141 research outputs found

    Adaptively Secure Garbling Schemes for Parallel Computations

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    We construct the first adaptively secure garbling scheme based on standard public-key assumptions for garbling a circuit C:{0,1}n{0,1}mC: \{0, 1\}^n \mapsto \{0, 1\}^m that simultaneously achieves a near-optimal online complexity n+m+poly(λ,logC)n + m + \textrm{poly}(\lambda, \log |C|) (where λ\lambda is the security parameter) and \emph{preserves the parallel efficiency} for evaluating the garbled circuit; namely, if the depth of CC is dd, then the garbled circuit can be evaluated in parallel time dpoly(logC,λ)d \cdot \textrm{poly}(\log|C|, \lambda). In particular, our construction improves over the recent seminal work of Garg et al. (Eurocrypt 2018), which constructs the first adaptively secure garbling scheme with a near-optimal online complexity under the same assumptions, but the garbled circuit can only be evaluated gate by gate in a sequential manner. Our construction combines their novel idea of linearization with several new ideas to achieve parallel efficiency without compromising online complexity. We take one step further to construct the first adaptively secure garbling scheme for parallel RAM (PRAM) programs under standard assumptions that preserves the parallel efficiency. Previous such constructions we are aware of is from strong assumptions like indistinguishability obfuscation. Our construction is based on the work of Garg et al. (Crypto 2018) for adaptively secure garbled RAM, but again introduces several new ideas to handle parallel RAM computation, which may be of independent interests. As an application, this yields the first constant round secure computation protocol for persistent PRAM programs in the malicious settings from standard assumptions

