A Generalization of Paillier\u27s Public-Key System With Fast Decryption

Paillier\u27s scheme is a homomorphic public key encryption scheme which is widely used in practical. For instance, Paillier\u27s scheme can be used in the data aggregation in smart grid. Damg$\mathring{a}$rd and Jurik generalized Paillier\u27s scheme to reduce the ciphertext expansion factor. However, the decryption scheme of Damg$\mathring{a}$rd and Jurik\u27s scheme is more complicated than Paillier\u27s original scheme. In this paper, we propose a new generalization of Paillier\u27s scheme and all the Paillier\u27s schemes to our knowledge are special cases of our scheme. We propose a very simple decryption algorithm which is more efficient than other generalization algorithms. We prove that our generalized Paillier\u27s scheme is IND-CPA secure. Our generalized Paillier\u27s scheme can be used in smart grid instead of Paillier\u27s scheme for higher flexibility

Actively Secure Two-Party Computation: Efficient Beaver Triple Generation

Töö kombineerib erinevaid ideid, et saavutada aktiivses mudelis turvalist kahe osapoolega ühisarvutust. Töö käigus defineerime Sharemindi raamistikku kaks uut turvaala. Kasutame aditiivset ühissalastust, sõnumiautentimisskeeme, aditiivselt homomorfset krüptosüsteemi ning nullteadmustõestusi. Protokollistikud jagame kahte osasse, vastavalt ettearvutamise ja töö faas. Ettearvutamise ajal valmistatakse ette juhuslikke väärtusi, mis võimaldavad töö faasis arvutusi kiirendada. Eelkõige keskendume korrutamise jaoks vajalike Beaveri kolmikute genereerimisele.This thesis combines currently popular ideas in actively secure multi-party computation to define two actively secure two-party protocol sets for Sharemind secure multi-party computation framework. This includes additive secret sharing, dividing work as online and precomputation phase, using Beaver triples for multiplication and using message authentication codes for integrity checks. Our protocols use additively homomorphic Paillier cryptosystem, especially in the precomputation phase. The thesis includes two different setups for secure two-party computation which are also implemented and compared to each other. In addition, we propose new ideas to use additively homomorphic cryptosystem to generate Beaver triples for any chosen modulus. The important aspects of Beaver triple generation are maximising the amount of useful bits we get from one generation and assuring that these triples are correct

Election Verifiability or Ballot Privacy: Do We Need to Choose?

We propose a new encryption primitive, \emph{commitment consistent encryption} (CCE), and instances of this primitive that enable building the first universally verifiable voting schemes with a perfectly private audit trail (PPAT) and practical complexity. That is: \begin{myitemize} \item the audit trail that is published for verifying elections guarantees everlasting privacy, and \item the computational load required from the participants is only increased by a small constant factor compared to traditional voting schemes, and is optimal in the sense of Cramer, Gennaro and Schoenmakers~\cite{CGS97}. \end{myitemize} These properties make it possible to introduce election verifiability in large scale elections as a pure benefit, that is, without loss of privacy compared to a non-verifiable scheme and at a similar level of efficiency. We propose different approaches for constructing voting schemes with PPAT from CCE, as well as two efficient CCE constructions: one is tailored for elections with a small number of candidates, while the second is suitable for elections with complex ballots

Image Classification using non-linear Support Vector Machines on Encrypted Data

In image processing, algorithms for object classification are typically based around machine learning. From the algorithm developer\u27s perspective, these can involve a considerable amount of effort and expertise to develop, which makes them commercially valuable. On the other hand, other parties may want to make use of these algorithms to classify their images, while protecting the privacy of their data. In this paper, we show how non-linear Support Vector Machines (SVMs) can be practically used for image classification on data encrypted with a Somewhat Homomorphic Encryption (SHE) scheme. Previous work has shown how an SVM with a linear kernel can be computed on encrypted data, but this only has limited applicability. By enabling SVMs with polynomial kernels, a much larger class of applications are possible with more accuracy in classification results

Theory and Practice of Cryptography and Network Security Protocols and Technologies

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities

Cloud-based homomorphic encryption for privacy-preserving machine learning in clinical decision support

While privacy and security concerns dominate public cloud services, Homomorphic Encryption (HE) is seen as an emerging solution that ensures secure processing of sensitive data via untrusted networks in the public cloud or by third-party cloud vendors. It relies on the fact that some encryption algorithms display the property of homomorphism, which allows them to manipulate data meaningfully while still in encrypted form; although there are major stumbling blocks to overcome before the technology is considered mature for production cloud environments. Such a framework would find particular relevance in Clinical Decision Support (CDS) applications deployed in the public cloud. CDS applications have an important computational and analytical role over confidential healthcare information with the aim of supporting decision-making in clinical practice. Machine Learning (ML) is employed in CDS applications that typically learn and can personalise actions based on individual behaviour. A relatively simple-to-implement, common and consistent framework is sought that can overcome most limitations of Fully Homomorphic Encryption (FHE) in order to offer an expanded and flexible set of HE capabilities. In the absence of a significant breakthrough in FHE efficiency and practical use, it would appear that a solution relying on client interactions is the best known entity for meeting the requirements of private CDS-based computation, so long as security is not significantly compromised. A hybrid solution is introduced, that intersperses limited two-party interactions amongst the main homomorphic computations, allowing exchange of both numerical and logical cryptographic contexts in addition to resolving other major FHE limitations. Interactions involve the use of client-based ciphertext decryptions blinded by data obfuscation techniques, to maintain privacy. This thesis explores the middle ground whereby HE schemes can provide improved and efficient arbitrary computational functionality over a significantly reduced two-party network interaction model involving data obfuscation techniques. This compromise allows for the powerful capabilities of HE to be leveraged, providing a more uniform, flexible and general approach to privacy-preserving system integration, which is suitable for cloud deployment. The proposed platform is uniquely designed to make HE more practical for mainstream clinical application use, equipped with a rich set of capabilities and potentially very complex depth of HE operations. Such a solution would be suitable for the long-term privacy preserving-processing requirements of a cloud-based CDS system, which would typically require complex combinatorial logic, workflow and ML capabilities

Distributed, Private, Sparse Histograms in the Two-Server Model

We consider the computation of sparse, $(\varepsilon, \delta)$-differentially private~(DP) histograms in the two-server model of secure multi-party computation~(MPC), which has recently gained traction in the context of privacy-preserving measurements of aggregate user data. We introduce protocols that enable two semi-honest non-colluding servers to compute histograms over the data held by multiple users, while only learning a private view of the data. Our solution achieves the same asymptotic $\ell_\infty$-error of $O\left(\frac{\log(1/\delta)}{\varepsilon}\right)$ as in the central model of DP, but \emph{without} relying on a trusted curator. The server communication and computation costs of our protocol are independent of the number of histogram buckets, and are linear in the number of users, while the client cost is independent of the number of users, $\varepsilon$, and $\delta$. Its linear dependence on the number of users lets our protocol scale well, which we confirm using microbenchmarks: for a billion users, $\varepsilon = 0.5$, and $\delta = 10^{-11}$, the per-user cost of our protocol is only $1.08$ ms of server computation and $339$ bytes of communication. In contrast, a baseline protocol using garbled circuits only allows up to $10^6$ users, where it requires 600 KB communication per user

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