A Study of Separations in Cryptography: New Results and New Models

For more than 20 years, black-box impossibility results have been used to argue the infeasibility of constructing certain cryptographic primitives (e.g., key agreement) from others (e.g., one-way functions). In this dissertation we further extend the frontier of this field by demonstrating several new impossibility results as well as a new framework for studying a more general class of constructions. Our first two results demonstrate impossibility of black-box constructions of two commonly used cryptographic primitives. In our first result we study the feasibility of black-box constructions of predicate encryption schemes from standard assumptions and demonstrate strong limitations on the types of schemes that can be constructed. In our second result we study black-box constructions of constant-round zero-knowledge proofs from one-way permutations and show that, under commonly believed complexity assumptions, no such constructions exist. A widely recognized limitation of black-box impossibility results, however, is that they say nothing about the usefulness of (known) non-black-box techniques. This state of affairs is unsatisfying as we would at least like to rule out constructions using the set of techniques we have at our disposal. With this motivation in mind, in the final result of this dissertation we propose a new framework for black-box constructions with a non-black-box flavor, specifically, those that rely on zero-knowledge proofs relative to some oracle. Our framework is powerful enough to capture a large class of known constructions, however we show that the original black-box separation of key agreement from one-way functions still holds even in this non-black-box setting that allows for zero-knowledge proofs

POPE: Partial Order Preserving Encoding

Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. In this paper, we propose an alternative approach to range queries over encrypted data that is optimized to support insert-heavy workloads as are common in "big data" applications while still maintaining search functionality and achieving stronger security. Specifically, we propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Using only O(1) persistent and $O(n^\epsilon)$ non-persistent client storage for $0<\epsilon<1$, our POPE scheme provides extremely fast batch insertion consisting of a single round, and efficient search with O(1) amortized cost for up to $O(n^{1-\epsilon})$ search queries. This improved security and performance makes our scheme better suited for today's insert-heavy databases.Comment: Appears in ACM CCS 2016 Proceeding

Computing on Masked Data to improve the Security of Big Data

Organizations that make use of large quantities of information require the ability to store and process data from central locations so that the product can be shared or distributed across a heterogeneous group of users. However, recent events underscore the need for improving the security of data stored in such untrusted servers or databases. Advances in cryptographic techniques and database technologies provide the necessary security functionality but rely on a computational model in which the cloud is used solely for storage and retrieval. Much of big data computation and analytics make use of signal processing fundamentals for computation. As the trend of moving data storage and computation to the cloud increases, homeland security missions should understand the impact of security on key signal processing kernels such as correlation or thresholding. In this article, we propose a tool called Computing on Masked Data (CMD), which combines advances in database technologies and cryptographic tools to provide a low overhead mechanism to offload certain mathematical operations securely to the cloud. This article describes the design and development of the CMD tool.Comment: 6 pages, Accepted to IEEE HST Conferenc

SoK: Cryptographically Protected Database Search

Protected database search systems cryptographically isolate the roles of reading from, writing to, and administering the database. This separation limits unnecessary administrator access and protects data in the case of system breaches. Since protected search was introduced in 2000, the area has grown rapidly; systems are offered by academia, start-ups, and established companies. However, there is no best protected search system or set of techniques. Design of such systems is a balancing act between security, functionality, performance, and usability. This challenge is made more difficult by ongoing database specialization, as some users will want the functionality of SQL, NoSQL, or NewSQL databases. This database evolution will continue, and the protected search community should be able to quickly provide functionality consistent with newly invented databases. At the same time, the community must accurately and clearly characterize the tradeoffs between different approaches. To address these challenges, we provide the following contributions: 1) An identification of the important primitive operations across database paradigms. We find there are a small number of base operations that can be used and combined to support a large number of database paradigms. 2) An evaluation of the current state of protected search systems in implementing these base operations. This evaluation describes the main approaches and tradeoffs for each base operation. Furthermore, it puts protected search in the context of unprotected search, identifying key gaps in functionality. 3) An analysis of attacks against protected search for different base queries. 4) A roadmap and tools for transforming a protected search system into a protected database, including an open-source performance evaluation platform and initial user opinions of protected search.Comment: 20 pages, to appear to IEEE Security and Privac

Fighting Fake News in Encrypted Messaging with the Fuzzy Anonymous Complaint Tally System (FACTS)

