using mobile network architectures for a PPNN does not necessarily achieve shorter inference latency. Despite having less parameters, a mobile network architecture typically introduces more layers and increases the HE multiplicative depth of a PPNN, thereby prolonging its inference latency. In this paper, we …
This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the homomorphic functional encryption retains homomorphic addition and scalar multiplication properties, but also allows for the user's inputs through polynomial variables. The proposed homomorphic encryption can be applied to any polynomials over a finite field, with their coefficients considered as their privacy. We denote the polynomials before homomorphic encrypti…
Cloud computing is a popular distributed network and utility model based technology. Since in cloud the data is outsourced to third parties, the protection of confidentiality and privacy of user data becomes important. Different methods for securing the data in cloud have been proposed by researchers including but not limited to Oblivious RAM, Searchable Encryption, Functional Encryption, Homomorphic Encryption etc. This paper focuses on Searchable and Homomorphic Encryption methods. Finally, a comparative study of these two efficient cloud cryptographic methods has been carried out and given …
Homomorphic encryption and blockchain technology are regarded as two significant technologies for improving e-voting systems. In this paper, we suggest a novel e-voting system using homomorphic encryption and blockchain technology that is focused on encrypting voter data. By encrypting voter information rather than cast votes, the system enables various statistical analyses regarding the vote result while securing the credibility, privacy, and verifiability of overall e-voting system. We checked the efficiency of the overall system by comparing the speed of the proposed system with the speed o…
A characterization of predicate encryption (PE) with support for homomorphic operations is presented and we describe the homomorphic properties of some existing PE constructions. Even for the special case of IBE, there are few known group-homomorphic cryptosystems. Our main construction is an XOR-homomorphic IBE scheme based on the quadratic residuosity problem (variant of the Cocks' scheme), which we show to be strongly homomorphic. We were unable to construct an anonymous variant that preserves this homomorphic property, but we achieved anonymity for a weaker notion of homomorphic encryption…
ZK111 is a fully homomorphic public key encryption algorithm which runs in quadratic time. It's security solely relies upon a very unique 'color-blind' function which is used to create p-adic ring homomorphism.
A database is a prime target for cyber-attacks as it contains confidential, sensitive, or protected information. With the increasing sophistication of the internet and dependencies on internet data transmission, it has become vital to be aware of various encryption technologies and trends. It can assist in safeguarding private information and sensitive data, as well as improve the security of client-server communication. Database encryption is a procedure that employs an algorithm to convert data contained in a database into "cipher text," which is incomprehensible until decoded. Homomorphic e…
We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a generalization of the Learning with Errors problem called the Hidden Subspace Membership problem and show that the semantic security of the proposed scheme can be reduced to the hardness of this problem.
This is a survey on some topics in Lattice based cryptography and Homomorphic Encryption. In particular, we define some lattice problems, LWE and RLWE, and state the reductions given by Regev and Peikert. We also give a full treatment of the recent CKKS homomorphic encryption scheme and give some worked out examples.
Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses automorphisms of affine space to create a form of homomorphic encryption for straight line programs. The encryption method used for the data is known as multivariate encryption. This gives a potentially powerful new method in cyber security based on techniques from algebraic geometry.
A Generative Adversarial Network (GAN) is a deep-learning generative model in the field of Machine Learning (ML) that involves training two Neural Networks (NN) using a sizable data set. In certain fields, such as medicine, the training data may be hospital patient records that are stored across different hospitals. The classic centralized approach would involve sending the data to a centralized server where the model would be trained. However, that would involve breaching the privacy and confidentiality of the patients and their data, which would be unacceptable. Therefore, Federated Learning…
The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining the correct outputs. Due to the computational cost, inflated ciphertext size and limited arithmetic operations that are allowed in most encryption schemes, feasible applications of homomorphic encryption are few. While theorists are working on the mathematical and cryptographical foundations of homomorphic encryption in order to overcome the current limitati…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information theoretically secure fully homomorphic encryption. Here we show, via an information localisation argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required.
