International Association
for Cryptologic Research

This work introduces the notion of secure multiparty computation: MPC with fall-back security. Fall-back security for an $n$-party protocol is defined with respect to an adversary structure $\cZ$ wherein security is guaranteed in the presence of both a computationally unbounded adversary with adversary structure $\cZ$, and a computationally bounded adversary corrupting an arbitrarily large subset of the parties. This notion was considered in the work of Chaum (Crypto 89) via the Spymaster's double agent problem where he showed a semi-honest secure protocol for the honest majority adversary structure. Our first main result is a compiler that can transform any $n$-party protocol that is semi-honestly secure with statistical security tolerating an adversary structure $\cZ$ to one that (additionally) provides semi-honest fall-back security w.r.t $\cZ$. The resulting protocol has optimal round complexity, up to a constant factor, and is optimal in assumptions and the adversary structure. Our second result fully characterizes when malicious fall-back security is feasible. More precisely, we show that malicious fallback secure protocol w.r.t $\cZ$ exists if and only if $\cZ$ admits unconditional MPC against a semi-honest adversary (namely, iff $\cZ \in \cQ^2$).

We obtain the first two-round two-party computation protocol, in the plain model, that is secure against passive adversaries who can adaptively corrupt all parties where the communication complexity is proportional to the square of the RAM complexity of the function up to polylogarithmic factors assuming the existence of non-committing encryption.

We put forth a new paradigm for program obfuscation, where obfuscated programs are endowed with proofs of ``well formedness.'' In addition to asserting existence of an underlying plaintext program with an attested structure, these proofs also prevent mauling attacks, whereby an adversary surreptitiously creates an obfuscated program based on secrets which are embedded in other obfuscated programs. We call this new guarantee Chosen Obfuscation Attacks (COA) security. We show how to enhance a large class of obfuscation mechanisms to be COA-secure, assuming subexponentially secure IO for circuits and subexponentially secure one-way functions.To demonstrate the power of the new notion, we also use it to realize: - A new form of software watermarking, which provides significantly broader protection than current schemes against counterfeits that pass a keyless, public verification process. - Completely CCA encryption, which is a strengthening of completely non-malleable encryption.

Deniable encryption (Canetti \emph{et al.}, Crypto 1996) enhances secret communication over public channels, providing the additional guarantee that the secrecy of communication is protected even if the parties are later coerced (or willingly bribed) to expose their entire internal states: plaintexts, keys and randomness. To date, constructions of deniable encryption --- and more generally, interactive deniable communication --- only address restricted cases where only {\em one} party is compromised (Sahai and Waters, STOC 2014). The main question --- whether deniable communication is at all possible if {\em both} parties are coerced at once --- has remained open. We resolve this question in the affirmative, presenting a communication protocol that is {\em fully deniable} under coercion of both parties. Our scheme has three rounds, assumes subexponentially secure indistinguishability obfuscation and one-way functions, and uses a short global reference string that is generated once at system set-up and suffices for an unbounded number of encryptions and decryptions. Of independent interest, we introduce a new notion called \emph{off-the-record deniability}, which protects parties even when their claimed internal states are inconsistent (a case not covered by prior definitions). Our scheme satisfies both standard deniability and off-the-record deniability.

Incoercible multi-party computation [Canetti-Gennaro ’96] allows parties to engage in secure computation with the additional guarantee that the public transcript of the computation cannot be used by a coercive external entity to verify representations made by the parties regarding their inputs to and outputs from the computation. That is, any deductions regarding the truthfulness of such representations made by the parties could be made even without access to the public transcript. To date, all incoercible secure computation protocols withstand coercion of only a fraction of the parties, or else assume that all parties use an execution environment that makes some crucial parts of their local states physically inaccessible even to themselves. We consider, for the first time, the setting where all parties are coerced, and the coercer expects to see the entire history of the computation.In this setting we construct: - A general multi-party computation protocol that withstands coercion of all parties, as long as none of the coerced parties cooperates with the coercer, namely they all use the prescribed ``faking algorithm'' upon coercion. We refer to this case as cooperative incoercibility. The protocol uses deniable encryption and indistiguishability obfuscation, and takes 4 rounds of communication. - A general two-party computation protocol that withstands even the ``mixed'' case where some of the coerced parties cooperate with the coercer and disclose their true local states. This protocol is limited to computing functions where the input of one of the parties is taken from a small (poly-size) domain. This protocol uses deniable encryption with public deniability for one of the parties; when instantiated using the deniable encryption of Canetti, Park, and Poburinnaya [Crypto'20], it takes 3 rounds of communication. Finally, we show that protocols with certain communication pattern cannot be incoercible, even in a weaker setting where only some parties are coerced.

Generating additive secret shares of a shuffled dataset - such that neither party knows the order in which it is permuted - is a fundamental building block in many protocols, such as secure collaborative filtering, oblivious sorting, and secure function evaluation on set intersection. Traditional approaches to this problem either involve expensive public-key based crypto or using symmetric crypto on permutation networks. While public-key-based solutions are bandwidth efficient, they are computation-heavy. On the other hand, constructions based on permutation networks are communication-bound, especially when the dataset contains large elements, for e.g., feature vectors in an ML context. We design a new 2-party protocol for this task of computing secret shares of shuffled data, which we refer to as secret-shared shuffle. Our protocol is secure against a static semi-honest adversary. At the heart of our approach is a new primitive we define (which we call ``Share Translation'') that generates two sets of pseudorandom values ``correlated via the permutation''. This allows us to reduce the problem of shuffling the dataset to the problem of shuffling pseudorandom values, which enables optimizations both in computation and communication. We then design a Share Translation protocol based on oblivious transfer and puncturable PRFs. Our final protocol for secret-shared shuffle uses lightweight operations like XOR and PRGs, and in particular doesn't use public-key operations besides the base OTs. As a result, our protocol is concretely more efficient than the existing solutions. In particular, we are two-three orders of magnitude faster than public-key-based approach and one order of magnitude faster compared to the best known symmetric-key approach when the elements are moderately large.