Zaryab Khan
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.
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Similarity Calculation Based on Homomorphic Encryption
针对同态加密密文下搜索查询需相似度度量的需求，本研究结合多种相似度与同态加密算法提出计算方法，经数学证明、案例阐释和不同安全强度下的性能验证，为密文场景的相似度计算提供可行方案。
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 Based on Lattice Post-Quantum Cryptography
针对现有同态加密易受量子攻击的漏洞，本研究提出一种基于格的后量子同态加密方案，提供数学证明与安全分析，为联邦学习等应用提供参考。
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.
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…
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…
Revisiting Fully Homomorphic Encryption Schemes
本文综述了文献中的多种全同态加密方案，分析并比较了各方案的结果，并提供了相关应用与开源工具。
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.
Towards Quantum-Safe Federated Learning via Homomorphic Encryption: Learning with Gradients
该研究提出基于私钥同态加密的隐私保护分布式学习框架，利用梯度量化随机性消除LWE加密的误差项，支持多参与者在诚实但好奇的服务器上安全协作深度学习。
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…
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…
This is a summarized follow up of the unconditional security and quadratic time O(n^2) efficiency of ZK111.
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…
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…
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,…
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. …
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 …
Evaluation of Privacy-aware Support Vector Machine (SVM) Learning using Homomorphic Encryption
本文评估了在全同态加密环境下使用OpenFHE库实现支持向量机（SVM）的性能开销，发现环维度和模数大小是影响性能的主要参数，且SVM-Poly与SVM-Linear性能相近。
Secure Change-Point Detection for Time Series under Homomorphic Encryption
本文提出基于同态加密的时间序列变化点检测方法，能够在不解密数据的情况下保持高实用性，适用于医疗和网络监控等实时场景。
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…
Homomorphic Encryption Based on Post-Quantum Cryptography
本文针对量子计算对传统同态加密的威胁，提出一种基于编码密码学和非负矩阵分解NP问题的后量子同态加密方法，实验表明其加解密时间短于RSA和ECC。
Homomorphic Encryption: An Analysis of its Applications in Searchable Encryption
本文针对云环境下加密数据高效检索的难题，全面分析了同态加密在可搜索加密中的应用进展，梳理了相关方案分类、技术特点与功能现状，并指明了未来研究方向。
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…
Efficient and Privacy-Preserving Federated Learning based on Full Homomorphic Encryption
本文利用最新全同态加密技术提出新颖联邦学习方案，在医疗、商业、生物识别和金融四个实际数据集上覆盖横纵联邦场景，显著提升安全性、效率和实用性。
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…
LightPHE: Integrating Partially Homomorphic Encryption into Python with Extensive Cloud Environment Evaluations
本文介绍LightPHE，一个轻量级混合部分同态加密框架，通过模块化设计集成多种PHE算法，并在多种云环境中评估其性能，展示了其在安全云数据处理中的高效性和可扩展性。
Homomorphic encryption schemes based on coding theory and polynomials
本文综述了基于编码理论和多项式的同态加密方案，介绍了其分类（部分同态、近似同态和全同态）及研究现状。
FLSSM: A Federated Learning Storage Security Model with Homomorphic Encryption
FLSSM通过同态加密技术解决联邦学习中的计算效率、攻击追溯和贡献评估问题，提升模型隐私保护和安全性能。
On the Feasibility of Hybrid Homomorphic Encryption for Intelligent Transportation Systems
本文研究了混合同态加密在智能交通系统中的可行性，通过理论模型和参数评估，证明HHE在减少密文大小和通信开销方面优于传统同态加密，适用于延迟受限的交通通信。
Compile-Time Fully Homomorphic Encryption of Vectors: Eliminating Online Encryption via Algebraic Basis Synthesis
本研究提出编译时FHE密文合成框架，用预计算加密基向量加运行时缩放零加密构造密文，消除在线加密，证明其IND-CPA安全性，降低内存开销且兼容标准FHE操作，适用于加密数据库等场景。
Neural Network Quantisation for Faster Homomorphic Encryption
本研究通过量化感知训练减小神经网络整数位宽，在BFV同态加密方案下分别将MNIST和CIFAR网络执行时间减少80%和40%，同时保持精度。
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.