We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous lattice-based homomorphic encryption schemes, where the message is hidden in the noisy part of the ciphertext, our scheme carries the message in the affine part of the transformation and applies noise only to achieve security. Our scheme can tolerate noise of arbitrary magnitude, as long as the noise vector has sufficiently small hamming weight (and its entries are independent). Our design achieves "proto-homomorphic" properti…
Homomorphic encryption is an encryption method that enables computing over encrypted data. This has a wide range of real world ramifications such as being able to blindly compute a search result sent to a remote server without revealing its content. This paper discusses how database search queries can be made secure using a homomorphic encryption scheme. We propose a new database search technique that can be used with the ring-based fully homomorphic encryption scheme proposed by Braserski.
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this appears sufficient for most practical applications. In this setting, our schemes lead to practical key and ciphertext sizes. We present a sequence of generalisations of our basic schemes, with increasing levels of security, but decreasing practicality. We have evaluated the first four of these algorithms by computing a low-degree inner product. The timings o…
Fully homomorphic encryption enables arbitrary computation on encrypted data without decrypting the data. Here it is studied in the context of quantum information processing. Based on universal quantum circuit, we present a quantum fully homomorphic encryption (QFHE) scheme, which permits arbitrary quantum transformation on an encrypted data. The QFHE scheme is proved to be perfectly secure. In the scheme, the decryption key is different from the encryption key, however, the encryption key cannot be public. Moreover, the evaluate algorithm of the scheme is independent of the encryption key, so…
Secure function evaluation (SFE) is the process of computing a function (or running an algorithm) on some data, while keeping the input, output and intermediate results hidden from the environment in which the function is evaluated. This can be done using fully homomorphic encryption, Yao's garbled circuits or secure multiparty computation. Applications are manifold, most prominently the outsourcing of computations to cloud service providers, where data is to be manipulated and processed in full confidentiality. Today, one of the most intensively studied solutions to SFE is fully homomorphic e…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity (mainly due to Shor's algorithm). This leads to the challenge of constructing quantum-resistant group homomorphic cryptosystems. In this work, we prove the general impossibility of (abelian) group homomorphic e…
Fully Homomorphic Encryption (FHE) emerges one of the most promising solutions to privacy-preserving computing in an untrusted cloud. FHE can be implemented by various schemes, each of which has distinctive advantages, i.e., some are good at arithmetic operations, while others are efficient when implementing Boolean logic operations. Therefore, it is difficult for even cryptography experts let alone average users to choose the "right" FHE scheme to efficiently implement a specific application. Prior work only qualitatively compares few FHE schemes. In this paper, we present an empirical study,…
We consider an architecture of confidential cloud-based control synthesis based on Homomorphic Encryption (HE). Our study is motivated by the recent surge of data-driven control such as deep reinforcement learning, whose heavy computational requirements often necessitate an outsourcing to the third party server. To achieve more flexibility than Partially Homomorphic Encryption (PHE) and less computational overhead than Fully Homomorphic Encryption (FHE), we consider a Reinforcement Learning (RL) architecture over Leveled Homomorphic Encryption (LHE). We first show that the impact of the encryp…
Secure signal processing is becoming a de facto model for preserving privacy. We propose a model based on the Fully Homomorphic Encryption (FHE) technique to mitigate security breaches. Our framework provides a method to perform a Fast Fourier Transform (FFT) on a user-specified signal. Using encryption of individual binary values and FHE operations over addition and multiplication, we enable a user to perform the FFT in a fixed point fractional representation in binary. Our approach bounds the error of the implementation to enable user-selectable parameters based on the specific application. …
Homomorphic encryption has been an area of study in classical computing for decades. The fundamental goal of homomorphic encryption is to enable (untrusted) Oscar to perform a computation for Alice without Oscar knowing the input to the computation or the output from the computation. Alice encrypts the input before sending it to Oscar, and Oscar performs the computation directly on the encrypted data, producing an encrypted result. Oscar then sends the encrypted result of the computation back to Alice, who can decrypt it. We describe an approach to homomorphic encryption for quantum annealing …
