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Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries.

Carmit Hazay, Yehuda Lindell

Published Jan 1, 2009• 4 citations
OpenAlex

Abstract

Abstract. In this paper we construct efficient secure protocols for set intersection and pattern matching. Our protocols for securely computing the set intersection functionality are based on secure pseudorandom function evaluations, in contrast to previous protocols that used secure polynomial evaluation. In addition to the above, we also use secure pseudorandom function evaluation in order to achieve secure pattern matching. In this case, we utilize specific properties of the Naor-Reingold pseudorandom function in order to achieve high efficiency. Our results are presented in two adversary models. Our protocol for secure pattern matching and one of our protocols for set intersection achieve security against malicious adversaries under a relaxed definition where one corruption case is simulatable and for the other only privacy (formalized through indistinguishability) is guaranteed. We also present a protocol for set intersection that is fully simulatable in the model of covert adversaries. Loosely speaking, this means that a malicious adversary can cheat, but will then be caught with good probability. 1

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We revisit the problem of constructing efficient secure two-party protocols for the problems of setintersection and set-union, focusing on the model of malicious parties. Our main results are constantround protocols that exhibit linear communication and a (practically) linear number of exponentiations with simulation based security. In the heart of these constructions is a technique based on a combination of a perfectly hiding commitment and an oblivious pseudorandom function evaluation protocol. Our protocols readily transform into protocols that are UC-secure, and we discuss how to perform these transformations. Keywords: Secure two-party computation, Simulation-based security, Set-intersection, Set-union, Oblivious pseudorandom function evaluation.

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Secure set intersection protocols confronting with covert adversary are efficient and guarantee correctness with a non-negligible probability, which is smaller than 1. However, they are not desirable when correctness is required to be achieved with probability 1, since correctness may be broken when the covert adversary successfully cheats. In order to get desirable result about correctness, we introduce a rational adversary instead of a covert adversary into the secure set-intersection protocol using smartcard tokens. The rational adversary has the same “deterrence factor” as a covert adversary but additionally has utilities defined as in the game theory. The main target of the rational adversary is to maximize his utilities by cheating in the protocol. Note that cheating does not bring him optimal utility, thus he has no incentives to cheat. We prove that given proper utilities, the strategy not to cheat induces Nash equilibrium for the rational adversary. Therefore, correctness can be guaranteed with probability 1. Furthermore, our protocol has the same round complexity as the secure setintersection protocol using smartcard tokens since the introduction of a rational adversary does not increase the round complexity.

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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.

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Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries

Carmit Hazay, Yehuda Lindell

Springer eBooks•Feb 25, 2008•270 citations

Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries

Carmit Hazay, Yehuda Lindell

Journal of Cryptology•Nov 17, 2008•98 citations
Abstract. In this paper we construct efficient secure protocols for set intersection and pattern matching. Our protocols for securely computing the set intersection functionality are based on secure pseudorandom function evaluations, in contrast to previous protocols that used secure polynomial evaluation. In addition to the above, we also use secure pseudorandom function evaluation in order to achieve secure pattern matching. In this case, we utilize specific properties of the Naor-Reingold pseudorandom function in order to achieve high efficiency. Our results are presented in two adversary models. Our protocol for secure pattern matching and one of our protocols for set intersection achieve security against malicious adversaries under a relaxed definition where one corruption case is simulatable and for the other only privacy (formalized through indistinguishability) is guaranteed. We also present a protocol for set intersection that is fully simulatable in the model of covert adversaries. Loosely speaking, this means that a malicious adversary can cheat, but will then be caught with good probability. 1
We revisit the problem of constructing efficient secure two-party protocols for the problems of setintersection and set-union, focusing on the model of malicious parties. Our main results are constantround protocols that exhibit linear communication and a (practically) linear number of exponentiations with simulation based security. In the heart of these constructions is a technique based on a combination of a perfectly hiding commitment and an oblivious pseudorandom function evaluation protocol. Our protocols readily transform into protocols that are UC-secure, and we discuss how to perform these transformations. Keywords: Secure two-party computation, Simulation-based security, Set-intersection, Set-union, Oblivious pseudorandom function evaluation.
Secure set intersection protocols confronting with covert adversary are efficient and guarantee correctness with a non-negligible probability, which is smaller than 1. However, they are not desirable when correctness is required to be achieved with probability 1, since correctness may be broken when the covert adversary successfully cheats. In order to get desirable result about correctness, we introduce a rational adversary instead of a covert adversary into the secure set-intersection protocol using smartcard tokens. The rational adversary has the same “deterrence factor” as a covert adversary but additionally has utilities defined as in the game theory. The main target of the rational adversary is to maximize his utilities by cheating in the protocol. Note that cheating does not bring him optimal utility, thus he has no incentives to cheat. We prove that given proper utilities, the strategy not to cheat induces Nash equilibrium for the rational adversary. Therefore, correctness can be guaranteed with probability 1. Furthermore, our protocol has the same round complexity as the secure setintersection protocol using smartcard tokens since the introduction of a rational adversary does not increase the round complexity.
The study of secure multiparty computation has yielded powerful feasibility results showing that any efficient functionality can be securely computed in the presence of malicious adversaries. Despite this, there are few problems of specific interest for which we have highly efficient protocols that are secure in the presence of malicious adversaries under full simulation based definitions (following the ideal/real model paradigm). Due to the difficulties of constructing such protocols, many researchers have resorted to weaker definitions of security and weaker adversary models. In this paper, we construct highly efficient protocols for the well-studied problem of oblivious polynomial evaluation. Our protocol is secure under standard cryptographic assumptions for the settings of malicious adversaries, and readily transform to protocols that are secure under universal composability and in the presence of covert adversaries. Our protocol is constant round and requires O(d · s) exponentiations, where d is the degree of the polynomial and s is a statistical security parameter (that should equal about 160 in practice).
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.