Outsourced Analysis of Encrypted Graphs in the Cloud with Privacy Protection

Huge diagrams have unique properties for organizations and research, such as client linkages in informal organizations and customer evaluation lattices in social channels. They necessitate a lot of financial assets to maintain because they are large and frequently continue to expand. Owners of large diagrams may need to use cloud resources due to the extensive arrangement of open cloud resources to increase capacity and computation flexibility. However, the cloud's accountability and protection of schematics have become a significant issue. In this study, we consider calculations for security savings for essential graph examination practices: schematic extraterrestrial examination for outsourcing graphs in the cloud server. We create the security-protecting variants of the two proposed Eigen decay computations. They are using two cryptographic algorithms: additional substance homomorphic encryption (ASHE) strategies and some degree homomorphic encryption (SDHE) methods. Inadequate networks also feature a distinctively confidential info adaptation convention to allow the trade-off between secrecy and data sparseness. Both dense and sparse structures are investigated. According to test results, calculations with sparse encoding can drastically reduce information. SDHE-based strategies have reduced computing time, while ASHE-based methods have reduced stockpiling expenses

Practical Homomorphic Encryption Over the Integers for Secure Computation in the Cloud

We present novel homomorphic encryption schemes for integer arithmetic, intended primarily for use in secure single-party computation in the cloud. These schemes are capable of securely computing arbitrary degree polynomials homomorphically. In practice, ciphertext size and running times limit the polynomial degree, but this appears sufficient for most practical applications. We present four schemes, with increasing levels of security, but increasing computational overhead. Two of the schemes provide strong security for high-entropy data. The remaining two schemes provide strong security regardless of this assumption. These four algorithms form the first two levels of a hierarchy of schemes which require linearly decreasing entropy. We have evaluated these four algorithms by computing low-degree polynomials. The timings of these computations are extremely favourable by comparison with even the best of existing methods, and dramatically out-perform running times of directly comparable schemes by a factor of up to 1000, and considerably more than that for fully homomorphic schemes, used in the same context. The results clearly demonstrate the practical applicability of our schemes

Constant bandwidth ORAM with small block size using PIR operations

Recently, server-with-computation model has been applied in Oblivious RAM scheme to achieve constant communication (constant number of blocks). However, existing works either result in large block size O(log^6N), or have some security flaws. Furthermore, a lower bound of sub-logarithmic bandwidth was given if we do not use expensive fully homomorphic operations. The question of \whether constant bandwidth with smaller block size without fully homomorphic operations is achievable remains open. In this paper, we provide an affirmative answer. We propose a constant bandwidth ORAM scheme with block size O(log^3N) using only additive homomorphic operations. Our scheme is secure under the standard model. Technically, we design a non-trivial oblivious clear algorithm with very small bandwidth to improve the eviction algorithm in ORAM for which the lower bound proof does not apply. As an additional benefit, we are able to reduce the server storage due to the reduction in bucket size

Constructive tt-secure Homomorphic Secret Sharing for Low Degree Polynomials

This paper proposes $t$-secure homomorphic secret sharing schemes for low degree polynomials. Homomorphic secret sharing is a cryptographic technique to outsource the computation to a set of servers while restricting some subsets of servers from learning the secret inputs. Prior to our work, at Asiacrypt 2018, Lai, Malavolta, and Schröder proposed a $1$-secure scheme for computing polynomial functions. They also alluded to $t$-secure schemes without giving explicit constructions; constructing such schemes would require solving set cover problems, which are generally NP-hard. Moreover, the resulting implicit schemes would require a large number of servers. In this paper, we provide a constructive solution for threshold-$t$ structures by combining homomorphic encryption with the classic secret sharing scheme for general access structure by Ito, Saito, and Nishizeki. Our scheme also quantitatively improves the number of required servers from $O(t^2)$ to $O(t)$, compared to the implicit scheme of Lai et al. We also suggest several ideas for future research directions

Homomorphic Secret Sharing for Multipartite and General Adversary Structures Supporting Parallel Evaluation of Low-degree Polynomials

Homomorphic secret sharing (HSS) for a function $f$ allows input parties to distribute shares for their private inputs and then locally compute output shares from which the value of $f$ is recovered. HSS can be directly used to obtain a two-round multiparty computation (MPC) protocol for possibly non-threshold adversary structures whose communication complexity is independent of the size of $f$. In this paper, we propose two constructions of HSS schemes supporting parallel evaluation of a single low-degree polynomial and tolerating multipartite and general adversary structures. Our multipartite scheme tolerates a wider class of adversary structures than the previous multipartite one in the particular case of a single evaluation and has exponentially smaller share size than the general construction. While restricting the range of tolerable adversary structures (but still applicable to non-threshold ones), our schemes perform $\ell$ parallel evaluations with communication complexity approximately $\ell/\log\ell$ times smaller than simply using $\ell$ independent instances. We also formalize two classes of adversary structures taking into account real-world situations to which the previous threshold schemes are inapplicable. Our schemes then perform $O(m)$ parallel evaluations with almost the same communication cost as a single evaluation, where $m$ is the number of parties

Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms

Cryptographic Foundations For Control And Optimization: Making Cloud-Based And Networked Decisions On Encrypted Data

Advances in communication technologies and computational power have determined a technological shift in the data paradigm. The resulting architecture requires sensors to send local data to the cloud for global processing such as estimation, control, decision and learning, leading to both performance improvement and privacy concerns. This thesis explores the emerging field of private control for Internet of Things, where it bridges dynamical systems and computations on encrypted data, using applied cryptography and information-theoretic tools.Our research contributions are privacy-preserving interactive protocols for cloud-outsourced decisions and data processing, as well as for aggregation over networks in multi-agent systems, both of which are essential in control theory and machine learning. In these settings, we guarantee privacy of the data providers\u27 local inputs over multiple time steps, as well as privacy of the cloud service provider\u27s proprietary information. Specifically, we focus on (i) private solutions to cloud-based constrained quadratic optimization problems from distributed private data; (ii) oblivious distributed weighted sum aggregation; (iii) linear and nonlinear cloud-based control on encrypted data; (iv) private evaluation of cloud-outsourced data-driven control policies with sparsity and low-complexity requirements. In these scenarios, we require computational privacy and stipulate that each participant is allowed to learn nothing more than its own result of the computation. Our protocols employ homomorphic encryption schemes and secure multi-party computation tools with the purpose of performing computations directly on encrypted data, such that leakage of private information at the computing entity is minimized. To this end, we co-design solutions with respect to both control performance and privacy specifications, and we streamline their implementation by exploiting the rich structure of the underlying private data