An Elementary Completeness Proof for Secure Two-Party Computation Primitives

In the secure two-party computation problem, two parties wish to compute a (possibly randomized) function of their inputs via an interactive protocol, while ensuring that neither party learns more than what can be inferred from only their own input and output. For semi-honest parties and information-theoretic security guarantees, it is well-known that, if only noiseless communication is available, only a limited set of functions can be securely computed; however, if interaction is also allowed over general communication primitives (multi-input/output channels), there are "complete" primitives that enable any function to be securely computed. The general set of complete primitives was characterized recently by Maji, Prabhakaran, and Rosulek leveraging an earlier specialized characterization by Kilian. Our contribution in this paper is a simple, self-contained, alternative derivation using elementary information-theoretic tools.Comment: 6 pages, extended version of ITW 2014 pape

Separating Two-Round Secure Computation From Oblivious Transfer

We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing a round preserving reduction to the task of secure 2-party computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions. Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT. As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed "non-compact" variant of 2-party homomorphic secret sharing from 2-round OT

Statistical Security in Two-Party Computation Revisited

We present a new framework for building round-optimal one-sided statistically secure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer $\textsf{eOT}$ with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables the first instantiations of round-optimal one-sided statistically secure 2PC protocols from the CDH assumption and certain families of isogeny-based assumptions. As part of our compiler, we introduce the following new one-sided statistically secure primitives in the pre-processing model that might also be of independent interest: 1. Three round statistically sender private random-OT where only the last OT message depends on the receiver\u27s choice bit and the sender receives random outputs generated by the protocol. 2. Four round delayed-input statistically sender private conditional disclosure of secrets where the first two rounds of the protocol are independent of the inputs of the parties. The above primitives are directly constructed from $\textsf{eOT}$ and hence we obtain their instantiations from the same set of assumptions as our 2PC

Compositional closure for Bayes Risk in probabilistic noninterference

We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our novel methodological contribution is the definition of a refinement order and its use to compare security measures between specifications and (their supposed) implementations. This contrasts with the more common practice of evaluating the security of individual programs in isolation. The appropriateness of our model and order is supported by our showing that our refinement order is the greatest compositional relation --the compositional closure-- with respect to our semantics and an "elementary" order based on Bayes Risk --- a security measure already in widespread use. We also relate refinement to other measures such as Shannon Entropy. By applying the approach to a non-trivial example, the anonymous-majority Three-Judges protocol, we demonstrate by example that correctness arguments can be simplified by the sort of layered developments --through levels of increasing detail-- that are allowed and encouraged by compositional semantics