Succinct Adaptive Garbled RAM

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

Reuse It Or Lose It: More Efficient Secure Computation Through Reuse of Encrypted Values

Two-party secure function evaluation (SFE) has become significantly more feasible, even on resource-constrained devices, because of advances in server-aided computation systems. However, there are still bottlenecks, particularly in the input validation stage of a computation. Moreover, SFE research has not yet devoted sufficient attention to the important problem of retaining state after a computation has been performed so that expensive processing does not have to be repeated if a similar computation is done again. This paper presents PartialGC, an SFE system that allows the reuse of encrypted values generated during a garbled-circuit computation. We show that using PartialGC can reduce computation time by as much as 96% and bandwidth by as much as 98% in comparison with previous outsourcing schemes for secure computation. We demonstrate the feasibility of our approach with two sets of experiments, one in which the garbled circuit is evaluated on a mobile device and one in which it is evaluated on a server. We also use PartialGC to build a privacy-preserving "friend finder" application for Android. The reuse of previous inputs to allow stateful evaluation represents a new way of looking at SFE and further reduces computational barriers.Comment: 20 pages, shorter conference version published in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Pages 582-596, ACM New York, NY, US

Cryptography

The Oberwolfach workshop Cryptography brought together scientists from cryptography with mathematicians specializing in the algorithmic problems underlying cryptographic security. The goal of the workshop was to stimulate interaction and collaboration that enables a holistic approach to designing cryptography from the mathematical foundations to practical applications. The workshop covered basic computational problems such as factoring and computing discrete logarithms and short vectors. It addressed fundamental research results leading to innovative cryptography for protecting security and privacy in cloud applications. It also covered some practical applications

ARM2GC: Succinct Garbled Processor for Secure Computation

We present ARM2GC, a novel secure computation framework based on Yao's Garbled Circuit (GC) protocol and the ARM processor. It allows users to develop privacy-preserving applications using standard high-level programming languages (e.g., C) and compile them using off-the-shelf ARM compilers (e.g., gcc-arm). The main enabler of this framework is the introduction of SkipGate, an algorithm that dynamically omits the communication and encryption cost of the gates whose outputs are independent of the private data. SkipGate greatly enhances the performance of ARM2GC by omitting costs of the gates associated with the instructions of the compiled binary, which is known by both parties involved in the computation. Our evaluation on benchmark functions demonstrates that ARM2GC not only outperforms the current GC frameworks that support high-level languages, it also achieves efficiency comparable to the best prior solutions based on hardware description languages. Moreover, in contrast to previous high-level frameworks with domain-specific languages and customized compilers, ARM2GC relies on standard ARM compiler which is rigorously verified and supports programs written in the standard syntax.Comment: 13 page

Black-Box Parallel Garbled RAM

In 1982, Yao introduced a fundamental technique of ``circuit garbling\u27\u27 that became a central building block in cryptography. Recently, the question of garbling general random-access memory (RAM) programs received a lot of attention in the literature where garbling an encrypted data can be done separately from garbling program(s) that execute on this (garbled) RAM. The most recent results of Garg, Lu, and Ostrovsky (FOCS 2015) achieve a garbled RAM with black-box use of any one-way functions and poly-log overhead of data and program garbling in all the relevant parameters, including program run-time. The advantage of their solution is that large data can be garbled first, and act as persistent garbled storage (e.g. in the cloud) and later programs can be garbled and sent to be executed on this garbled database in a non-interactive manner. One of the main advantages of cloud computing is not only that it has large storage but also that it has a large number of parallel processors. Despite multiple successful efforts on parallelizing (interactive) Oblivious RAM, the non-interactive garbling of parallel programs remained open until very recently. Specifically, Boyle, Chung and Pass in their upcoming TCC 2016 paper (see their recently updated eprint version) have recently shown how to garbled PRAM program with poly-logarithmic (parallel) overhead assuming non-black-box use of identity-based encryption. The question whether such a strong assumption and non-black-box use of such a strong assumption are needed. In this paper, we resolve this important open question and show how to garble parallel programs, with only black-box use one one-way functions and with only poly-log overhead in the (parallel) running time. Our result works for any number of parallel processors

