Efficient Fuzzy Search on Encrypted Data

We study the problem of efficient (sub-linear) fuzzy search on encrypted outsourced data, in the symmetric-key setting. In particular, a user who stores encrypted data on a remote untrusted server forms queries that enable the server to efficiently locate the records containing the requested keywords, even though the user may misspell keywords or provide noisy data in the query. We define an appropriate primitive for a general \emph{closeness} function on the message space that we call \emph{efficiently fuzzy-searchable encryption} (\emph{EFSE}). Next we identify an optimal security notion for EFSE. We demonstrate that existing schemes do not meet our security definition and propose a new scheme that we prove secure under basic assumptions. Unfortunately, the scheme requires large ciphertext length, but we show that, in a sense, this space-inefficiency is unavoidable for a general, optimally-secure scheme. Seeking the right balance between efficiency and security, we then show how to construct schemes that are more efficient and satisfy a weaker security notion that we propose. To illustrate, we present and analyze a more space-efficient scheme for supporting fuzzy search on biometric data that achieves the weaker notion

Five-coloring graphs on the Klein bottle

We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list.Comment: 40 pages, 7 figure

Order-Preserving Encryption Revisited: Improved Security Analysis and Alternative Solutions

We further the study of order-preserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by Boldyreva et al.~(Eurocrypt \u2709). First, we address the open problem of characterizing what encryption via a random order-preserving function (ROPF) leaks about underlying data (ROPF being the ``ideal object\u27\u27 in the security definition, POPF, satisfied by their scheme.) In particular, we show that, for a database of randomly distributed plaintexts and appropriate choice of parameters, ROPF encryption leaks neither the precise value of any plaintext nor the precise distance between any two of them. The analysis here introduces useful new techniques. On the other hand, we show that ROPF encryption leaks approximate value of any plaintext as well as approximate distance between any two plaintexts, each to an accuracy of about square root of the domain size. We then study schemes that are not order-preserving, but which nevertheless allow efficient range queries and achieve security notions stronger than POPF. In a setting where the entire database is known in advance of key-generation (considered in several prior works), we show that recent constructions of ``monotone minimal perfect hash functions\u27\u27 allow to efficiently achieve (an adaptation of) the notion of IND-O(rdered) CPA also considered by Boldyreva et al., which asks that \emph{only} the order relations among the plaintexts is leaked. Finally, we introduce {\em modular} order-preserving encryption (MOPE), in which the scheme of Boldyreva et al. is prepended with a random shift cipher. MOPE improves the security of OPE in a sense, as it does not leak any information about plaintext location. We clarify that our work should not be interpreted as saying the original scheme of Boldyreva et al., or the variants that we introduce, are ``secure\u27\u27 or ``insecure.\u27\u27 Rather, the goal of this line of research is to help practitioners decide whether the options provide a suitable security-functionality tradeoff for a given application

Preserving Both Privacy and Utility in Network Trace Anonymization

As network security monitoring grows more sophisticated, there is an increasing need for outsourcing such tasks to third-party analysts. However, organizations are usually reluctant to share their network traces due to privacy concerns over sensitive information, e.g., network and system configuration, which may potentially be exploited for attacks. In cases where data owners are convinced to share their network traces, the data are typically subjected to certain anonymization techniques, e.g., CryptoPAn, which replaces real IP addresses with prefix-preserving pseudonyms. However, most such techniques either are vulnerable to adversaries with prior knowledge about some network flows in the traces, or require heavy data sanitization or perturbation, both of which may result in a significant loss of data utility. In this paper, we aim to preserve both privacy and utility through shifting the trade-off from between privacy and utility to between privacy and computational cost. The key idea is for the analysts to generate and analyze multiple anonymized views of the original network traces; those views are designed to be sufficiently indistinguishable even to adversaries armed with prior knowledge, which preserves the privacy, whereas one of the views will yield true analysis results privately retrieved by the data owner, which preserves the utility. We present the general approach and instantiate it based on CryptoPAn. We formally analyze the privacy of our solution and experimentally evaluate it using real network traces provided by a major ISP. The results show that our approach can significantly reduce the level of information leakage (e.g., less than 1\% of the information leaked by CryptoPAn) with comparable utility