    Garbling Schemes and Applications

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    The topic of this thesis is garbling schemes and their applications. A garbling scheme is a set of algorithms for realizing secure two-party computation. A party called a client possesses a private algorithm as well as a private input and would like to compute the algorithm with this input. However, the client might not have enough computational resources to evaluate the function with the input on his own. The client outsources the computation to another party, called an evaluator. Since the client wants to protect the algorithm and the input, he cannot just send the algorithm and the input to the evaluator. With a garbling scheme, the client can protect the privacy of the algorithm, the input and possibly also the privacy of the output. The increase in network-based applications has arisen concerns about the privacy of user data. Therefore, privacy-preserving or privacy-enhancing techniques have gained interest in recent research. Garbling schemes seem to be an ideal solution for privacy-preserving applications. First of all, secure garbling schemes hide the algorithm and its input. Secondly, garbling schemes are known to have efficient implementations. In this thesis, we propose two applications utilizing garbling schemes. The first application provides privacy-preserving electronic surveillance. The second application extends electronic surveillance to more versatile monitoring, including also health telemetry. This kind of application would be ideal for assisted living services. In this work, we also present theoretical results related to garbling schemes. We present several new security definitions for garbling schemes which are of practical use. Traditionally, the same garbled algorithm can be evaluated once with garbled input. In applications, the same function is often evaluated several times with different inputs. Recently, a solution based on fully homomorphic encryption provides arbitrarily reusable garbling schemes. The disadvantage in this approach is that the arbitrary reuse cannot be efficiently implemented due to the inefficiency of fully homomorphic encryption. We propose an alternative approach. Instead of arbitrary reusability, the same garbled algorithm could be used a limited number of times. This gives us a set of new security classes for garbling schemes. We prove several relations between new and established security definitions. As a result, we obtain a complex hierarchy which can be represented as a product of three directed graphs. The three graphs in turn represent the different flavors of security: the security notion, the security model and the level of reusability. In addition to defining new security classes, we improve the definition of side-information function, which has a central role in defining the security of a garbling scheme. The information allowed to be leaked by the garbled algorithm and the garbled input depend on the representation of the algorithm. The established definition of side-information models the side-information of circuits perfectly but does not model side-information of Turing machines as well. The established model requires that the length of the argument, the length of the final result and the length of the function can be efficiently computable from the side-information function. Moreover, the side-information depends only on the function. In other words, the length of the argument, the length of the final result and the length of the function should only depend on the function. For circuits this is a natural requirement since the number of input wires tells the size of the argument, the number of output wires tells the size of the final result and the number of gates and wires tell the size of the function. On the other hand, the description of a Turing machine does not set any limitation to the size of the argument. Therefore, side-information that depends only on the function cannot provide information about the length of the argument. To tackle this problem, we extend the model of side-information so that side-information depends on both the function and the argument. The new model of side information allows us to define new security classes. We show that the old security classes are compatible with the new model of side-information. We also prove relations between the new security classes.Tämä väitöskirja käsittelee garblausskeemoja ja niiden sovelluksia. Garblausskeema on työkalu, jota käytetään turvallisen kahden osapuolen laskennan toteuttamiseen. Asiakas pitää hallussaan yksityistä algoritmia ja sen yksityistä syötettä, joilla hän haluaisi suorittaa tietyn laskennan. Asiakkaalla ei välttämättä ole riittävästi laskentatehoa, minkä vuoksi hän ei pysty suorittamaan laskentaa itse, vaan joutuu ulkoistamaan laskennan toiselle osapuolelle, palvelimelle. Koska asiakas tahtoo suojella algoritmiaan ja syötettään, hän ei voi vain lähettää niitä palvelimen laskettavaksi. Asiakas pystyy suojelemaan syötteensä ja algoritminsa yksityisyyttä käyttämällä garblausskeemaa. Verkkopohjaisten sovellusten kasvu on herättänyt huolta käyttäjien datan yksityisyyden turvasta. Siksi yksityisyyden säilyttävien tai yksityisyyden suojaa lisäävien tekniikoiden tutkimus on saanut huomiota. Garblaustekniikan avulla voidaan suojata sekä syöte että algoritmi. Lisäksi garblaukselle tiedetään olevan useita tehokkaita toteutuksia. Näiden syiden vuoksi garblausskeemat ovat houkutteleva tekniikka käytettäväksi yksityisyyden säilyttävien sovellusten toteutuksessa. Tässä työssä esittelemme kaksi sovellusta, jotka hyödyntävät garblaustekniikkaa. Näistä ensimmäinen on yksityisyyden säilyttävä sähköinen seuranta. Toinen sovellus laajentaa seurantaa monipuolisempaan monitorointiin, kuten terveyden kaukoseurantaan. Tästä voi olla hyötyä etenkin kotihoidon palveluille. Tässä työssä esitämme myös teoreettisia tuloksia garblausskeemoihin liittyen. Esitämme garblausskeemoille uusia turvallisuusmääritelmiä, joiden tarve kumpuaa käytännön sovelluksista. Perinteisen määritelmän mukaan samaa garblattua algoritmia voi käyttää vain yhdellä garblatulla syötteellä laskemiseen. Käytännössä kuitenkin samaa algoritmia käytetään usean eri syötteen evaluoimiseen. Hiljattain on esitetty tähän ongelmaan ratkaisu, joka perustuu täysin homomorfiseen salaukseen. Tämän ratkaisun ansiosta samaa garblattua algoritmia voi turvallisesti käyttää mielivaltaisen monta kertaa. Ratkaisun haittapuoli kuitenkin on, ettei sille ole tiedossa tehokasta toteutusta, sillä täysin homomorfiseen salaukseen ei ole vielä onnistuttu löytämään sellaista. Esitämme vaihtoehtoisen näkökulman: sen sijaan, että samaa garblattua algoritmia voisi käyttää mielivaltaisen monta kertaa, sitä voikin käyttää vain tietyn, ennalta rajatun määrän kertoja. Tämä näkökulman avulla voidaan määritellä lukuisia uusia turvallisuusluokkia. Todistamme useita relaatioita uusien ja vanhojen turvallisuusmääritelmien välillä. Relaatioiden avulla garblausskeemojen turvallisuusluokille saadaan muodostettua hierarkia, joka koostuu kolmesta komponentista. Tieto, joka paljastuu garblatusta algoritmista tai garblatusta syötteestä riippuu siitä, millaisessa muodossa algoritmi on esitetty, kutsutaan sivutiedoksi. Vakiintunut määritelmä mallintaa loogisen piiriin liittyvää sivutietoa täydellisesti, mutta ei yhtä hyvin Turingin koneeseen liittyvää sivutietoa. Tämä johtuu siitä, että jokainen yksittäinen looginen piiri asettaa syötteensä pituudelle rajan, mutta yksittäisellä Turingin koneella vastaavanlaista rajoitusta ei ole. Parannamme sivutiedon määritelmää, jolloin tämä ongelma poistuu. Uudenlaisen sivutiedon avulla voidaan määritellä uusia turvallisuusluokkia. Osoitamme, että vanhat turvallisuusluokat voidaan esittää uudenkin sivutiedon avulla. Todistamme myös relaatioita uusien luokkien välillä.Siirretty Doriast