Adaptive Garbled Circuits and Garbled RAM from Non-Programmable Random Oracles

Garbled circuit techniques that are secure in the adaptive setting -- where inputs are chosen after the garbled program is sent -- are motivated by practice, but they are notoriously difficult to achieve. Prior adaptive garbling is either impractically expensive or encrypts the entire garbled program with the output of a programmable random oracle (PRO), a strong assumption. We present a simple framework for proving adaptive security of garbling schemes in the non-programmable random oracle (NPRO) model. NPRO is a much milder assumption than PRO, and it is close to the assumption required by the widely used Free XOR extension. Our framework is applicable to a number of GC techniques. As our main goal and as an application of the framework, we construct and prove adaptively secure a garbling scheme for tri-state circuits, a recently proposed circuit model that captures both Boolean circuits and RAM programs (Heath et al., Crypto 2023). For a given TSC $C$, our garbling of $C$ is at most $|C|\cdot \lambda$ bits long, where $\lambda$ is the security parameter. This implies both an adaptively secure garbled Boolean circuit scheme, as well an adaptively secure garbled RAM scheme where the garbling of $T$ steps of a RAM program has size $O(T \cdot \log^3 T \cdot \log \log T \cdot \lambda)$ bits. Our scheme is concretely efficient: its Boolean circuit handling matches the performance of the popular half-gates, and it is adaptively secure from NPRO

Tri-State Circuits: A Circuit Model that Captures RAM

We introduce tri-state circuits (TSCs). TSCs form a natural model of computation that, to our knowledge, has not been considered by theorists. The model captures a surprising combination of simplicity and power. TSCs are simple in that they allow only three wire values ($0,1,$ and undefined - $\mathcal{Z}$) and three types of fan-in two gates; they are powerful in that their statically placed gates fire (execute) eagerly as their inputs become defined, implying orders of execution that depend on input. This behavior is sufficient to efficiently evaluate RAM programs. We construct a TSC that emulates $T$ steps of any RAM program and that has only $O(T \cdot \log^3 T \cdot \log \log T)$ gates. Contrast this with the reduction from RAM to Boolean circuits, where the best approach scans all of memory on each access, incurring quadratic cost. We connect TSCs with cryptography by using them to improve Yao\u27s Garbled Circuit (GC) technique. TSCs capture the power of garbling far better than Boolean Circuits, offering a more expressive model of computation that leaves per-gate cost essentially unchanged. As an important application, we construct authenticated Garbled RAM (GRAM), enabling constant-round maliciously-secure 2PC of RAM programs. Let $\lambda$ denote the security parameter. We extend authenticated garbling to TSCs; by simply plugging in our TSC-based RAM, we obtain authenticated GRAM running at cost $O(T \cdot \log^3 T \cdot \log \log T \cdot \lambda)$, outperforming all prior work, including prior semi-honest GRAM. We also give semi-honest garbling of TSCs from a one-way function (OWF). This yields OWF-based GRAM at cost $O(T \cdot \log^3 T \cdot \log \log T \cdot \lambda)$, outperforming the best prior OWF-based GRAM by more than factor $\lambda$

Garbling Schemes and Applications

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

Constant-Round Maliciously Secure Two-Party Computation in the RAM Model

The random-access memory (RAM) model of computation allows program constant-time memory lookup and is more applicable in practice today, covering many important algorithms. This is in contrast to the classic setting of secure 2-party computation (2PC) that mostly follows the approach for which the desired functionality must be represented as a boolean circuit. In this work we design the first constant round maliciously secure two-party protocol in the RAM model. Our starting point is the garbled RAM construction of Gentry et al. (EUROCRYPT 2014) that readily induces a constant round semi-honest two-party protocol for any RAM program assuming identity-based encryption schemes. We show how to enhance the security of their construction into the malicious setting while facing several challenges that stem due to handling the data memory. Next, we show how to apply our techniques to a more recent garbled RAM construction by Garg et al. (STOC 2015) that is based on one-way functions