Viet Tung Hoang

Foundations of garbled circuits

Garbled circuits, a classical idea rooted in the work of Yao, have long been understood as a cryptographic technique, not a cryptographic goal. Here we cull out a primitive corresponding to this technique. We call it a garbling scheme. We provide a provable-security treatment for garbling schemes, endowing them with a versatile syntax and multiple security definitions. The most basic of these, privacy, suffices for two-party secure function evaluation (SFE) and private function evaluation (PFE). Starting from a PRF, we provide an efficient garbling scheme achieving privacy and we analyze its concrete security. We next consider obliviousness and authenticity, properties needed for private and verifiable outsourcing of computation. We extend our scheme to achieve these ends. We provide highly efficient blockcipher-based instantiations of both schemes. Our treatment of garbling schemes presages more efficient garbling, more rigorous analyses, and more modularly designed higher-level protocols.

Efficient Garbling from a Fixed-Key Blockcipher

We advocate schemes based on fixed-key AES as the best route to highly efficient circuit-garbling. We provide such schemes making only one AES call per garbled-gate evaluation. On the theoretical side, we justify the security of these methods in the random-permutation model, where parties have access to a public random permutation. On the practical side, we provide the Just Garble system, which implements our schemes. Just Garble evaluates moderate-sized garbled-circuits at an amortized cost of 23.2 cycles per gate (7.25 nsec), far faster than any prior reported results.

Instantiating Random Oracles via UCEs

This paper provides a (standard-model) notion of security for (keyed) hash functions, called UCE, that we show enables instantiation of random oracles (ROs) in a fairly broad and systematic way. Goals and schemes we consider include deterministic PKE; message-locked encryption; hardcore functions; point-function obfuscation; OAEP; encryption secure for key-dependent messages; encryption secure under related-key attack; proofs of storage; and adaptively-secure garbled circuits with short tokens. We can take existing, natural and efficient ROM schemes and show that the instantiated scheme resulting from replacing the RO with a UCE function is secure in the standard model. In several cases this results in the first standard-model schemes for these goals. The definition of UCE-security itself is quite simple, asking that outputs of the function look random given some “leakage,” even if the adversary knows the key, as long as the leakage does not permit the adversary to compute the inputs.

Robust Authenticated-Encryption AEZ and the Problem That It Solves

With a scheme for robust authenticated-encryption a user can select an arbitrary value \(\lambda \!\ge 0\) and then encrypt a plaintext of any length into a ciphertext that’s \(\lambda \) characters longer. The scheme must provide all the privacy and authenticity possible for the requested \(\lambda \). We formalize and investigate this idea, and construct a well-optimized solution, AEZ, from the AES round function. Our scheme encrypts strings at almost the same rate as OCB-AES or CTR-AES (on Haswell, AEZ has a peak speed of about 0.7 cpb). To accomplish this we employ an approach we call prove-then-prune: prove security and then instantiate with a scaled-down primitive (e.g., reducing rounds for blockcipher calls).

Adaptively secure garbling with applications to one-time programs and secure outsourcing

Standard constructions of garbled circuits provide only static security, meaning the input x is not allowed to depend on the garbled circuit F. But some applications--notably one-time programs (Goldwasser, Kalai, and Rothblum 2008) and secure outsourcing (Gennaro, Gentry, Parno 2010)--need adaptive security, where x may depend on F. We identify gaps in proofs from these papers with regard to adaptive security and suggest the need of a better abstraction boundary. To this end we investigate the adaptive security of garbling schemes, an abstraction of Yaos garbled-circuit technique that we recently introduced (Bellare, Hoang, Rogaway 2012). Building on that framework, we give definitions encompassing privacy, authenticity, and obliviousness, with either coarse-grained or fine-grained adaptivity. We show how adaptively secure garbling schemes support simple solutions for one-time programs and secure outsourcing, with privacy being the goal in the first case and obliviousness and authenticity the goal in the second. We give transforms that promote static-secure garbling schemes to adaptive-secure ones. Our work advances the thesis that conceptualizing garbling schemes as a first-class cryptographic primitive can simplify, unify, or improve treatments for higher-level protocols.