    Succinct Adaptive Garbled RAM

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    We show how to garble a large persistent database and then garble, one by one, a sequence of adaptively and adversarially chosen RAM programs that query and modify the database in arbitrary ways. Still, it is guaranteed that the garbled database and programs reveal only the outputs of the programs when run in sequence on the database. The runtime, space requirements and description size of the garbled programs are proportional only to those of the plaintext programs and the security parameter. We assume indistinguishability obfuscation for circuits and poly-to-one collision-resistant hash functions. The latter can be constructed based on standard algebraic assumptions such as the hardness of discrete log or factoring. In contrast, all previous garbling schemes with persistent data were shown secure only in the static setting where all the programs are known in advance. As an immediate application, our scheme is the first to provide a way to outsource large databases to untrusted servers, and later query and update the database over time in a private and verifiable way, with complexity and description size proportional to those of the unprotected queries. Our scheme extends the non-adaptive RAM garbling scheme of Canetti and Holmgren [ITCS 2016]. We also define and use a new primitive, called adaptive accumulators, which is an adaptive alternative to the positional accumulators of Koppula et al [STOC 2015] and somewhere statistical binding hashing of Hubacek and Wichs [ITCS 2015]. This primitive might well be useful elsewhere

    Garbling Schemes and Applications

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    The topic of this thesis is garbling schemes and their applications. A garbling scheme is a set of algorithms for realizing secure two-party computation. A party called a client possesses a private algorithm as well as a private input and would like to compute the algorithm with this input. However, the client might not have enough computational resources to evaluate the function with the input on his own. The client outsources the computation to another party, called an evaluator. Since the client wants to protect the algorithm and the input, he cannot just send the algorithm and the input to the evaluator. With a garbling scheme, the client can protect the privacy of the algorithm, the input and possibly also the privacy of the output.  The increase in network-based applications has arisen concerns about the privacy of user data. Therefore, privacy-preserving or privacy-enhancing techniques have gained interest in recent research. Garbling schemes seem to be an ideal solution for privacy-preserving applications. First of all, secure garbling schemes hide the algorithm and its input. Secondly, garbling schemes are known to have efficient implementations.  In this thesis, we propose two applications utilizing garbling schemes. The first application provides privacy-preserving electronic surveillance. The second application extends electronic surveillance to more versatile monitoring, including also health telemetry. This kind of application would be ideal for assisted living services.  In this work, we also present theoretical results related to garbling schemes. We present several new security definitions for garbling schemes which are of practical use. Traditionally, the same garbled algorithm can be evaluated once with garbled input. In applications, the same function is often evaluated several times with different inputs. Recently, a solution based on fully homomorphic encryption provides arbitrarily reusable garbling schemes. The disadvantage in this approach is that the arbitrary reuse cannot be efficiently implemented due to the inefficiency of fully homomorphic encryption.  We propose an alternative approach. Instead of arbitrary reusability, the same garbled algorithm could be used a limited number of times. This gives us a set of new security classes for garbling schemes. We prove several relations between new and established security definitions. As a result, we obtain a complex hierarchy which can be represented as a product of three directed graphs. The three graphs in turn represent the different flavors of security: the security notion, the security model and the level of reusability.  In addition to defining new security classes, we improve the definition of side-information function, which has a central role in defining the security of a garbling scheme. The information allowed to be leaked by the garbled algorithm and the garbled input depend on the representation of the algorithm. The established definition of side-information models the side-information of circuits perfectly but does not model side-information of Turing machines as well. The established model requires that the length of the argument, the length of the final result and the length of the function can be efficiently computable from the side-information function. Moreover, the side-information depends only on the function. In other words, the length of the argument, the length of the final result and the length of the function should only depend on the function. For circuits this is a natural requirement since the number of input wires tells the size of the argument, the number of output wires tells the size of the final result and the number of gates and wires tell the size of the function. On the other hand, the description of a Turing machine does not set any limitation to the size of the argument. Therefore, side-information that depends only on the function cannot provide information about the length of the argument. To tackle this problem, we extend the model of side-information so that side-information depends on both the function and the argument. The new model of side information allows us to define new security classes. We show that the old security classes are compatible with the new model of side-information. We also prove relations between the new security classes.</p

