On Strong Simulation and Composable Point Obfuscation

The Virtual Black Box (VBB) property for program obfuscators provides a strong guarantee: Anything computable by an efficient adversary given the obfuscated program can also be computed by an efficient simulator with only oracle access to the program. However, we know how to achieve this notion only for very restricted classes of programs. This work studies a simple relaxation of VBB: Allow the simulator unbounded computation time, while still allowing only polynomially many queries to the oracle. We then demonstrate the viability of this relaxed notion, which we call Virtual Grey Box (VGB), in the context of fully composable obfuscators for point programs: It is known that, w.r.t. VBB, if such obfuscators exist then there exist multi-bit point obfuscators (aka ``digital lockers\u27\u27) and subsequently also very strong variants of encryption that are resilient to various attacks, such as key leakage and key-dependent-messages. However, no composable VBB-obfuscators for point programs have been shown. We show fully composable {\em VGB}-obfuscators for point programs under a strong variant of the Decision Diffie Hellman assumption. We show they suffice for the above applications and even for extensions to the public key setting as well as for encryption schemes with resistance to certain related key attacks (RKA)

Obfuscation for Cryptographic Purposes

An obfuscation of a function F should satisfy two requirements: firstly, using it should be possible to evaluate F; secondly, should not reveal anything about F that cannot be learnt from oracle access to F. Several definitions for obfuscation exist. However, most of them are either too weak for or incompatible with cryptographic applications, or have been shown impossible to achieve, or both. We give a new definition of obfuscation and argue for its reasonability and usefulness. In particular, we show that it is strong enough for cryptographic applications, yet we show that it has the potential for interesting positive results. We illustrat

Functional Encryption as Mediated Obfuscation

We introduce a new model for program obfuscation, called mediated obfuscation. A mediated obfuscation is a 3-party protocol for evaluating an obfuscated program that requires minimal interaction and limited trust. The party who originally supplies the obfuscated program need not be online when the client wants to evaluate the program. A semi-trusted third-party mediator allows the client to evaluate the program, while learning nothing about the obfuscated program or the client’s inputs and outputs. Mediated obfuscation would provide the ability for a software vendor to safely outsource the less savory aspects (like accounting of usage statistics, and remaining online to facilitate access) of “renting out” access to proprietary software. We give security definitions for this new obfuscation paradigm, and then present a simple and generic construction based on functional encryption. If a functional encryption scheme supports decryption functionality F (m, k), then our construction yields a mediated obfuscation of the class of functions {F (m, ·) | m}. In our construction, the interaction between the client and the mediator is minimal (much more efficient than a general- purpose multi-party computation protocol). Instantiating with existing FE constructions, we achieve obfuscation for point-functions with output (under a strong “virtual black-box” notion of security), and a general feasibility result for obfuscating conjunctive normal form and disjunctive normal form formulae (under a weaker “semantic” notion of security). Finally, we use mediated obfuscation to illustrate a connection between worst-case and average-case static obfuscation. In short, an average-case (static) obfuscation of some component of a suitable functional encryption scheme yields a worst-case (static) obfuscation for a related class of functions. We use this connection to demonstrate new impossibility results for average-case (static) obfuscation

On Symmetric Encryption and Point Obfuscation

We show tight connections between several cryptographic primitives, namely encryption with weakly random keys, encryption with key-dependent messages (KDM), and obfuscation of point functions with multi-bit output(which we call multi-bit point functions, or MBPFs, for short). These primitives, which have been studied mostly separately in recent works, bear some apparent similarities, both in the flavor of their security requirements and in the flavor of their constructions and assumptions. Still, rigorous connections have not been drawn. Our results can be interpreted as indicating that MBPF obfuscators imply a very strong form of encryption that simultaneously achieves security for weakly-random keys and key-dependent messages as special cases. Similarly, each one of the other primitives implies a certain restricted form of MBPF obfuscation. Our results carry both constructions and impossibility results from one primitive to others. In particular: - The recent impossibility result for KDM security of Haitner and Holenstein (TCC \u2709) carries over to MBPF obfuscators. - The Canetti-Dakdouk construction of MBPF obfuscators based on a strong variant of the DDH assumption (EC \u2708) gives an encryption scheme which is secure w.r.t. any weak key distribution of super-logarithmic min-entropy (and in particular, also has very strong leakage resilient properties). - All the recent constructions of encryption schemes that are secure w.r.t. weak keys imply a weak form of MBPF obfuscators

