Garbled Circuits Checking Garbled Circuits: More Efficient and Secure Two-Party Computation.

Applying cut-and-choose techniques to Yao's garbled circuit protocol has been a promising approach for designing efficient Two-Party Computation (2PC) with malicious and covert security, as is evident from various optimizations and software implementations in the recent years. We revisit the security and efficiency properties of this popular approach and propose alternative constructions and a new definition that are more suitable for use in practice. We design an efficient fully-secure 2PC protocol for two-output functions that only requires O(t vertical bar C vertical bar) symmetric-key operations (with small constant factors, and ignoring factors that are independent of the circuit in use) in the Random Oracle Model, where vertical bar C vertical bar is the circuit size and t is a statistical security parameter. This is essentially the 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 garbler's input consistency and handling two-output functions that are more efficient than all prior solutions. Motivated by the goal of eliminating the 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 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 single bit of information leaked, in case of an abort. We present two efficient 2PC constructions achieving our new notion. Both protocols are competitive with the previous covert 2PC protocols based on cut-and-choose. 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 garbled circuits, and to verify validity of these gadgets using multi-stage cut-and-choose openings.