    IST Austria Thesis

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    Many security definitions come in two flavors: a stronger “adaptive” flavor, where the adversary can arbitrarily make various choices during the course of the attack, and a weaker “selective” flavor where the adversary must commit to some or all of their choices a-priori. For example, in the context of identity-based encryption, selective security requires the adversary to decide on the identity of the attacked party at the very beginning of the game whereas adaptive security allows the attacker to first see the master public key and some secret keys before making this choice. Often, it appears to be much easier to achieve selective security than it is to achieve adaptive security. A series of several recent works shows how to cleverly achieve adaptive security in several such scenarios including generalized selective decryption [Pan07][FJP15], constrained PRFs [FKPR14], and Yao’s garbled circuits [JW16]. Although the above works expressed vague intuition that they share a common technique, the connection was never made precise. In this work we present a new framework (published at Crypto ’17 [JKK+17a]) that connects all of these works and allows us to present them in a unified and simplified fashion. Having the framework in place, we show how to achieve adaptive security for proxy re-encryption schemes (published at PKC ’19 [FKKP19]) and provide the first adaptive security proofs for continuous group key agreement protocols (published at S&P ’21 [KPW+21]). Questioning optimality of our framework, we then show that currently used proof techniques cannot lead to significantly better security guarantees for "graph-building" games (published at TCC ’21 [KKPW21a]). These games cover generalized selective decryption, as well as the security of prominent constructions for constrained PRFs, continuous group key agreement, and proxy re-encryption. Finally, we revisit the adaptive security of Yao’s garbled circuits and extend the analysis of Jafargholi and Wichs in two directions: While they prove adaptive security only for a modified construction with increased online complexity, we provide the first positive results for the original construction by Yao (published at TCC ’21 [KKP21a]). On the negative side, we prove that the results of Jafargholi and Wichs are essentially optimal by showing that no black-box reduction can provide a significantly better security bound (published at Crypto ’21 [KKPW21c])

    Collusion-Resistant Functional Encryption for RAMs

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    In recent years, functional encryption (FE) has established itself as one of the fundamental primitives in cryptography. The choice of model of computation to represent the functions associated with the functional keys plays a critical role in the complexity of the algorithms of an FE scheme. Historically, the functions are represented as circuits. However, this results in the decryption time of the FE scheme growing proportional to not only the worst case running time of the function but also the size of the input, which in many applications can be quite large. In this work, we present the first construction of a public-key collusion-resistant FE scheme, where the functions, associated with the keys, are represented as random access machines (RAMs). We base the security of our construction on the existence of: (i) public-key collusion- resistant FE for circuits and, (ii) public-key doubly-efficient private-information retrieval [Boyle et al., Canetti et al., TCC 2017]. Our scheme enjoys many nice efficiency properties, including input-specific decryption time. We also show how to achieve FE for RAMs in the bounded-key setting with weaker efficiency guarantees from laconic oblivious transfer, which can be based on standard cryptographic assumptions. En route to achieving our result, we present conceptually simpler constructions of succinct garbling for RAMs [Canetti et al., Chen et al., ITCS 2016] from weaker assumptions

    Succinct Garbling Schemes from Functional Encryption through a Local Simulation Paradigm

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    We study a simulation paradigm, referred to as local simulation, in garbling schemes. This paradigm captures simulation proof strategies in which the simulator consists of many local simulators that generate different blocks of the garbled circuit. A useful property of such a simulation strategy is that only a few of these local simulators depend on the input, whereas the rest of the local simulators only depend on the circuit. We formalize this notion by defining locally simulatable garbling schemes. By suitably realizing this notion, we give a new construction of succinct garbling schemes for Turing machines assuming the polynomial hardness of compact functional encryption and standard assumptions (such as either CDH or LWE). Prior constructions of succinct garbling schemes either assumed sub-exponential hardness of compact functional encryption or were designed only for small-space Turing machines. We also show that a variant of locally simulatable garbling schemes can be used to generically obtain adaptively secure garbling schemes for circuits. All prior constructions of adaptively secure garbling that use somewhere equivocal encryption can be seen as instantiations of our construction

