The section on Secure Multiparty Computation started with the very good presentation given by abhi shelat on “Fast two-party Secure Computation with Minimal Assumptions” (joint work with Chih-Hao Shen). He started the talk pointing out how in recent times multiparty computation have become more and more practical: since the Yao's seminal work in 1982, many different protocols have been proposed providing, in the last few years, drastic improvements and efficient implementations relevant for real-world applications.
The approach presented in the talk for secure two-party computation is essentially based on Yao's construction and on cut-and-choose technique to achieve security in the active model.
Informally speaking the protocol works as follows: we have two parties, Alice and Bob, that want to securely and privately evaluate an arbitrary function represented by a Boolean circuit C. Then one party, say Alice, prepares a “garbled” (or “encrypted”) version of the circuit C and gives it to Bob together with her appropriate input keys, in such a way that he can evaluate the circuit without learning anything about Alice's inputs and intermediate values. To achieve security against active adversary Alice creates many copies of the garbled circuit (with different randomness) and sends them to Bob. Then he asks Alice to open a fixed fraction of these circuits checking that they are correctly encoded.
Unfortunately using this technique we have three main issues to resolve: 1) Input inconsistency: we need that Alice use the same inputs in each evaluated circuits 2) Output authentication and privacy: a malicious Bob could learn Alice's output or outputs an incorrect value 3) Selective failure attack: a malicious Alice can use inconsistent inputs in the OTs and in creation of the garbled circuits to learn Bob's inputs. There are many different approaches to address these issues.
Abhi started focusing on the output authentication and privacy issue. The problem has been studied in many prior works: in [LP07] a very elegant solution has been proposed, but it requires O(k^2n ) symmetric operations (where k is the security parameter and n is the inputs size); the subsequent protocols in [LP11, Kir08, SS11] require only O(kn) symmetric operations but they also need some extra expansive operations. The new approach they proposed consists essentially in a new witness-indistinguishable proof and it does not need any extra computations or any number-theoretic assumptions. To ensure the input consistency they use an auxiliary 2-universal hash circuit; and for the selective failure attack they propose the same solution as in [LP07], but with a different and more efficient implementation. All in all they manage to obtain a two-party computation protocol in the malicious setting that is faster than prior protocols, which use the same techniques, and with fewer assumptions.
The talk concluded with a brief comparison with other works on secure computation in the malicious setting, and in particular with [NNOB12]. More specifically the protocol in [NNOB12] turns out to be more efficient in terms of computation complexity (it requires O(k/log(n) C) symmetric operations in the RA model, while the one presented in the talk requires O(kC) operations in the standard model), but it is worst in terms of communication complexity.
Finally Abhi discussed about the advantage of using garbled circuits for secure two-party computation, in particular because, using this technique, we do not have any asymptotic overhead in passing from passive to active security.
In the second talk of the section Michael Zohner presented a joint work with Gilad Asharov, Yehuda Lindell and Thomas Schnesider on More Efficient Oblivious Transfer and Extensions for Faster Secure Computation. In this work the authors describe a more efficient protocol for OT extensions in the passive model. In addition they provide specific functionalities for OT extensions especially designed for secure computation protocols and an open source optimized OT implementation.
The last talk of the section was given by Marcel. He very well presented the Bristolian work An Architecture for Practical Actively Secure MPC with Dishonest Majority (joint work with Peter and Nigel).