A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

On Black-Box Complexity and Adaptive, Universal Composability of Cryptographic Tasks

Two main goals of modern cryptography are to identify the minimal assumptions necessary to construct secure cryptographic primitives as well as to construct secure protocols in strong and realistic adversarial models. In this thesis, we address both of these fundamental questions. In the first part of this thesis, we present results on the black-box complexity of two basic cryptographic primitives: non-malleable encryption and optimally-fair coin tossing. Black-box reductions are reductions in which both the underlying primitive as well as the adversary are accessed only in an input-output (or black-box) manner. Most known cryptographic reductions are black-box. Moreover, black-box reductions are typically more efficient than non-black-box reductions. Thus, the black-box complexity of cryptographic primitives is a meaningful and important area of study which allows us to gain insight into the primitive. We study the black box complexity of non-malleable encryption and optimally-fair coin tossing, showing a positive result for the former and a negative one for the latter. Non-malleable encryption is a strong security notion for public-key encryption, guaranteeing that it is impossible to "maul" a ciphertext of a message m into a ciphertext of a related message. This security guarantee is essential for many applications such as auctions. We show how to transform, in a black-box manner, any public-key encryption scheme satisfying a weak form of security, semantic security, to a scheme satisfying non-malleability. Coin tossing is perhaps the most basic cryptographic primitive, allowing two distrustful parties to flip a coin whose outcome is 0 or 1 with probability 1/2. A fair coin tossing protocol is one in which the outputted bit is unbiased, even in the case where one of the parties may abort early. However, in the setting where parties may abort early, there is always a strategy for one of the parties to impose bias of Omega(1/r) in an r-round protocol. Thus, achieving bias of O(1/r) in r rounds is optimal, and it was recently shown that optimally-fair coin tossing can be achieved via a black-box reduction to oblivious transfer. We show that it cannot be achieved via a black-box reduction to one-way function, unless the number of rounds is at least Omega(n/log n), where n is the input/output length of the one-way function. In the second part of this thesis, we present protocols for multiparty computation (MPC) in the Universal Composability (UC) model that are secure against malicious, adaptive adversaries. In the standard model, security is only guaranteed in a stand-alone setting; however, nothing is guaranteed when multiple protocols are arbitrarily composed. In contrast, the UC model, introduced by (Canetti, 2000), considers the execution of an unbounded number of concurrent protocols, in an arbitrary, and adversarially controlled network environment. Another drawback of the standard model is that the adversary must decide which parties to corrupt before the execution of the protocol commences. A more realistic model allows the adversary to adaptively choose which parties to corrupt based on its evolving view during the protocol. In our work we consider the the adaptive UC model, which combines these two security requirements by allowing both arbitrary composition of protocols and adaptive corruption of parties. In our first result, we introduce an improved, efficient construction of non-committing encryption (NCE) with optimal round complexity, from a weaker primitive we introduce called trapdoor-simulatable public key encryption (PKE). NCE is a basic primitive necessary to construct protocols secure under adaptive corruptions and in particular, is used to construct oblivious transfer (OT) protocols secure against semi-honest, adaptive adversaries. Additionally, we show how to realize trapdoor-simulatable PKE from hardness of factoring Blum integers, thus achieving the first construction of NCE from hardness of factoring. In our second result, we present a compiler for transforming an OT protocol secure against a semi-honest, adaptive adversary into one that is secure against a malicious, adaptive adversary. Our compiler achieves security in the UC model, assuming access to an ideal commitment functionality, and improves over previous work achieving the same security guarantee in two ways: it uses black-box access to the underlying protocol and achieves a constant multiplicative overhead in the round complexity. Combining our two results with the work of (Ishai et al., 2008), we obtain the first black-box construction of UC and adaptively secure MPC from trapdoor-simulatable PKE and the ideal commitment functionality

Round-Optimal Black-Box Two-Party Computation

In [Eurocrypt 2004] Katz and Ostrovsky establish the exact round complexity of secure two-party computation with respect to black-box proofs of security. They prove that 5 rounds are necessary for secure two-party protocols (4-round are sufficient if only one party receives the output) and provide a protocol that matches such lower bound. The main challenge when designing such protocol is to parallelize the proofs of consistency provided by both parties – necessary when security against malicious adversaries is considered– in 4 rounds. Toward this goal they employ specific proofs in which the statement can be unspecified till the last round but that require non-black-box access to the underlying primitives. A rich line of work [IKLP06, Hai08, CDSMW09, IKOS07, PW09] has shown that the non- black-box use of the cryptographic primitive in secure two-party computation is not necessary by providing black-box constructions matching basically all the feasibility results that were previously demonstrated only via non-black-box protocols. All such constructions however are far from being round optimal. The reason is that they are based on cut-and-choose mechanisms where one party can safely take an action only after the other party has successfully completed the cut-and-choose phase, therefore requiring additional rounds. A natural question is whether round-optimal constructions do inherently require non-black- box access to the primitives, and whether the lower bound shown by Katz and Ostrovsky can only be matched by a non-black-box protocol. In this work we show that round-optimality is achievable even with only black-box access to the primitives. We provide the first 4-round black-box oblivious transfer based on any enhanced trapdoor permutation. Plugging a parallel version of our oblivious transfer into the black- box non-interactive secure computation protocol of [IKO+11] we obtain the first round-optimal black-box two-party protocol in the plain model for any functionality