Order-Preserving Symmetric Encryption

We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al.~(SIGMOD \u2704) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look ``as-random-as-possible subject to the order-preserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random order-preserving function and the hypergeometric probability distribution. In particular, it makes black-box use of an efficient sampling algorithm for the latter

Practical Order-Revealing Encryption with Limited Leakage

In an order-preserving encryption scheme, the encryption algorithm produces ciphertexts that preserve the order of their plaintexts. Order-preserving encryption schemes have been studied intensely in the last decade, and yet not much is known about the security of these schemes. Very recently, Boneh et al. (Eurocrypt 2015) introduced a generalization of order-preserving encryption, called order-revealing encryption, and presented a construction which achieves this notion with best-possible security. Because their construction relies on multilinear maps, it is too impractical for most applications and therefore remains a theoretical result. In this work, we build efficiently implementable order-revealing encryption from pseudorandom functions. We present the first efficient order-revealing encryption scheme which achieves a simulation-based security notion with respect to a leakage function that precisely quantifies what is leaked by the scheme. In fact, ciphertexts in our scheme are only about 1.6 times longer than their plaintexts. Moreover, we show how composing our construction with existing order-preserving encryption schemes results in order-revealing encryption that is strictly more secure than all preceding order-preserving encryption schemes

Symmetric schemes for efficient range and error-tolerant search on encrypted data

Large-scale data management systems rely more and more on cloud storage, where the need for efficient search capabilities clashes with the need for data confidentiality. Encryption and efficient accessibility are naturally at odds, as for instance strong encryption necessitates that ciphertexts reveal nothing about underlying data. Searchable encryption is an active field in cryptography studying encryption schemes that provide varying levels of efficiency, functionality, and security, and efficient searchable encryption focuses on schemes enabling sub-linear (in the size of the database) search time. I present the first cryptographic study of efficient searchable symmetric encryption schemes supporting two types of search queries, range queries and error-tolerant queries. The natural solution to accommodate efficient range queries on ciphertexts is to use order-preserving encryption (OPE). I propose a security definition for OPE schemes, construct the first OPE scheme with provable security, and further analyze security by characterizing one-wayness of the scheme. Efficient error-tolerant queries are enabled by efficient fuzzy-searchable encryption (EFSE). For EFSE, I introduce relevant primitives, an optimal security definition and a (somewhat space-inefficient, but in a sense efficient as possible) scheme achieving it, and more efficient schemes that achieve a weaker, but practical, security notion. In all cases, I introduce new appropriate security definitions, construct novel schemes, and prove those schemes secure under standard assumptions. The goal of this line of research is to provide constructions and provable security analysis that should help practitioners decide whether OPE or FSE provides a suitable efficiency-security-functionality tradeoff for a given application.Ph.D

Practical Order-Revealing Encryption with Limited Leakage

In an order-preserving encryption scheme, the encryption algorithm produces ciphertexts that preserve the order of their plaintexts. Order-preserving encryption schemes have been studied intensely in the last decade, and yet not much is known about the security of these schemes. Very recently, Boneh et al. (Eurocrypt 2015) introduced a generalization of order-preserving encryption, called order-revealing encryption, and presented a construction which achieves this notion with best-possible security. Because their construction relies on multilinear maps, it is too impractical for most applications and therefore remains a theoretical result. In this work, we build efficiently implementable order-revealing encryption from pseudoran-dom functions. We present the first efficient order-revealing encryption scheme which achieves a simulation-based security notion with respect to a leakage function that precisely quantifies what is leaked by the scheme. Moreover, we show how composing our construction with existing order-preserving encryption schemes results in order-revealing encryption that is strictly more secure than all preceding order-preserving encryption schemes.