Cloud computing is the broad and diverse phenomenon. Users are allowed to store huge amount of data on cloud storage for future use. Most of the cloud service providers store data in plain text format or in secured manner but client will not be known the method in which it is stored. Homomorphic encryption is the encryption which allows the operation on cipher text thus generating an encrypted result which when decrypted, matches the result of operations performed on the plaintext. This is sometimes a desirable feature in modern communication system architectures. There are several homomorphic…
Fully homomorphic encryption (FHE) allows anyone to perform computations on encrypted data, despite not having the secret decryption key. Since the Gentry's work in 2009, the primitive has interested many researchers. In this paper, we stress that any computations performed on encrypted data are constrained to the encrypted domain (finite fields or rings). This restriction makes the primitive useless for most computations involving common arithmetic expressions and relational expressions. It is only applicable to the computations related to modular arithmetic. We want to reaffirm that cryptogr…
Puncturable encryption (PE), proposed by Green and Miers at IEEE S&P 2015, is a kind of public key encryption that allows recipients to revoke individual messages by repeatedly updating decryption keys without communicating with senders. PE is an essential tool for constructing many interesting applications, such as asynchronous messaging systems, forward-secret zero round-trip time protocols, public-key watermarking schemes and forward-secret proxy re-encryptions. This paper revisits PEs from the observation that the puncturing property can be implemented as efficiently computable functions. …
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.
HE-DKSAP: Privacy-Preserving Stealth Address Protocol via Additively Homomorphic Encryption
针对基础隐形地址易受密钥泄露与量子攻击的问题，提出基于加法同态加密的HE-DKSAP双密钥协议，并可扩展为FHE-DKSAP，以增强区块链交易隐私、安全与可扩展性。
Privacy has gained a growing interest nowadays due to the increasing and unmanageable amount of produced confidential data. Concerns about the possibility of sharing data with third parties, to gain fruitful insights, beset enterprise environments; value not only resides in data but also in the intellectual property of algorithms and models that offer analysis results. This impasse locks both the availability of high-performance computing resources in the "as-a-service" paradigm and the exchange of knowledge with the scientific community in a collaborative view. Privacy-preserving data science…
This paper studies how a system operator and a set of agents securely execute a distributed projected gradient-based algorithm. In particular, each participant holds a set of problem coefficients and/or states whose values are private to the data owner. The concerned problem raises two questions: how to securely compute given functions; and which functions should be computed in the first place. For the first question, by using the techniques of homomorphic encryption, we propose novel algorithms which can achieve secure multiparty computation with perfect correctness. For the second question, …
Location-Based Recommendation Services (LBRS) has seen an unprecedented rise in its usage in recent years. LBRS facilitates a user by recommending services based on his location and past preferences. However, leveraging such services comes at a cost of compromising one's sensitive information like their shopping preferences, lodging places, food habits, recently visited places, etc. to the third-party servers. Losing such information could be crucial and threatens one's privacy. Nowadays, the privacy-aware society seeks solutions that can provide such services, with minimized risks. Recently, …
Encryption scheme based on Automorphism Group of Hermitian Function Field with Homomorphic Encryption
本文提出基于埃尔米特函数域自同构群的加密方案，通过三参数群的对数表示增强同态加密能力，其攻击复杂度与加密消息大小均与群阶直接相关。
TFHE-SBC: Software Designs for Fully Homomorphic Encryption over the Torus on Single Board Computers
针对单板计算机上TFHE加密效率低、密文大及硬件加速受限的问题，提出专用软件设计TFHE-SBC，加速客户端操作，使加密速度提升2486倍、通信效率提升512倍、能效提升12至2004倍。
HEIR: A Universal Compiler for Homomorphic Encryption
本文提出基于MLIR的同态加密编译器统一框架HEIR，支持主流技术、软硬件集成及多种前端，通过移植大量文献验证其处理复杂程序的能力，正成为学术与工业界事实上的标准。
We introduce a novel method and implementation architecture to train neural networks which preserves the confidentiality of both the model and the data. Our method relies on homomorphic capability of lattice based encryption scheme. Our procedure is optimized for operations on packed ciphertexts in order to achieve efficient updates of the model parameters. Our method achieves a significant reduction of computations due to our way to perform multiplications and rotations on packed ciphertexts from a feedforward network to a back-propagation network. To verify the accuracy of the training model…
Blind-Touch: Homomorphic Encryption-Based Distributed Neural Network Inference for Privacy-Preserving Fingerprint Authentication
本文提出Blind-Touch系统，通过同态加密和分布式神经网络推理实现隐私保护指纹认证，在保持高准确率的同时显著提升云端处理效率。
Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encry…
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