Recent years have seen a strong uptick in both the prevalence and real-world consequences of false information spread through online platforms. At the same time, encrypted messaging systems such as WhatsApp, Signal, and Telegram, are rapidly gaining popularity as users seek increased privacy in their digital lives. The challenge we address is how to combat the viral spread of misinformation without compromising privacy. Our FACTS system tracks user complaints on messages obliviously, only revealing the message\u27s contents and originator once sufficiently many complaints have been lodged. Our system is private, meaning it does not reveal anything about the senders or contents of messages which have received few or no complaints; secure, meaning there is no way for a malicious user to evade the system or gain an outsized impact over the complaint system; and scalable, as we demonstrate excellent practical efficiency for up to millions of complaints per day. Our main technical contribution is a new collaborative counting Bloom filter, a simple construction with difficult probabilistic analysis, which may have independent interest as a privacy-preserving randomized count sketch data structure. Compared to prior work on message flagging and tracing in end-to-end encrypted messaging, our novel contribution is the addition of a high threshold of multiple complaints that are needed before a message is audited or flagged. We present and carefully analyze the probabilistic performance of our data structure, provide a precise security definition and proof, and then measure the accuracy and scalability of our scheme via experimentation

Bounded-Collusion Attribute-Based Encryption from Minimal Assumptions

Attribute-based encryption (ABE) enables encryption of messages under access policies so that only users with attributes satisfying the policy can decrypt the ciphertext. In standard ABE, an arbitrary number of colluding users, each without an authorized attribute set, cannot decrypt the ciphertext. However, all existing ABE schemes rely on concrete cryptographic assumptions such as the hardness of certain problems over bilinear maps or integer lattices. Furthermore, it is known that ABE cannot be constructed from generic assumptions such as public-key encryption using black-box techniques. In this work, we revisit the problem of constructing ABE that tolerates collusions of arbitrary but a priori bounded size. We present an ABE scheme secure against bounded collusions that requires only semantically secure public-key encryption. Our scheme achieves significant improvement in the size of the public parameters, secret keys, and ciphertexts over the previous construction of bounded-collusion ABE from minimal assumptions by Gorbunov et al. (CRYPTO 2012). We also obtain bounded-collusion symmetric-key ABE (which requires the secret key for encryption) by replacing the public-key encryption with symmetric-key encryption, which can be built from the minimal assumption of one-way functions

CompGC: Efficient Offline/Online Semi-honest Two-party Computation

We introduce a new technique, component-based garbled circuits, for increasing the efficiency of secure two-party computation in the offline/online semi-honest setting. We observe that real-world functions are generally constructed in a modular way, comprising many standard components such as arithmetic operations and other common tasks. Our technique allows circuits for these common tasks to be garbled and shared during an offline phase; once the function to compute is specified, these pre-shared components can be chained together to create a larger garbled circuit. We stress that we do not assume that the function is known during the offline phase --- only that it uses some common, predictable components. We give an implementation, CompGC, of this technique and measure the efficiency gains for various examples. We find that our technique results in roughly an order of magnitude performance improvement over standard garbled circuit-based secure two-party computation

Cryptography for Big Data Security

As big data collection and analysis becomes prevalent in today’s computing environments there is a growing need for techniques to ensure security of the collected data. To make matters worse, due to its large volume and velocity, big data is commonly stored on distributed or shared computing resources not fully controlled by the data owner. Thus, tools are needed to ensure both the confidentiality of the stored data and the integrity of the analytics results even in untrusted environments. In this chapter, we present several cryptographic approaches for securing big data and discuss the appropriate use scenarios for each. We begin with the problem of securing big data storage. We first address the problem of secure block storage for big data allowing data owners to store and retrieve their data from an untrusted server. We present techniques that allow a data owner to both control access to their data and ensure that none of their data is modified or lost while in storage. However, in most big data applications, it is not sufficient to simply store and retrieve one’s data and a search functionality is necessary to allow one to select only the relevant data. Thus, we present several techniques for searchable encryption allowing database- style queries over encrypted data. We review the performance, functionality, and security provided by each of these schemes and describe appropriate use-cases. However, the volume of big data often makes it infeasible for an analyst to retrieve all relevant data. Instead, it is desirable to be able to perform analytics directly on the stored data without compromising the confidentiality of the data or the integrity of the computation results. We describe several recent cryptographic breakthroughs that make such processing possible for varying classes of analytics. We review the performance and security characteristics of each of these schemes and summarize how they can be used to protect big data analytics especially when deployed in a cloud setting. We hope that the exposition in this chapter will raise awareness of the latest types of tools and protections available for securing big data. We believe better understanding and closer collaboration between the data science and cryptography communities will be critical to enabling the future of big data processing