Fully homomorphic encryption (FHE) protects data privacy in cloud computing by enabling computations to directly occur on ciphertexts. To improve the time-consuming FHE operations, we present an electro-optical (EO) FHE accelerator, CryptoLight. Compared to prior FHE accelerators, on average, CryptoLight reduces the latency of various FHE applications by >94.4% and the energy consumption by >95%
Cloud computing emerges as an attractive solution that can be delegated to store and process confidential data. However, several security risks are encountered with such a system as the securely encrypted data should be decrypted before processing them. Therefore, the decrypted data is susceptible to reading and alterations. As a result, processing encrypted data has been a research subject since the publication of the RSA encryption scheme in 1978. In this paper we present a relational database system based on homomorphic encryption schemes to preserve the integrity and confidentiality of the…
Although homomorphic encryption can be incorporated into neural network layers for securing machine learning tasks, such as confidential inference over encrypted data samples and encrypted local models in federated learning, the computational overhead has been an Achilles heel. This paper proposes a caching protocol, namely CHEM, such that tensor ciphertexts can be constructed from a pool of cached radixes rather than carrying out expensive encryption operations. From a theoretical perspective, we demonstrate that CHEM is semantically secure and can be parameterized with straightforward analys…
Performing smart computations in a context of cloud computing and big data is highly appreciated today. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that allows working with the data in its encrypted form. It permits us to preserve confidentiality of our sensible data and to benefit from cloud computing powers. Currently, it has been demonstrated by many existing schemes that the theory is feasible but the efficiency needs to be dramatically improved in order to make it usable for real applications. One subtle difficulty is how to efficiently handle the noise. T…
With the rapid development of cloud computing, the privacy security incidents occur frequently, especially data security issues. Cloud users would like to upload their sensitive information to cloud service providers in encrypted form rather than the raw data, and to prevent the misuse of data. The main challenge is to securely process or analyze these encrypted data without disclosing any useful information, and to achieve the rights management efficiently. In this paper, we propose the encrypted data processing protocols for cloud computing by utilizing additively homomorphic encryption and …
Biometric matching involves storing and processing sensitive user information. Maintaining the privacy of this data is thus a major challenge, and homomorphic encryption offers a possible solution. We propose a privacy-preserving biometrics-based authentication protocol based on fully homomorphic encryption, where the biometric sample for a user is gathered by a local device but matched against a biometric template by a remote server operating solely on encrypted data. The design ensures that 1) the user's sensitive biometric data remains private, and 2) the user and client device are securely…
Modern implementations of homomorphic encryption (HE) rely heavily on polynomial arithmetic over a finite field. This is particularly true of the CKKS, BFV, and BGV HE schemes. Two of the biggest performance bottlenecks in HE primitives and applications are polynomial modular multiplication and the forward and inverse number-theoretic transform (NTT). Here, we introduce Intel Homomorphic Encryption Acceleration Library (Intel HEXL), a C++ library which provides optimized implementations of polynomial arithmetic for Intel processors. Intel HEXL takes advantage of the recent Intel Advanced Vecto…
We propose a homomorphic search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key-update process to a trusted key center, Alice only needs to prepare and encrypt her original data and to decrypt the ciphered search result in linear time. Besides, we also present a compact and perfectly secure quantum homomorphic evaluation protocol for Cliford circuits, where the decryption key can be…
One of the biggest concerns for many applications in cloud computing lies in data privacy. A potential solution to this problem is homomorphic encryption (HE), which supports certain operations directly over the ciphertexts. Conventional HE schemes, however, exhibit significant performance overhead and are hardly applicable to real-world applications. This paper presents Rache, a caching optimization for accelerating the performance of HE schemes. The key insights of Rache include (i) caching some homomorphic ciphertexts before encrypting the large volume of plaintexts; (ii) expanding the plai…
In this work, we propose an open-source, first-of-its-kind, arithmetic hardware library with a focus on accelerating the arithmetic operations involved in Ring Learning with Error (RLWE)-based somewhat homomorphic encryption (SHE). We design and implement a hardware accelerator consisting of submodules like Residue Number System (RNS), Chinese Remainder Theorem (CRT), NTT-based polynomial multiplication, modulo inverse, modulo reduction, and all the other polynomial and scalar operations involved in SHE. For all of these operations, wherever possible, we include a hardware-cost efficient seria…