An Enciphering Scheme Based on a Card Shuffle

We introduce the swap-or-not shuffle and show that the technique gives rise to a new method to convert a pseudorandom function PRF into a pseudorandom permutation PRP or, alternatively, to directly build a confusion/diffusion blockcipher. We then prove that swap-or-not has excellent quantitative security bounds, giving a Luby-Rackoff type result that ensures security assuming an ideal round function to a number of adversarial queries that is nearly the size of the constructions domain. Swap-or-not provides a direct solution for building a small-domain cipher and achieving format-preserving encryption, yielding the best bounds known for a practical scheme for enciphering credit-card numbers. The analysis of swap-or-not is based on the theory of mixing times of Markov chains.

Resisting Randomness Subversion: Fast Deterministic and Hedged Public-Key Encryption in the Standard Model

This paper provides the first efficient, standard-model, fully-secure schemes for some related and challenging forms of public-key encryption (PKE), namely deterministic and hedged PKE. These forms of PKE defend against subversion of random number generators, an end given new urgency by recent revelations on the nature and extent of such subversion.We resolve the (recognized) technical challenges in reaching these goals via a new paradigm that combines UCEs (universal computational extractors) with LTDFs (lossy trapdoor functions). Crucially, we rely only on a weak form of UCE, namely security for statistically (rather than computationally) unpredictable sources. We then define and achieve unique-ciphertext PKE as a way to defend against implementation subversion via algorithm-substitution attacks.

Online Authenticated-Encryption and its Nonce-Reuse Misuse-Resistance

A definition of online authenticated-encryption (OAE), call it OAE1, was given by Fleischmann, Forler, and Lucks (2012). It has become a popular definitional target because, despite allowing encryption to be online, security is supposed to be maintained even if nonces get reused. We argue that this expectation is effectively wrong. OAE1 security has also been claimed to capture best-possible security for any online-AE scheme. We claim that this understanding is wrong, too. So motivated, we redefine OAE-security, providing a radically different formulation, OAE2. The new notion effectively does capture best-possible security for a user’s choice of plaintext segmentation and ciphertext expansion. It is achievable by simple techniques from standard tools. Yet even for OAE2, nonce-reuse can still be devastating. The picture to emerge is that no OAE definition can meaningfully tolerate nonce-reuse, but, at the same time, OAE security ought never have been understood to turn on this question.

Adaptive Witness Encryption and Asymmetric Password-Based Cryptography

We show by counter-example that the soundness security requirement for witness encryption given by Garg, Gentry, Sahai and Waters (STOC 2013) does not suffice for the security of their own applications. We introduce adaptively-sound (AS) witness encryption to fill the gap. We then introduce asymmetric password-based encryption (A-PBE). This offers gains over classical, symmetric password-based encryption in the face of attacks that compromise servers to recover hashed passwords. We distinguish between invasive A-PBE schemes (they introduce new password-based key-derivation functions) and non-invasive ones (they can use existing, deployed password-based key-derivation functions). We give simple and efficient invasive A-PBE schemes and use AS-secure witness encryption to give non-invasive A-PBE schemes.

Cryptography from Compression Functions: The UCE Bridge to the ROM

This paper suggests and explores the use of UCE security for the task of turning VIL-ROM schemes into FIL-ROM ones. The benefits we offer over indifferentiability, the current leading method for this task, are the ability to handle multi-stage games and greater efficiency. The paradigm consists of (1) Showing that a VIL UCE function can instantiate the VIL RO in the scheme, and (2) Constructing the VIL UCE function given a FIL random oracle. The main technical contributions of the paper are domain extension transforms that implement the second step. Leveraging known results for the first step we automatically obtain FIL-ROM constructions for several primitives whose security notions are underlain by multi-stage games.Our first domain extender exploits indifferentiability, showing that although the latter does not work directly for multi-stage games it can be used indirectly, through UCE, as a tool for this end. Our second domain extender targets performance. It is parallelizable and shown through implementation to provide significant performance gains over indifferentiable domain extenders.