Proofs of Encrypted Data Retrievability with Probabilistic and Homomorphic Message Authenticators

Real-world applications of authenticated encryption often require the encryption to be computable online, e.g. to compute the i th block of ciphertext after having processed the first i blocks of plaintext. A significant line of research was dedicated to identifying security notions for online authenticated encryption schemes, that capture various security goals related to real-life scenarios. Fouque, Joux, Martinet and Valette proposed definitions of privacy and integrity against adversaries that can query their oracles in a blockwise-adaptive manner, to model memory-constrained applications. A decade later, Fleischmann, Forler and Lucks proposed the notion of online nonce misuse-resistant authenticated encryption (OAE) to capture the security of online authenticated encryption under nonce-reuse. In this work we investigate the relation between these notions. We first recast the blockwise notions of Fouque et al. to make them compatible with online authenticated encryption schemes that support headers. We then show that OAE and the conjunction of the blockwise notions are “almost” equivalent. We identify the missing property on the side of blockwise notions, and formalize it under the name PR-TAG. With PR-TAG being just an auxiliary definition, the equivalence we finally show suggests that OAE and the blockwise model for online authenticated encryption capture essentially the same notion of security.

In cryptography, there has been tremendous success in building various two-party protocols with small communication complexity out of homomorphic semantically-secure encryption schemes, using their homomorphic properties in a black-box way. A few notable examples of such primitives include items like single database Private Information Retrieval (PIR) schemes (introduced in [15]) and private database update with small communication (introduced in [5]). In this paper, we illustrate a general methodology for determining what types of protocols can and cannot be implemented with small communication by using homomorphic encryption in a black-box way. We hope that this work will provide a simple litmus test of feasibility for black-box use of known homomorphic encryption schemes by other cryptographic researchers attempting to develop new protocols with low communication. Additionally, a precise mathematical language for reasoning about such problems is developed in this work, which may be of independent interest. We stress that the class of algebraic structures for which we prove communication complexity lower bounds is large, and covers practically all known semantically-secure homomorphic cryptosystems (including those based upon bilinear maps). Finally, we show the following equivalence which relates group homomorphic encryption and a major open question of designing a so-called fully-homomorphic cryptosystem: a fully homomorphic encryption scheme (over a non-zero ring) exists if and only if there exists homomorphic encryption over any finite non-abelian simple group. This result somewhat generalizes results of Barrington [1] (to any group containing a finite non-abelian simple subgroup) and of Maurer and Rhodes [18], and in fact gives a constructiveproof of the 1974 result Werner [28]. (This also answers an open question posed by Rappe in [23], who in 2004 proved a special case of this result.)

Previously, two schemes were proposed to enhance the security of EIGamal encryption. The weakness of the original scheme is improved by adding a message authentication tag to ciphertext. The resultant schemes are non-malleable encryption under chosen ciphertext attack. We observed that the same security goal can be achieved with less computational cost The proposed scheme saves 33% of computing power on average In processing decryption, it can save at most 46% of computations if the technique of multiple simultaneous exponentiations is used.

Homomorphic encryption (HE) schemes enable computing functions on encrypted data, by means of a public Eval procedure that can be applied to ciphertexts. But the evaluated ciphertexts so generated may differ from freshly encrypted ones. This brings up the question of whether one can keep computing on evaluated ciphertexts. An i-hop homomorphic encryption scheme is one where Eval can be called on its own output up to i times, while still being able to decrypt the result. A multi-hop homomorphic encryption is a scheme which is i-hop for all i. In this work we study i-hop and multi-hop schemes in conjunction with the properties of function-privacy (i.e., Eval's output hides the function) and compactness (i.e., the output of Eval is short). We provide formal definitions and describe several constructions. First, we observe that bootstrapping techniques can be used to convert any (1-hop) homomorphic encryption scheme into an i-hop scheme for any i, and the result inherits the function-privacy and/or compactness of the underlying scheme. However, if the underlying scheme is not compact (such as schemes derived from Yao circuits) then the complexity of the resulting i-hop scheme can be as high as nO(i). We then describe a specific DDH-based multi-hop homomorphic encryption scheme that does not suffer from this exponential blowup. Although not compact, this scheme has complexity linear in the size of the composed function, independently of the number of hops. The main technical ingredient in this solution is a re-randomizable variant of the Yao circuits. Namely, given a garbled circuit, anyone can re-garble it in such a way that even the party that generated the original garbled circuit cannot recognize it. This construction may be of independent interest.

