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

Classical Cryptographic Protocols in a Quantum World

Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world.Comment: Full version of an old paper in Crypto'11. Invited to IJQI. This is authors' copy with different formattin

Composability in quantum cryptography

In this article, we review several aspects of composability in the context of quantum cryptography. The first part is devoted to key distribution. We discuss the security criteria that a quantum key distribution protocol must fulfill to allow its safe use within a larger security application (e.g., for secure message transmission). To illustrate the practical use of composability, we show how to generate a continuous key stream by sequentially composing rounds of a quantum key distribution protocol. In a second part, we take a more general point of view, which is necessary for the study of cryptographic situations involving, for example, mutually distrustful parties. We explain the universal composability framework and state the composition theorem which guarantees that secure protocols can securely be composed to larger applicationsComment: 18 pages, 2 figure

Universally Composable Quantum Multi-Party Computation

The Universal Composability model (UC) by Canetti (FOCS 2001) allows for secure composition of arbitrary protocols. We present a quantum version of the UC model which enjoys the same compositionality guarantees. We prove that in this model statistically secure oblivious transfer protocols can be constructed from commitments. Furthermore, we show that every statistically classically UC secure protocol is also statistically quantum UC secure. Such implications are not known for other quantum security definitions. As a corollary, we get that quantum UC secure protocols for general multi-party computation can be constructed from commitments

Improved Black-Box Constructions of Composable Secure Computation

We close the gap between black-box and non-black-box constructions of $\mathit{composable}$ secure multiparty computation in the plain model under the $\mathit{minimal}$ assumption of semi-honest oblivious transfer. The notion of protocol composition we target is $\mathit{angel\text{-}based}$ security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an $\mathit{angel}$ that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone. Angel-based security can be achieved using non-black-box constructions in $\max(R_{\mathsf{OT}},\widetilde{O}(\log n))$ rounds where $R_{\mathsf{OT}}$ is the round-complexity of the semi-honest oblivious transfer. However, currently, the best known $\mathit{black\text{-}box}$ constructions under the same assumption require $\max(R_{\mathsf{OT}},\widetilde{O}(\log^2 n))$ rounds. If $R_{\mathsf{OT}}$ is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor $\log n$. We close this gap by presenting a $\max(R_{\mathsf{OT}},\widetilde{O}(\log n))$-round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions

Round-Optimal Multi-party Computation with Identifiable Abort

Secure multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort, which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016, Garg et al. showed that, assuming access to a simultaneous message exchange channel for all the parties, at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. Following Garg et al., a sequence of works has matched this lower bound, but none of them achieved security with identifiable abort. In this work, we close this gap and show that four rounds of communication are also sufficient to securely realize any functionality with identifiable abort using standard and generic polynomial-time assumptions. To achieve this result we introduce the new notion of bounded-rewind secure MPC that guarantees security even against an adversary that performs a mild form of reset attacks. We show how to instantiate this primitive starting from any MPC protocol and by assuming trapdoor-permutations. The notion of bounded-rewind secure MPC allows for easier parallel composition of MPC protocols with other (interactive) cryptographic primitives. Therefore, we believe that this primitive can be useful in other contexts in which it is crucial to combine multiple primitives with MPC protocols while keeping the round complexity of the final protocol low

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference