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 proxy cryptography. For the traditional homomorphic encryption schemes with many limitations, which are not suitable for cloud computing applications. We simulate a cloud computing scenario with flexible access control and extend the original homomorphic cryptosystem to suit our scenario by supporting various arithmetical calculations. We also prove the correctness and security of our protocols, and analyze the advantages and performance by comparing with some latest works.
With the increasing number of mobile applications and the popularity of cloud computing, the combination of these two techniques that named mobile cloud computing (MCC) attracts great attention in recent years. A promising public key encryption scheme, Attribute-Based Encryption (ABE), especially the Ciphertext Policy Attribute-Based Encryption (CP-ABE), has been used for realizing fine-grained access control on encrypted data stored in MCC. However, the computational overhead of encryption and decryption grow with the complexity of the access policy. Thus, maintaining data security as well as…
In this paper, we present a novel Secured Outsourced Content Based Image Retrieval solution, which allows looking for similar images stored into the cloud in a homomorphically encrypted form. Its originality is fourfold. In a first time, it extracts from a Paillier encrypted image a wavelet based global image signature. In second, this signature is extracted in an encrypted form and gives no clues about the image content. In a third time, its calculation does not require the cloud to communicate with a trusted third party as usually proposed by other existing schemes. More clearly, all computa…
As more sensitive data is shared and stored by third-party sites on the internet, there will be a need to encrypt data stored at these sites. One drawback of encrypting data is that it can be selectively shared only at a coarse-grained level. Attribute based encryption is a public-key-based one-to-many encryption that allows users to encrypt and decry pt data based on user attributes. A promising application of ABE is flexible access control of encrypted data stored in the cloud using access policies and ascribed attributes associated with private keys and cipher text. One.One of the main effi…
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.
The cloud paradigm enables users to outsource their data to computationally powerful third-party service providers for data management. Many data management tasks rely on the data dependencies in the outsourced data. This raises an important issue of how the data owner can protect the sensitive information in the outsourced data while preserving the data dependencies. In this paper, we consider functional dependency FD, an important type of data dependency. We design a FD-preserving encryption scheme, named F2, that enables the service provider to discover the FDs from the encrypted dataset. W…
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…
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.
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…
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. …
IoT is the fastest-growing technology with a wide range of applications in various domains. IoT devices generate data from a real-world environment every second and transfer it to the cloud due to the less storage at the edge site. An outsourced cloud is a solution for handling the storage problem. Users' privacy can be exposed by storing the data on the cloud. Therefore, we propose a Private Data Storage model that stores IoT data on the outsourced cloud with privacy preservation. Fog nodes are used at the edge side for data partition and encryption. Partitioned and encrypted data is aggregat…
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…
In this work, we propose an outsourced Secure Multilayer Perceptron (SMLP) scheme where privacy and confidentiality of both the data and the model are ensured during the training and the classification phases. More clearly, this SMLP : i) can be trained by a cloud server based on data previously outsourced by a user in an homomorphically encrypted form; ii) its parameters are homomorphically encrypted giving thus no clues to the cloud; and iii) it can also be used for classifying new encrypted data sent by the user returning him the encrypted classification result encrypted. The originality of…
Homomorphic secret sharing (HSS) allows multiple input clients to secret-share their data among multiple servers such that each server is able to locally compute a function on its shares to obtain a partial result and all partial results enable the reconstruction of the function's value on the outsourced data by an output client. The existing HSS schemes for {\em high-degree} polynomials either {\em require a large number of servers} or {\em lack verifiability}, which is essential for ensuring the correctness of the outsourced computations. In this paper, we propose a two-server verifiable HSS…
Ciphertext-policy hierarchical attribute-based encryption (CP-HABE) is a promising cryptographic primitive for enforcing the fine-grained access control with scalable key delegation and user revocation mechanisms on the outsourced encrypted data in a cloud. Wang et al. (2011) proposed the first CP-HABE scheme and showed that the scheme is semantically secure in the random oracle model [4, 5]. Due to some weakness in its key delegation mechanism, by presenting two attacks, we demonstrate the scheme does not offer any confidentiality and fine-grained access control. In this way, anyone who has j…
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…
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…
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. …