e18725 Background: Healthcare data sharing is important for the creation of diverse and large data sets, supporting clinical decision making, and accelerating efficient research to improve patient outcomes. This is especially vital in the case of real world data analysis. However, stakeholders are reluctant to share their data without ensuring patients’ privacy, proper protection of their data sets and the ways they are being used. Homomorphic encryption is a cryptographic capability that can address these issues by enabling computation on encrypted data without ever decrypting it, so the analytics results are obtained without revealing the raw data. The aim of this study is to prove the accuracy of analytics results and the practical efficiency of the technology. Methods: A real-world data set of colorectal cancer patients’ survival data, following two different treatment interventions, including 623 patients and 24 variables, amounting to 14,952 items of data, was encrypted using leveled homomorphic encryption implemented in the PALISADE software library. Statistical analysis of key oncological endpoints was blindly performed on both the raw data and the homomorphically-encrypted data using descriptive statistics and survival analysis with Kaplan-Meier curves. Results were then compared with an accuracy goal of two decimals. Results: The difference between the raw data and the homomorphically encrypted data results, regarding all variables analyzed was within the pre-determined accuracy range goal, as well as the practical efficiency of the encrypted computation measured by run time, are presented in table. Conclusions: This study demonstrates that data encrypted with Homomorphic Encryption can be statistical analyzed with a precision of at least two decimal places, allowing safe clinical conclusions drawing while preserving patients’ privacy and protecting data owners’ data assets. Homomorphic encryption allows performing efficient computation on encrypted data non-interactively and without requiring decryption during computation time. Utilizing the technology will empower large-scale cross-institution and cross- stakeholder collaboration, allowing safe international collaborations. Clinical trial information: 0048-19-TLV. [Table: see text]

Abstract: Encryption is essential in preventing unauthorized access to sensitive data in light of the growing concerns about data security in cloud computing. Homomorphic encryption promises to enable secure calculations on encrypted data without the need for decryption, particularly for cloud-based operations. To evaluate the effectiveness and applicability of several homomorphic encryption algorithms for safe cloud computing, we compare and contrast them in this research paper. Partially homomorphic encryption (PHE), somewhat homomorphic encryption (SHE), and fully homomorphic encryption (FHE) are the three basic homomorphic encryption subtypes that we examine. The implications of this study can aid cloud service providers and organizations in selecting the most appropriate homomorphic encryption scheme based on their specific security requirements and performance considerations. The research contributes to the ongoing efforts to enhance data privacy in cloud computing environments, opening new possibilities for secure data processing in an increasingly connected digital world. The exploration of homomorphic encryption schemes in this study opens new avenues for research and development in the field of cryptographic techniques. As technology continues to evolve, so too must our approaches to safeguarding data. This research serves as a catalyst for further innovations in homomorphic encryption algorithms, enabling even more efficient and robust methods for secure data processing in cloud environments and beyond. The insights derived from this research paper not only empower cloud service providers and organizations to make informed decisions about selecting the most appropriate homomorphic encryption scheme but also contribute to the broader mission of fortifying data privacy and security in cloud computing.