08491 Abstracts Collection -- Theoretical Foundations of Practical Information Security

From 30.11. to 05.12.2008, the Dagstuhl Seminar 08491 ``Theoretical Foundations of Practical Information Security \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

LNCS

Composable notions of incoercibility aim to forbid a coercer from using anything beyond the coerced parties’ inputs and outputs to catch them when they try to deceive him. Existing definitions are restricted to weak coercion types, and/or are not universally composable. Furthermore, they often make too strong assumptions on the knowledge of coerced parties—e.g., they assume they known the identities and/or the strategies of other coerced parties, or those of corrupted parties— which makes them unsuitable for applications of incoercibility such as e-voting, where colluding adversarial parties may attempt to coerce honest voters, e.g., by offering them money for a promised vote, and use their own view to check that the voter keeps his end of the bargain. In this work we put forward the first universally composable notion of incoercible multi-party computation, which satisfies the above intuition and does not assume collusions among coerced parties or knowledge of the corrupted set. We define natural notions of UC incoercibility corresponding to standard coercion-types, i.e., receipt-freeness and resistance to full-active coercion. Importantly, our suggested notion has the unique property that it builds on top of the well studied UC framework by Canetti instead of modifying it. This guarantees backwards compatibility, and allows us to inherit results from the rich UC literature. We then present MPC protocols which realize our notions of UC incoercibility given access to an arguably minimal setup—namely honestly generate tamper-proof hardware performing a very simple cryptographic operation—e.g., a smart card. This is, to our knowledge, the first proposed construction of an MPC protocol (for more than two parties) that is incoercibly secure and universally composable, and therefore the first construction of a universally composable receipt-free e-voting protocol

Studies in program obfuscation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 159-164).Program obfuscation is the software analog to the problem of tamper-proofing hardware. The goal of program obfuscation is to construct a compiler, called an "obfuscator," that garbles the code of a computer program while maintaining its functionality. Commercial products exist to perform this procedure, but they do not provide a rigorous security guarantee. Over the past decade, program obfuscation has been studied by the theoretical cryptography community, where rigorous definitions of security have been proposed and obfuscators have been constructed for some families of programs. This thesis presents three contributions based on the virtual black-box security definition of Barak et al [10]. First, we show tight connections between obfuscation and symmetric-key encryption. Specifically, obfuscation can be used to construct an encryption scheme with strong leakage resilience and key-dependent message security. The converse is also true, and these connections scale with the level of security desired. As a result, the known constructions and impossibility results for each primitive carry over to the other. Second, we present two new security definitions that augment the virtual black-box property to incorporate non-malleability. The virtual black-box definition does not prevent an adversary from modifying an obfuscated program intelligently. By contrast, our new definitions provide software with the same security guarantees as tamper-proof and tamper-evident hardware, respectively. The first definition prohibits tampering, and the second definition requires that tampering is detectable after the fact. We construct non-malleable obfuscators of both favors for some program families of interest. Third, we present an obfuscator for programs that test for membership in a hyperplane. This generalizes prior works that obfuscate equality testing. We prove the security of the obfuscator under a new strong variant of the Decisional Diffie-Hellman assumption that holds in the generic group model. Additionally, we show a cryptographic application of the new obfuscator to leak-ageresilient one-time digital signatures. The thesis also includes a survey of the prior results in the field.by Mayank Varia.Ph.D

Point-Function Obfuscation: A Framework and Generic Constructions

We give a definitional framework for point-function obfuscation in which security is parameterized by a class of algorithms we call target generators. Existing and new notions are captured and explained as corresponding to different choices of this class. This leads to an elegant question: Is it possible to provide a generic construction, meaning one that takes an arbitrary class of target generators and returns a point-function obfuscator secure for it? We answer this in the affirmative with three generic constructions, the first based on indistinguishability obfuscation, the second on deterministic public-key encryption and the third on universal computational extractors. By exploiting known constructions of the primitives assumed, we obtain new point-function obfuscators, including many under standard assumptions. We end with a broader look that relates different known and possible notions of point function obfuscation to each other and to ours