* We design an efficient fully-secure malicious 2PC protocol for two-output functions that only requires $O(t|C|)$ symmetric-key operations (with small constant factors) where $|C|$ is the circuit size and $t$ is a statistical security parameter. This is essentially the {\em optimal} complexity for protocols based on cut-and-choose, resolving a main question left open by the previous work on the subject.
Our protocol utilizes novel techniques for enforcing \emph{garbler's input consistency} and handling \emph{two-output functions} that are more efficient than all prior solutions.
* Motivated by the goal of eliminating the \emph{all-or-nothing} nature of 2PC with covert security (that privacy and correctness are fully compromised if the adversary is not caught in the challenge phase), we propose a new security definition for 2PC that strengthens the guarantees provided by the standard covert model, and offers a smoother security vs. efficiency tradeoff to protocol designers in choosing the \emph{right deterrence factor}. In our new notion, correctness is always guaranteed, privacy is fully guaranteed with probability ($1-\epsilon$), and with probability $\epsilon$ (i.e. the event of undetected cheating), privacy is only ``partially compromised" with at most a {\em single bit} of information leaked, in \emph{case of an abort}.
We present two efficient 2PC constructions achieving our new notion. Both protocols are competitive with the previous 2PC based on cut-and-choose. E.g., the price of strengthening a covert 2PC to satisfy our notion (to obtain full correctness and maximum leakage of a single bit), is only $\frac{1}{\epsilon}$ additional garbled circuits.
A distinct feature of the techniques we use in all our constructions is to check consistency of inputs and outputs using new gadgets that are themselves \emph{garbled circuits}, and to verify validity of these gadgets using \emph{multi-stage} cut-and-choose openings. These techniques may be of an independent interest.
Category / Keywords: Secure Two-Party Computation, Cut-and-choose 2PC Date: received 1 Feb 2013, last revised 3 Feb 2013 Contact author: benriva at post tau ac il Available formats: PDF | BibTeX Citation Version: 20130206:153750 (All versions of this report) Discussion forum: Show discussion | Start new discussion