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International Conference on Communications

Oblivious Keyword Search Protocols in the Public Database Model

Huafei Zhu, Feng Bao

Published Jun 1, 2007• 11 citations

Abstract

Databases associated with keywords, can be public, private or hybrid, as a result the solutions to keyword search protocols for each type are different. In this paper, we study the problem of privacy-preserving keyword search in the public database model where the data-item is public but a client wishes to retrieve some data-item or search data-item, without revealing to the server which item it is. The contribution of this paper is of three fold. In the first fold, an efficient implementation of oblivious linear function evaluation protocols for secure two-party computation of a linear function over a finite field that does not emulate the circuit for computing oblivious linear function while at the same time it is provably secure against malicious adversary is presented. We show our implementation is provably secure assuming that the underlying Fujisaki-Okamoto's commitment scheme is informational hiding and computational binding as well Paillier's encryption scheme is semantically secure in the common reference string model. In the second fold, we further extend the techniques to non-linear polynomials and thus provide a secure reduction of OPE protocols of a polynomial of degree m, to m OPEs of linear polynomials. In the third fold, we use the OPEs for solving the oblivious keyword search problem along the Ogata and Kurosawa's ad hoc methodology, and show that our implementation is provably secure assuming that the underlying Fujisaki-Okamoto's commitment scheme is informational hiding and computational binding, Paillier's encryption scheme is semantically secure, G is a pseudo-random function in the common reference string model.

DOI: 10.1109/icc.2007.225

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Databases associated with keywords, can be public, private or hybrid, as a result the solutions to keyword search protocols for each type are different. In this paper, we study the problem of privacy-preserving keyword search in the public database model where the data-item is public but a client wishes to retrieve some data-item or search data-item, without revealing to the server which item it is. The contribution of this paper is of three fold. In the first fold, an efficient implementation of oblivious linear function evaluation protocols for secure two-party computation of a linear function over a finite field that does not emulate the circuit for computing oblivious linear function while at the same time it is provably secure against malicious adversary is presented. We show our implementation is provably secure assuming that the underlying Fujisaki-Okamoto's commitment scheme is informational hiding and computational binding as well Paillier's encryption scheme is semantically secure in the common reference string model. In the second fold, we further extend the techniques to non-linear polynomials and thus provide a secure reduction of OPE protocols of a polynomial of degree m, to m OPEs of linear polynomials. In the third fold, we use the OPEs for solving the oblivious keyword search problem along the Ogata and Kurosawa's ad hoc methodology, and show that our implementation is provably secure assuming that the underlying Fujisaki-Okamoto's commitment scheme is informational hiding and computational binding, Paillier's encryption scheme is semantically secure, G is a pseudo-random function in the common reference string model.

In this study, the authors design efficient protocols for a number of ‘oblivious decision program (DP) evaluation’ problems. Consider a general form of the problem where a client who holds a private input interacts with a server who holds a private DP (e.g. a decision tree or a branching program) with the goal of evaluating his input on the DP without learning any additional information. Many known private database query problems such as symmetric private information retrieval and private keyword search can be formulated as special cases of this problem. Most of the existing works on the same problem focus on optimising communication. However, in some environments (supported by a few experimental studies), it is the computation and not the communication that may be the performance bottleneck. In this study, we design ‘computationally efficient’ protocols for the above general problem, and a few of its special cases. In addition to being one‐round and requiring a small amount of work by the client (in the RAM model), the proposed protocols only require a small number of exponentiations (independent of the server's input) by both parties. The proposed constructions are, in essence, efficient and black‐box reductions of the above problem to 1‐out‐of‐2 oblivious transfer. It is proved that the proposed protocols secure (private) against ‘malicious’ adversaries in the standard ideal/real‐world simulation‐based paradigm.

In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [BGV11] technique (CRYPTO 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulation-based definitions in the presence of malicious adversaries.

Oblivious transfer is such a strong cryptographic tool that it is directly used both in private data retrieval techniques and secure, multi-party computation paradigms. We propose an optimal oblivious transfer, where the communication complexity is logarithmic in size of the database with minimum computation overhead - the computational complexity in any oblivious transfer protocol is at least linear in the size of the database. Our communication-efficient oblivious transfer protocol is a non-interactive, single-database scheme that is generally based on homomorphic encryption functions.

Security and privacy are of paramount importance in the modern information age. Secure multi-party computation and private information retrieval are canonical and representative problems in cryptography that capture the key challenges in understanding the fundamentals of security and privacy. In this dissertation, we use information theoretic tools to tackle these two classical cryptographic primitives. In the first part, we consider the secure multi-party computation problem, where multiple users, each holding an independent message, wish to compute a function on the messages without revealing any additional information. We present an efficient protocol in terms of randomness cost to securely compute a vector linear function. In the second part, we discuss the symmetric private information retrieval problem, where a user wishes to retrieve one message from a number of replicated databases while keeping the desired message index a secret from each individual database. Further, the user learns nothing about the other messages. We present an optimal protocol that achieves the minimum upload cost for symmetric private information retrieval, i.e., the queries sent from the user to the databases have the minimum number of bits.

A lot of interest has been drawn recently into public-key encryption with keyword search (PEKS), which keeps publickey encrypted documents amendable to secure keyword search. However, PEKS resist against keyword guessing attack by assuming that the size of the keyword space is beyond the polynomial level. But this assumption is ineffective in practice. PEKS are insecure under keyword guessing attack. As we observe, the key to defend such attack is to avoid the availability of the exact search trapdoor to adversaries. Accordingly, we compromise the exactness of search trapdoor by mapping at least two different keywords into a fuzzy search trapdoor. We propose a novel concept called public-key encryption with fuzzy keyword search (PEFKS), by which the un-trusted server only obtains the fuzzy search trapdoor instead of the exact search trapdoor, and define its semantic security under chosen keyword attack (SS-CKA) and indistinguishability of keywords under non-adaptively chosen keywords and keyword guessing attack (IK-NCK-KGA). For the keyword space with and without uniform distribution, we respectively present two universal transformations from anonymous identity-based encryption to PEFKS, and prove their SSCKA and IK-NCK-KGA securities. To our knowledge, PEFKS is the first scheme to resist against keyword guessing attack on condition that the keyword space is not more than the polynomial level.

Abstract. We propose a one-round 1-out-of-n computationally-private information retrieval protocol for ℓ-bit strings with low-degree polylogarithmic receivercomputation, linear sender-computation and communication Θ(k · log 2 n + ℓ · log n), where k is a possibly non-constant security parameter. The new protocol is receiver-private if the underlying length-flexible additively homomorphic public-key cryptosystem is IND-CPA secure. It can be transformed to a one-round computationally receiver-private and information-theoretically sender-private 1out-of-n oblivious-transfer protocol for ℓ-bit strings, that has the same asymptotic communication and is private in the standard complexity-theoretic model. Keywords. Computationally-private information retrieval, length-flexible additively homomorphic public-key cryptosystem, oblivious transfer. 1