International Association
for Cryptologic Research

Common randomness is an essential resource in many applications. However, a celebrated result of Cleve (STOC 86) rules out the possibility of tossing a fair coin from scratch in the presence of a dishonest majority. A second-best alternative is a Coin Tossing Extension (CTE) protocol, which uses an "online" oracle that produces a small number of common random bits to generate a large number of common random-looking bits.This work initiates the systematic study of fully-secure CTE, which guarantees output even in the presence of malicious behavior. A fully-secure two-party statistical CTE protocol with black-box simulation was implicit in Hofheinz et al. (Eurocrypt 06), but its round complexity is nearly linear in its output length. The problem of constant-round CTE with superlogarithmic stretch remained open. We prove that any statistical CTE with full black-box security and superlogarithmic stretch must have superconstant rounds. To circumvent this impossibility we investigate fully-secure computational CTE, and prove that with N parties and any polynomial stretch: • One round suffices for CTE under subexponential LWE, even with Universally Composable security against adaptive corruptions. • One-round CTE is implied by DDH or the hidden subgroup assumption in class groups, with a short, reusable Uniform Random String, and by both DCR and QR, with a reusable Structured Reference String. • One-way functions imply CTE with O(N) rounds, and thus constant-round CTE for any constant number of parties. Such results were not known even in the two-party setting with standalone, static security. Furthermore, we extend one-round CTE to sample from any efficient distribution, via strong assumptions that include indistinguishability obfuscation. Our one-round CTE protocols can be interpreted as explainable variants of classical randomness extractors, wherein a (short) seed and a source instance can be efficiently reverse-sampled given a random output. Such explainable extractors may be of independent interest.

We investigate the conditions under which straight-line extractable NIZKs in the random oracle model (i.e. without a CRS) permit multiparty realizations that are black-box in the same random oracle. We show that even in the semi-honest setting, any MPC protocol to compute such a NIZK cannot make black-box use of the random oracle or a hash function instantiating it if security against all-but-one corruptions is desired, unless the number of queries made by the verifier to the oracle grows linearly with the number of parties. This presents a fundamental barrier to constructing efficient protocols to securely distribute the computation of NIZKs (and signatures) based on MPC-in-the-head, PCPs/IOPs, and sigma protocols compiled with transformations due to Fischlin, Pass, or Unruh. When the adversary is restricted to corrupt only a constant fraction of parties, we give a positive result by means of a tailored construction, which demonstrates that our impossibility does not extend to weaker corruption models in general.

In the dishonest-majority setting, secure multiparty computation (MPC) with identifiable abort (IA) guarantees that honest parties can identify and agree upon at least one cheating party if the protocol does not produce an output. Known MPC constructions with IA rely on generic zero-knowledge proofs, adaptively secure oblivious transfer (OT) protocols, or homomorphic primitives, and thus incur a substantial penalty with respect to protocols that abort without identifiability. We introduce a new, weaker notion of IA called input-revealing IA (IRIA), which can be constructed through selective revealing of committed input values---a technique we call vindicating release. We show that this weaker form of IA can be achieved with small concrete overheads for many interesting protocols in the literature, including the pre-processing protocols needed for several state-of-the-art MPC protocols. We next show how to assemble these IRIA components into an MPC protocol for any functionality with standard IA. Such a realization differs minimally in terms of cost, techniques, and analysis from the equivalent realization that lacks identifiability, e.g., our total bandwidth overhead incurred is less than 2x, which is an asymptotic improvement over prior work on IA. On a practical level, we apply our techniques to the problem of threshold ECDSA, and show that the resulting protocol with standard IA is concretely efficient. On a theoretical level, we present a compiler that transforms any secure protocol into one with standard IA assuming only a variant of statically-corruptable ideal OT.

We introduce a notion of round-robin secure sampling that captures several protocols in the literature, such as the "powers-of-tau" setup protocol for pairing-based polynomial commitments and zk-SNARKs, and certain verifiable mixnets. Due to their round-robin structure, protocols of this class inherently require n sequential broadcast rounds, where n is the number of participants. We describe how to compile them generically into protocols that require only O(sqrt(n)) broadcast rounds. Our compiled protocols guarantee output delivery against any dishonest majority. This stands in contrast to prior techniques, which require Omega(n) sequential broadcasts in most cases (and sometimes many more). Our compiled protocols permit a certain amount of adversarial bias in the output, as all sampling protocols with guaranteed output must, due to Cleve's impossibility result (STOC'86). We show that in the context of the aforementioned applications, this bias is harmless.

We present a new multiparty protocol for the distributed generation of biprime RSA moduli, with security against any subset of maliciously colluding parties assuming oblivious transfer and the hardness of factoring. Our protocol is highly modular, and its uppermost layer can be viewed as a template that generalizes the structure of prior works and leads to a simpler security proof. We introduce a combined sampling-and-sieving technique that eliminates both the inherent leakage in the approach of Frederiksen et al. (Crypto’18) and the dependence upon additively homomorphic encryption in the approach of Hazay et al. (JCrypt’19). We combine this technique with an efficient, privacy-free check to detect malicious behavior retroactively when a sampled candidate is not a biprime and thereby overcome covert rejection-sampling attacks and achieve both asymptotic and concrete efficiency improvements over the previous state of the art.

We present a new multiparty protocol for the distributed generation of biprime RSA moduli, with security against any subset of maliciously colluding parties assuming oblivious transfer and the hardness of factoring. Our protocol is highly modular, and its uppermost layer can be viewed as a template that generalizes the structure of prior works and leads to a simpler security proof. We introduce a combined sampling-and-sieving technique that eliminates both the inherent leakage in the approach of Frederiksen et al. (Crypto'18), and the dependence upon additively homomorphic encryption in the approach of Hazay et al. (JCrypt'19). We combine this technique with an efficient, privacy-free check to detect malicious behavior retroactively when a sampled candidate is not a biprime, and thereby overcome covert rejection-sampling attacks and achieve both asymptotic and concrete efficiency improvements over the previous state of the art.