International Association for Cryptologic Research

International Association
for Cryptologic Research


Bar Alon


MPC with Friends and Foes 📺
Classical definitions for secure multiparty computation assume the existence of a single adversarial entity controlling the set of corrupted parties. Intuitively, the definition requires that the view of the adversary, corrupting t parties, in a real-world execution can be simulated by an adversary in an ideal model, where parties interact only via a trusted-party. No restrictions, however, are imposed on the view of honest parties in the protocol, thus, if honest parties obtain information about the private inputs of other honest parties -- it is not counted as a violation of privacy. This is arguably undesirable in many situations that fall into the MPC framework. Nevertheless, there are secure protocols (e.g., the 2-round multiparty protocol of Ishai et al. [CRYPTO 2010] tolerating a single corrupted party) that instruct the honest parties to reveal their private inputs to all other honest parties (once the malicious party is somehow identified). In this paper, we put forth a new security notion, which we call FaF-security, extending the classical notion. In essence, (t,h^*)-FaF-security requires the view of a subset of up to h^* honest parties to also be simulatable in the ideal model (in addition to the view of the malicious adversary, corrupting up to t parties). This property should still hold, even if the adversary leaks information to honest parties by sending them non-prescribed messages. We provide a thorough exploration of the new notion, investigating it in relation to a variety of existing security notions. We further investigate the feasibility of achieving FaF-security and show that every functionality can be computed with (computational) (t,h^*)-FaF full-security, if and only if 2t+ h^*<m. Interestingly, the lower-bound result actually shows that even fair FaF-security is impossible in general when 2t+ h^*\ge m (surprisingly, the view of the malicious attacker is not used as the trigger for the attack). We also investigate the optimal round complexity for (t,h^*)-Faf-secure protocols and give evidence that the leakage of private inputs of honest parties in the protocol of Ishai et al. [CRYPTO 2010] is inherent.
On the Power of an Honest Majority in Three-Party Computation Without Broadcast
Fully secure multiparty computation (MPC) allows a set of parties to compute some function of their inputs, while guaranteeing correctness, privacy, fairness, and output delivery. Understanding the necessary and sufficient assumptions that allow for fully secure MPC is an important goal. Cleve (STOC'86) showed that full security cannot be obtained in general without an honest majority. Conversely, by Rabin and Ben-Or (FOCS'89), assuming a broadcast channel and an honest majority, any function can be computed with full security. Our goal is to characterize the set of functionalities that can be computed with full security, assuming an honest majority, but no broadcast. This question was fully answered by Cohen et al. (TCC'16) -- for the restricted class of \emph{symmetric} functionalities (where all parties receive the same output). Instructively, their results crucially rely on \emph{agreement} and do not carry over to general \emph{asymmetric} functionalities. In this work, we focus on the case of three-party asymmetric functionalities, providing a variety of necessary and sufficient conditions to enable fully secure computation. An interesting use-case of our results is \emph{server-aided} computation, where an untrusted server helps two parties to carry out their computation. We show that without a broadcast assumption, the resource of an external non-colluding server provides no additional power. Namely, a functionality can be computed with the help of the server if and only if it can be computed without it. For fair coin tossing, we further show that the optimal bias for three-party (server-aided) $r$-round protocol remains $\Theta(1/r)$ (as in the two-party setting).
On Perfectly Secure 2PC in the OT-Hybrid Model
A well known result by Kilian [22] (ACM 1988) asserts that general secure two computation (2PC) with statistical security, can be based on OT. Specifically, in the client-server model, where only one party – the client – receives an output, Kilian’s result shows that given the ability to call an ideal oracle that computes OT, two parties can securely compute an arbitrary function of their inputs with unconditional security. Ishai et al. [19] (EUROCRYPT 2011) further showed that this can be done efficiently for every two-party functionality in $$\mathrm {NC}^1$$ in a single round.However, their results only achieve statistical security, namely, it is allowed to have some error in security. This leaves open the natural question as to which client-server functionalities can be computed with perfect security in the OT-hybrid model, and what is the round complexity of such computation. So far, only a handful of functionalities were known to have such protocols. In addition to the obvious theoretical appeal of the question towards better understanding secure computation, perfect, as opposed to statistical reductions, may be useful for designing secure multiparty protocols with high concrete efficiency, achieved by eliminating the dependence on a security parameter.In this work, we identify a large class of client-server functionalities $$f:\mathcal {X}\times \mathcal {Y}\mapsto \{0,1\}$$, where the server’s domain $$\mathcal {X}$$ is larger than the client’s domain $$\mathcal {Y}$$, that have a perfect reduction to OT. Furthermore, our reduction is 1-round using an oracle to secure evaluation of many parallel invocations of $$\left( {\begin{array}{c}2\\ 1\end{array}}\right) \text {-bit-OT}$$, as done by Ishai et al. [19] (EUROCRYPT 2011). Interestingly, the set of functions that we are able to compute was previously identified by Asharov [2] (TCC 2014) in the context of fairness in two-party computation, naming these functions full-dimensional. Our result also extends to randomized non-Boolean functions $$f: \mathcal {X}\times \mathcal {Y}\mapsto \left\{ 0,\ldots ,k-1\right\} $$ satisfying $$|\mathcal {X}|>(k-1)\cdot |\mathcal {Y}|$$.