## CryptoDB

### Eran Omri

#### Publications

**Year**

**Venue**

**Title**

2021

EUROCRYPT

Large Scale, Actively Secure Computation from LPN and Free-XOR Garbled Circuits
Abstract

Whilst secure multiparty computation (MPC) based on garbled circuits is concretely efficient for
a small number of parties $n$, the gap between the complexity of practical protocols, which
is $O(n^2)$ per party, and the theoretical complexity, which is $O(n)$ per party, is prohibitive for large values of $n$.
In order to bridge this gap, Ben-Efraim, Lindell and Omri (ASIACRYPT 2017)
introduced a garbled-circuit-based MPC protocol with an almost-practical pre-processing, yielding $O(n)$ complexity per party.
However, this protocol is only passively secure and does not support
the free-XOR technique by Kolesnikov and Schneider (ICALP 2008), on which almost all practical garbled-circuit-based protocols rely on for their efficiency.
In this work, to further bridge the gap between theory and practice, we present a new $n$-party garbling technique based on a new variant of standard LPN-based encryption.
Using this approach we can describe two new garbled-circuit based protocols,
which have practical evaluation phases.
Both protocols are in the preprocessing model, have $O(n)$ complexity per party,
are actively secure and support the free-XOR technique.
The first protocol tolerates full threshold corruption and ensures the garbled circuit
contains no adversarially introduced errors, using a rather expensive garbling phase.
The second protocol assumes that at least $n/c$ of the parties are honest (for an
arbitrary fixed value $c$) and allows a significantly lighter preprocessing, at the cost of a small sacrifice in online efficiency.
We demonstrate the practicality of our approach with an implementation of the evaluation phase using different circuits.
We show that like the passively-secure protocol of Ben-Efraim, Lindell and Omri,
our approach starts to improve upon other practical protocols with $O(n^2)$ complexity when the number of parties is around $100$.

2020

TCC

On the Power of an Honest Majority in Three-Party Computation Without Broadcast
📺
Abstract

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).

2020

JOFC

${\varvec{1/p}}$-Secure Multiparty Computation without an Honest Majority and the Best of Both Worlds
Abstract

A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation, where parties give their inputs to a trusted party that returns the output of the functionality to all parties. In particular, in the ideal model, such computation is fair—if the corrupted parties get the output, then the honest parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition—1/ p -secure computation—which guarantees partial fairness. For two parties, they constructed 1/ p -secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/ p -secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/ p -secure protocols that are resilient against any number of corrupted parties provided that the number of parties is constant and the size of the range of the functionality is at most polynomial (in the security parameter $${n}$$ n ). If fewer than 2/3 of the parties are corrupted, the size of the domain of each party is constant, and the functionality is deterministic, then our protocols are efficient even when the number of parties is $$\log \log {n}$$ log log n . On the negative side, we show that when the number of parties is super-constant, 1/ p -secure protocols are not possible when the size of the domain of each party is polynomial. Thus, our feasibility results for 1/ p -secure computation are essentially tight. We further motivate our results by constructing protocols with stronger guarantees: If in the execution of the protocol there is a majority of honest parties, then our protocols provide full security. However, if only a minority of the parties are honest, then our protocols are 1/ p -secure. Thus, our protocols provide the best of both worlds, where the 1/ p -security is only a fall-back option if there is no honest majority.

2018

TCC

On the Complexity of Fair Coin Flipping
Abstract

A two-party coin-flipping protocol is $$\varepsilon $$ε-fair if no efficient adversary can bias the output of the honest party (who always outputs a bit, even if the other party aborts) by more than $$\varepsilon $$ε. Cleve [STOC ’86] showed that r-round o(1 / r)-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript ’85] constructed a $$\varTheta (1/\sqrt{r})$$Θ(1/r)-fair coin-flipping protocol, assuming the existence of one-way functions. Moran et al. [Journal of Cryptology ’16] constructed an r-round coin-flipping protocol that is $$\varTheta (1/r)$$Θ(1/r)-fair (thus matching the aforementioned lower bound of Cleve [STOC ’86]), assuming the existence of oblivious transfer.The above gives rise to the intriguing question of whether oblivious transfer, or more generally “public-key primitives”, is required for an $$o(1/\sqrt{r})$$o(1/r)-fair coin flipping. This question was partially answered by Dachman-Soled et al. [TCC ’11] and Dachman-Soled et al. [TCC ’14], who showed that restricted types of fully black-box reductions cannot establish $$o(1/\sqrt{r})$$o(1/r)-fair coin-flipping protocols from one-way functions. In particular, for constant-round coin-flipping protocols, [10] yields that black-box techniques from one-way functions can only guarantee fairness of order $$1/\sqrt{r}$$1/r.We make progress towards answering the above question by showing that, for any constant , the existence of an $$1/(c\cdot \sqrt{r})$$1/(c·r)-fair, r-round coin-flipping protocol implies the existence of an infinitely-often key-agreement protocol, where c denotes some universal constant (independent of r). Our reduction is non black-box and makes a novel use of the recent dichotomy for two-party protocols of Haitner et al. [FOCS ’18] to facilitate a two-party variant of the attack of Beimel et al. [FOCS ’18] on multi-party coin-flipping protocols.

2011

CRYPTO

#### Program Committees

- Eurocrypt 2018
- TCC 2018

#### Coauthors

- Bar Alon (2)
- Gilad Asharov (1)
- Amos Beimel (6)
- Aner Ben-Efraim (2)
- Ran Cohen (4)
- Kelong Cong (1)
- Iftach Haitner (7)
- Yuval Ishai (1)
- Yehuda Lindell (6)
- Nikolaos Makriyannis (2)
- Kobbi Nissim (1)
- Ilan Orlov (4)
- Emmanuela Orsini (1)
- Lior Rotem (3)
- Ronen Shaltiel (1)
- Nigel P. Smart (1)
- Eduardo Soria-Vazquez (1)
- Tom Suad (1)
- Hila Zarosim (5)