Histograms are widely used for summarizing data distributions, detecting anomalies, and improving machine learning models’ accuracy. However, traditional histogram-based methods require access to raw data, raising privacy concerns, particularly in sensitive IoT applications. Encryption-based techniques offer potential solutions; however, they secure the data in transit or storage, requiring decryption during analysis, which exposes raw data to potential privacy risks. In this paper, we propose a method for constructing privacy-preserving histograms directly on homomorphically encrypted IoT data, leveraging the Fast Fully Homomorphic Encryption over the Torus (TFHE) scheme implemented in the Concrete framework. To overcome the challenges posed by homomorphic encryption, we redesign the traditional histogram construction algorithm, optimizing it for secure computation by addressing constraints related to nested loops and conditional statements. As an evaluation use case, we have considered an outlier detection mechanism based on histogram frequency counts, ensuring that all data and computations remain encrypted throughout the process. Our method achieves results consistent with plaintext-based outlier detection while maintaining reasonable computational overhead compared to those reported in the existing literature.

With the wide application of cloud computing in multi-tenant, heterogeneous nodes and high-concurrency environments, model parameters frequently interact during distributed training, which easily leads to privacy leakage, communication redundancy, and decreased aggregation efficiency. To realize the collaborative optimization of privacy protection and computing performance, this study proposes the Heterogeneous Federated Homomorphic Encryption Cloud (HFHE-Cloud) model, which integrates federated learning (FL) and homomorphic encryption and constructs a secure and efficient collaborative learning framework for cloud platforms. Under the condition of not exposing the original data, the model effectively reduces the performance bottleneck caused by encryption calculation and communication delay through hierarchical key mapping and dynamic scheduling mechanism of heterogeneous nodes. The experimental results show that HFHE-Cloud is significantly superior to Federated Averaging (FedAvg), Federated Proximal (FedProx), Federated Personalization (FedPer) and Federated Normalized Averaging (FedNova) in comprehensive performance, Homomorphically Encrypted Federated Averaging (HE-FedAvg) and other five baseline models. In the dimension of privacy protection, the global accuracy is up to 94.25%, and the Loss is stable within 0.09. In terms of computing performance, the encryption and decryption time is shortened by about one third, and the encryption overhead is controlled at 13%. In terms of distributed training efficiency, the number of communication rounds is reduced by about one fifth, and the node participation rate is stable at over 90%. The results verify the model's ability to achieve high security and high scalability in multi-tenant environment. This study aims to provide cloud service providers and enterprise data holders with a technical solution of high-intensity privacy protection and efficient collaborative training that can be deployed in real cloud platforms.

Fully homomorphic encryption allows cloud servers to evaluate any computable functions for clients without revealing any information. It attracts much attention from both of the scientific community and the industry since Gentry’s seminal scheme. Currently, the Brakerski-Gentry-Vaikuntanathan scheme with its optimizations is one of the most potentially practical schemes and has been implemented in a homomorphic encryption C++ library HElib. HElib supplies friendly interfaces for arithmetic operations of polynomials over finite fields. Based on HElib, Chen and Guang (2015) implemented arithmetic over encrypted integers. In this paper, we revisit the HElib-based implementation of homomorphically arithmetic operations on encrypted integers. Due to several optimizations and more suitable arithmetic circuits for homomorphic encryption evaluation, our implementation is able to homomorphically evaluate 64-bit addition/subtraction and 16-bit multiplication for encrypted integers without bootstrapping. Experiments show that our implementation outperforms Chen and Guang’s significantly.

Public key encryption schemes developed based on learning with error problem became popular for homomorphic encryption, and are proved as secured schemes based on the worst-case hardness of short vector problems. Homomorphic encryption allows computations over the cipher text without decryption. Implementation of the scheme is not considered to be practical because of its larger public keys and larger cipher texts. Large public key and cipher texts require huge space in the cloud storages. However, there are some approaches proposed to shorten the cipher texts and public keys of LWE-based homomorphic encryption scheme. The objective of the paper is to introduce an idea to shorten the public keys and cipher texts in the storage. Also, support homomorphic addition operation on reduced cipher texts. The aim of the paper is not only to give the practical implementation of standard LWE-based homomorphic encryption operation (Addition) on the reduced cipher texts and also the performance of the proposed scheme.