Knowledge Encryption and Its Applications to Simulatable Protocols With Low Round-Complexity

We introduce a new notion of public key encryption, knowledge encryption, for which its ciphertexts can be reduced to the public-key, i.e., any algorithm that can break the ciphertext indistinguishability can be used to extract the (partial) secret key. We show that knowledge encryption can be built solely on any two-round oblivious transfer with game-based security, which are known based on various standard (polynomial-hardness) assumptions, such as the DDH, the Quadratic($N^{th}$) Residuosity or the LWE assumption. We use knowledge encryption to construct the first three-round (weakly) simulatable oblivious transfer. This protocol satisfies (fully) simulatable security for the receiver, and weakly simulatable security ($(T, \epsilon)$-simulatability) for the sender in the following sense: for any polynomial $T$ and any inverse polynomial $\epsilon$, there exists an efficient simulator such that the distinguishing gap of any distinguisher of size less than $T$ is at most $\epsilon$. Equipped with these tools, we construct a variety of fundamental cryptographic protocols with low round-complexity, assuming only the existence of two-round oblivious transfer with game-based security. These protocols include three-round delayed-input weak zero knowledge argument, three-round weakly secure two-party computation, three-round concurrent weak zero knowledge in the BPK model, and a two-round commitment with weak security under selective opening attack. These results improve upon the assumptions required by the previous constructions. Furthermore, all our protocols enjoy the above $(T, \epsilon)$-simulatability (stronger than the distinguisher-dependent simulatability), and are quasi-polynomial time simulatable under the same (polynomial hardness) assumption

Generic Fully Simulatable Adaptive Oblivious Transfer

We aim at constructing adaptive oblivious transfer protocols, enjoying fully simulatable security, from various well-known assumptions such as DDH, $d$-Linear, QR, DCR, and LWE. To this end, we present two generic constructions of adaptive OT, one of which utilizes verifiable shuffles together with threshold decryption schemes, while the other uses permutation networks together with what we call {\em loosely-homomorphic} key encapsulation schemes. We then show that specific choices of the building blocks lead to concrete adaptive OT protocols with fully simulatable security in the standard model under the targeted assumptions. Our generic methods can be extended to build universally composable (UC) secure, and leakage-resilient OT protocols

Somewhat Non-Committing Encryption and Efficient Adaptively Secure Oblivious Transfer

Designing efficient cryptographic protocols tolerating adaptive adversaries, who are able to corrupt parties on the fly as the computation proceeds, has been an elusive task. Indeed, thus far no \emph{efficient} protocols achieve adaptive security for general multi-party computation, or even for many specific two-party tasks such as oblivious transfer (OT). In fact, it is difficult and expensive to achieve adaptive security even for the task of \emph{secure communication}, which is arguably the most basic task in cryptography. In this paper we make progress in this area. First, we introduce a new notion called \emph{semi-adaptive} security which is slightly stronger than static security but \emph{significantly weaker than fully adaptive security}. The main difference between adaptive and semi-adaptive security is that, for semi-adaptive security, the simulator is not required to handle the case where \emph{both} parties start out honest and one becomes corrupted later on during the protocol execution. As such, semi-adaptive security is much easier to achieve than fully adaptive security. We then give a simple, generic protocol compiler which transforms any semi-adaptively secure protocol into a fully adaptively secure one. The compilation effectively decomposes the problem of adaptive security into two (simpler) problems which can be tackled separately: the problem of semi-adaptive security and the problem of realizing a weaker variant of secure channels. We solve the latter problem by means of a new primitive that we call {\em somewhat non-committing encryption} resulting in significant efficiency improvements over the standard method for realizing (fully) secure channels using (fully) non-committing encryption. Somewhat non-committing encryption has two parameters: an equivocality parameter $\ell$ (measuring the number of ways that a ciphertext can be ``opened\u27\u27) and the message sizes $k$. Our implementation is very efficient for small values $\ell$, \emph{even} when $k$ is large. This translates into a very efficient compilation of many semi-adaptively secure protocols (in particular, for a task with small input/output domains such as bit-OT) into a fully adaptively secure protocol. Finally, we showcase our methodology by applying it to the recent Oblivious Transfer protocol by Peikert \etal\ [Crypto 2008], which is only secure against static corruptions, to obtain the first efficient, adaptively secure and composable OT protocol. In particular, to transfer an $n$-bit message, we use a constant number of rounds and $O(n)$ public key operations

Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round

From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first $\epsilon$-simulatable two-party computation (2PC) against quantum polynomial-time (QPT) adversaries that is both constant-round and black-box (for both the construction and security reduction). A recent work by Chia, Chung, Liu, and Yamakawa (FOCS\u2721) shows that post-quantum 2PC with standard simulation-based security is impossible in constant rounds, unless either $NP \subseteq BQP$ or relying on non-black-box simulation. The $\epsilon$-simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error $\epsilon$. Moreover, when quantum communication is allowed, we can further weaken the assumption to post-quantum secure one-way functions (PQ-OWFs), while maintaining the constant-round and black-box property. Our techniques also yield the following set of constant-round and black-box two-party protocols secure against QPT adversaries, only assuming black-box access to PQ-OWFs: - extractable commitments for which the extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge commit-and-prove whose commit stage is extractable with $\epsilon$-simulation; - $\epsilon$-simulatable coin-flipping; - $\epsilon$-zero-knowledge arguments of knowledge for $NP$ for which the knowledge extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge arguments for $QMA$. At the heart of the above results is a black-box extraction lemma showing how to efficiently extract secrets from QPT adversaries while disturbing their quantum state in a controllable manner, i.e., achieving $\epsilon$-simulatability of the post-extraction state of the adversary

Physical Unclonable Functions in Cryptographic Protocols: Security Proofs and Impossibility Results

We investigate the power of physical unclonable functions (PUFs) as a new primitive in cryptographic protocols. Our contributions split into three parts. Firstly, we focus on the realizability of PUF-protocols in a special type of stand-alone setting (the “stand-alone, good PUF setting”) under minimal assumptions. We provide new PUF definitions that require only weak average security properties of the PUF, and prove that these definitions suffice to realize secure PUF-based oblivious transfer (OT), bit commitment (BC) and key exchange (KE) in said setting. Our protocols for OT, BC and KE are partly new, and have certain practicality and security advantages compared to existing schemes. In the second part of the paper, we formally prove that there are very sharp limits on the usability of PUFs for OT and KE {\em beyond} the above stand-alone, good PUF scenario. We introduce two new and realistic attack models, the so-called posterior access model (PAM) and the bad PUF model, and prove several impossibility results in these models. First, OT and KE protocols whose security is solely based on PUFs are generally impossible in the PAM. More precisely, one-time access of an adversary to the PUF after the end of a single protocol (sub-)session makes all previous (sub-)sessions provably insecure. Second, OT whose security is solely based on PUFs is impossible in the bad PUF model, even if only a stand alone execution of the protocol is considered (i.e., even if no adversarial PUF access after the protocol is allowed). Our impossibility proofs do not only hold for the weak PUF definition of the first part of the paper, but even apply if ideal randomness and unpredictability is assumed in the PUF, i.e., if the PUF is modeled as a random permutation oracle. In the third part, we investigate the feasibility of PUF-based bit commitment beyond the stand-alone, good PUF setting. For a number of reasons, this case is more complicated than OT and KE. We first prove that BC is impossible in the bad PUF model if players have got access to the PUF between the commit and the reveal phase. Again, this result holds even if the PUF is “ideal” and modeled as a random permutation oracle. Secondly, we sketch (without proof) two new BC-protocols, which can deal with bad PUFs or with adversarial access between the commit and reveal phase, but not with both. We hope that our results can contribute to a clarification of the usability of PUFs in cryptographic protocols. They show that new hardware properties such as offline certifiability and the erasure of PUF responses would be required in order to make PUFs a broadly applicable cryptographic tool. These features have not yet been realized in practical PUF-implementations and generally seem hard to achieve at low costs. Our findings also show that the question how PUFs can be modeled comprehensively in a UC-setting must be considered at least partly open

Oblivious Transfer from Trapdoor Permutations in Minimal Rounds

Oblivious transfer (OT) is a foundational primitive within cryptography owing to its connection with secure computation. One of the oldest constructions of oblivious transfer was from certified trapdoor permutations (TDPs). However several decades later, we do not know if a similar construction can be obtained from TDPs in general. In this work, we study the problem of constructing round optimal oblivious transfer from trapdoor permutations. In particular, we obtain the following new results (in the plain model) relying on TDPs in a black-box manner: 1) Three-round oblivious transfer protocol that guarantees indistinguishability-security against malicious senders (and semi-honest receivers). 2) Four-round oblivious transfer protocol secure against malicious adversaries with black-box simulation-based security. By combining our second result with an already known compiler we obtain the first round-optimal 2-party computation protocol that relies in a black-box way on TDPs. A key technical tool underlying our results is a new primitive we call dual witness encryption (DWE) that may be of independent interest