Non-interactive secure 2PC in the offline/online and batch settings

Abstract

In cut-and-choose protocols for two-party secure computation (2PC) the main overhead is the number of garbled circuits that must be sent. Recent work (Lindell and Riva; Huang et al. Crypto 2014) has shown that in a batched setting, when the parties plan to evaluate the same function N times, the number of garbled circuits per execution can be reduced by a O(logN) factor compared to the single-execution setting. This improvement is significant in practice: an order of magnitude for N as low as one thousand. Besides the number of garbled circuits, communication round trips are another significant performance bottleneck. Afshar et al. (Eurocrypt 2014) proposed an efficient cut-and choose 2PC that is round-optimal (one message from each party), but in the single-execution setting. In this work we present new malicious-secure 2PC protocols that are round-optimal and also take advantage of batching to reduce cost. Our contributions include: – A 2-message protocol for batch secure computation (N instances of the same function). The number of garbled circuits is reduced by a O(logN) factor over the single-execution case. However, other aspects of the protocol that depend on the input/output size of the function do not benefit from the same O(logN)-factor savings. – A 2-message protocol for batch secure computation, in the random oracle model. All aspects of this protocol benefit from the O(logN)- factor improvement, except for small terms that do not depend on the function being evaluated. – A protocol in the offline/online setting. After an offline preprocessing phase that depends only on the function f and N, the parties can securely evaluate f, N times (not necessarily all at once). Our protocol’s online phase is only 2 messages, and the total online communication is only ℓ + O(κ) bits, where ℓ is the input length of f and κ is a computational security parameter. This is only O(κ) bits more than the information-theoretic lower bound for malicious 2PC.