    Self-Processing Private Sensor Data via Garbled Encryption

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    We introduce garbled encryption, a relaxation of secret-key multi-input functional encryption (MiFE) where a function key can be used to jointly compute upon only a particular subset of all possible tuples of ciphertexts. We construct garbled encryption for general functionalities based on one-way functions. We show that garbled encryption can be used to build a self-processing private sensor data system where after a one-time trusted setup phase, sensors deployed in the field can periodically broadcast encrypted readings of private data that can be computed upon by anyone holding function keys to learn processed output, without any interaction. Such a system can be used to periodically check, e.g., whether a cluster of servers are in an alarm state. We implement our garbled encryption scheme and find that it performs quite well, with function evaluations in the microseconds. The performance of our scheme was tested on a standard commodity laptop

    Delegating RAM Computations with Adaptive Soundness and Privacy

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    We consider the problem of delegating RAM computations over persistent databases. A user wishes to delegate a sequence of computations over a database to a server, where each computation may read and modify the database and the modifications persist between computations. Delegating RAM computations is important as it has the distinct feature that the run-time of computations maybe sub-linear in the size of the database. We present the first RAM delegation scheme that provide both soundness and privacy guarantees in the adaptive setting, where the sequence of delegated RAM programs are chosen adaptively, depending potentially on the encodings of the database and previously chosen programs. Prior works either achieved only adaptive soundness without privacy [Kalai and Paneth, ePrint\u2715], or only security in the selective setting where all RAM programs are chosen statically [Chen et al. ITCS\u2716, Canetti and Holmgren ITCS\u2716]. Our scheme assumes the existence of indistinguishability obfuscation (\iO) for circuits and the decisional Diffie-Hellman (DDH) assumption. However, our techniques are quite general and in particular, might be applicable even in settings where iO is not used. We provide a security lifting technique that lifts any proof of selective security satisfying certain special properties into a proof of adaptive security, for arbitrary cryptographic schemes. We then apply this technique to the delegation scheme of Chen et al. and its selective security proof, obtaining that their scheme is essentially already adaptively secure. Because of the general approach, we can also easily extend to delegating parallel RAM (PRAM) computations. We believe that the security lifting technique can potentially find other applications and is of independent interest

    Attribute-Based Encryption for Circuits of Unbounded Depth from Lattices: Garbled Circuits of Optimal Size, Laconic Functional Evaluation, and More

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    Although we have known about fully homomorphic encryption (FHE) from circular security assumptions for over a decade [Gentry, STOC \u2709; Brakerski–Vaikuntanathan, FOCS \u2711], there is still a significant gap in understanding related homomorphic primitives supporting all *unrestricted* polynomial-size computations. One prominent example is attribute-based encryption (ABE). The state-of-the-art constructions, relying on the hardness of learning with errors (LWE) [Gorbunov–Vaikuntanathan–Wee, STOC \u2713; Boneh et al., Eurocrypt \u2714], only accommodate circuits up to a *predetermined* depth, akin to leveled homomorphic encryption. In addition, their components (master public key, secret keys, and ciphertexts) have sizes polynomial in the maximum circuit depth. Even in the simpler setting where a single key is published (or a single circuit is involved), the depth dependency persists, showing up in constructions of 1-key ABE and related primitives, including laconic function evaluation (LFE), 1-key functional encryption (FE), and reusable garbling schemes. So far, the only approach of eliminating depth dependency relies on indistinguishability obfuscation. An interesting question that has remained open for over a decade is whether the circular security assumptions enabling FHE can similarly benefit ABE. In this work, we introduce new lattice-based techniques to overcome the depth-dependency limitations: - Relying on a circular security assumption, we construct LFE, 1-key FE, 1-key ABE, and reusable garbling schemes capable of evaluating circuits of unbounded depth and size. - Based on the *evasive circular* LWE assumption, a stronger variant of the recently proposed *evasive* LWE assumption [Wee, Eurocrypt \u2722; Tsabary, Crypto \u2722], we construct a full-fledged ABE scheme for circuits of unbounded depth and size. Our LFE, 1-key FE, and reusable garbling schemes achieve optimal succinctness (up to polynomial factors in the security parameter). Their ciphertexts and input encodings have sizes linear in the input length, while function digest, secret keys, and garbled circuits have constant sizes independent of circuit parameters (for Boolean outputs). In fact, this gives the first constant-size garbled circuits without relying on indistinguishability obfuscation. Our ABE schemes offer short components, with master public key and ciphertext sizes linear in the attribute length and secret key being constant-size
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