Homomorphic Encryption (HE) allows encrypted data to be processed without decryption, which could maximize the protection of user privacy without affecting the data utility. Thanks to strides made by cryptographers in the past few years, the efficiency of HE has been drastically improved, and machine learning on homomorphically encrypted data has become possible. Several works have explored machine learning based on HE, but most of them are restricted to the outsourced scenario, where all the data comes from a single data owner. We propose HomoPAI, an HE-based secure collaborative machine learning system, enabling a more promising scenario, where data from multiple data owners could be securely processed. Moreover, we integrate our system with the popular MPI framework to achieve parallel HE computations. Experiments show that our system can train a logistic regression model on millions of homomorphically encrypted data in less than two minutes.

This paper presents a lightweight, sponge-based authenticated encryption (AE) family called Beetle. When instantiated with the PHOTON permutation from CRYPTO 2011, Beetle achieves the smallest footprint—consuming only a few more than 600 LUTs on FPGA while maintaining 64-bit security. This figure is significantly smaller than all known lightweight AE candidates which consume more than 1,000 LUTs, including the latest COFB-AES from CHES 2017. In order to realize such small hardware implementation, we equip Beetle with an “extremely tight” bound of security. The trick is to use combined feedback to create a difference between the cipher text block and the rate part of the next feedback (in traditional sponge these two values are the same). Then we are able to show that Beetle is provably secure up to min{ c − log r , b /2, r } bits, where b is the permutation size and r and c are parameters called rate and capacity, respectively. The tight security bound allows us to select the smallest security parameters, which in turn result in the smallest footprint.

At present study, homomorphic encryption scheme is most focusing on algorithm efficiency and security and the rare for homomorphic encryption simulation research. This paper for the Gentry's Somewhat Homomorphic Encryption scheme for the simulation research, in clear text size within a certain range simulation was Somewhat Homomorphic Encryption scheme, and presents the relationship between the length of plaintext and ciphertext size.

An encryption scheme is homomorphic if it supports operations on encrypted data. Homomorphic encryption allows a device to perform arbitrary computations on encrypted data without user secret key. Recently it is introduced new homomorphic encryption schemes with improved performance that can be implemented in IoT device in production environments. The IoT concept encompasses devices, sensors, and services existing within an interconnected infrastructure with an efficient access to sample computational facilities. In this paper we evaluated features of exact arithmetic homomorphic encryption mechanisms: BFV and BGV and approximate homomorphic encryption scheme: CKKS. In the paper we measured performances of operations of homomorphic encryption schemes: BGV, BFV and CKKS that are implemented in Raspberry Pi 4 IoT device.

The objective of this research is to develop a novel image encryption method that can be used to considerably increase the security of encrypted images. To solve this image security problem, we propose a distributed homomorphic image encryption scheme where the images of interest are those in the visible electromagnetic spectrum. In our encryption phase, a red green blue (RGB) image is first separated into its constituent channel images, and then the numerical intensity value of a pixel from each channel is written as a sum of smaller pixel intensity sub-values, leading to having several component images for each of the R, G, and B-channel images. A homomorphic encryption function is used to separately encrypted each of the pixel intensity sub-values in each component image using an encryption key, leading to a distributed image encryption approach. Each of the encrypted component images can be compressed before transmission and/or storage. In our decryption phase, each encrypted component image is decompressed if necessary, and then the homomorphic property of the encryption function is used to transform the product of individually encrypted pixel intensity sub-values in each encrypted component images, to the encryption of their sum, before applying the corresponding decryption function with a decryption key to recover the original pixel's intensity values for each channel image, and then recovering the original RGB image. Furthermore, a special case of an RGB image encryption and decryption where a pixel's intensity value from each channel is written as a sum of only two sub-values is implemented and simulated with a software. The resulting cipher-images are subject to a range of security tests and analyses. Results from these tests shown that our proposed homomorphic image encryption scheme is robust and can resist security attacks, as well as increases the security of the associated encrypted images. Our proposed homomorphic image encryption scheme has produced highly secure encrypted images.