Founding Cryptography on Smooth Projective Hashing

Oblivious transfer (OT) is a fundamental primitive in cryptography. Halevi-Kalai OT (Halevi, S. and Y. Kalai (2012), Journal of Cryptology 25(1)), which is based on smooth projective hash(SPH), is a famous and the most efficient framework for $1$-out-of-$2$ oblivious transfer (\mbox{OT}^{2}_{1}) against malicious adversaries in plain model. However, it does not provide simulation-based security. Thus, it is harder to use it as a building block in secure multiparty computation (SMPC) protocols. A natural question however, which so far has not been answered, is whether it can be can be made fully-simulatable. In this paper, we give a positive answer. Further, we present a fully-simulatable framework for general \mbox{OT}^{n}_{t} ($n,t\in \mathbb{N}$ and $n>t$). Our framework can be interpreted as a constant-round blackbox reduction of \mbox{OT}^{n}_{t} (or \mbox{OT}^{2}_{1}) to SPH. To our knowledge, this is the first such reduction. Combining Kilian\u27s famous completeness result, we immediately obtain a black-box reduction of SMPC to SPH

Commitment and Oblivious Transfer in the Bounded Storage Model with Errors

The bounded storage model restricts the memory of an adversary in a cryptographic protocol, rather than restricting its computational power, making information theoretically secure protocols feasible. We present the first protocols for commitment and oblivious transfer in the bounded storage model with errors, i.e., the model where the public random sources available to the two parties are not exactly the same, but instead are only required to have a small Hamming distance between themselves. Commitment and oblivious transfer protocols were known previously only for the error-free variant of the bounded storage model, which is harder to realize

Analysis Of The Simulatability Of An Oblivious Transfer

In the Journal of Cryptology (25(1): 158-193. 2012), Shai Halevi and Yael Kalai proposed a general framework for constructing two-message oblivious transfer protocols using smooth projective hashing. The authors asserts that this framework gives a simulation-based security guarantee when the sender is corrupted. Later this work has been believed to be half-simulatable in literatures. In this paper, we show that the assertion is not true and present our ideas to construct a fully-simulatable oblivious transfer framework

New Smooth Projective Hashing For Oblivious Transfer

Oblivious transfer is an important tool against malicious cloud server providers. Halevi-Kalai OT, which is based on smooth projective hash(SPH), is a famous and the most efficient framework for $1$-out-of-$2$ oblivious transfer (\mbox{OT}^{2}_{1}) against malicious adversaries in plain model. A natural question however, which so far has not been answered, is whether its security level can be improved, i.e., whether it can be made fully-simulatable. In this paper, we press a new SPH variant, which enables a positive answer to above question. In more details, it even makes fully-simulatable \mbox{OT}^{n}_{t} ($n,t\in \mathbb{N}$ and $n>t$) possible. We instantiate this new SPH variant under not only the decisional Diffie-Hellman assumption, the decisional $N$-th residuosity assumption and the decisional quadratic residuosity assumption as currently existing SPH constructions, but also the learning with errors (LWE) problem. Before this paper, there is a folklore that it is technically difficult to instantiate SPH under the lattice assumption (e.g., LWE). Considering quantum adversaries in the future, lattice-based SPH makes important sense

Quantum to Classical Randomness Extractors

The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum system. To tackle this question we here take on the study of quantum-to-classical randomness extractors (QC-extractors). We provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.Comment: 6+31 pages, 2 tables, 1 figure, v2: improved converse parameters, typos corrected, new discussion, v3: new reference

On the Efficiency of Classical and Quantum Secure Function Evaluation

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of protocols that use different variants of OT as a black-box. When applied to implementations of OT, these bounds generalize most known results to the statistical case. Our results hold in particular for transformations between a finite number of primitives and for any error. In the second part we study the efficiency of quantum protocols implementing OT. While most classical lower bounds for perfectly secure reductions of OT to distributed randomness still hold in the quantum setting, we present a statistically secure protocol that violates these bounds by an arbitrarily large factor. We then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend OT. Finally, we present two lower bounds for reductions of OT to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds

A Framework for Fully-Simulatable tt-out-of-nn Oblivious Transfer

Oblivious transfer is a fundamental building block for multiparty computation protocols. In this paper, we present a generally realizable framework for fully-simulatable $t$-out-of-$n$ oblivious transfer (\mbox{OT}^{n}_{t}) with security against non-adaptive malicious adversaries in the plain mode. Our construction relies on a single cryptographic primitive which is a variant of smooth projective hashing (SPH). A direct consequence of our work is that the existence of protocols for \mbox{OT}^{n}_{t} is reduced to the existence of this SPH variant. Before this paper, the only known reductions provided half-simulatable security and every known efficient protocol involved at least two distinct cryptographic primitives. We show how to instantiate this new SPH variant under not only the decisional Diffie-Hellman assumption, the decisional $N$-th residuosity assumption and the decisional quadratic residuosity assumption as currently existing SPH constructions, but also the learning with errors problem. Our framework only needs $4$ communication rounds, which implies that it is more round-efficient than known protocols holding identical features

Private Set Intersection with Linear Communication from General Assumptions

This work presents a hashing-based algorithm for Private Set Intersection (PSI) in the honest-but-curious setting. The protocol is generic, modular and provides both asymptotic and concrete efficiency improvements over existing PSI protocols. If each player has $m$ elements, our scheme requires only O(m \secpar) communication between the parties, where \secpar is a security parameter. Our protocol builds on the hashing-based PSI protocol of Pinkas et al. (USENIX 2014, USENIX 2015), but we replace one of the sub-protocols (handling the cuckoo ``stash\u27\u27) with a special-purpose PSI protocol that is optimized for comparing sets of unbalanced size. This brings the asymptotic communication complexity of the overall protocol down from \omega(m \secpar) to O(m\secpar), and provides concrete performance improvements (10-15\% reduction in communication costs) over Kolesnikov et al. (CCS 2016) under real-world parameter choices. Our protocol is simple, generic and benefits from the permutation-hashing optimizations of Pinkas et al. (USENIX 2015) and the Batched, Relaxed Oblivious Pseudo Random Functions of Kolesnikov et al. (CCS 2016)