International Association
for Cryptologic Research

We describe robust high-throughput threshold protocols for generating Schnorr signatures in an asynchronous setting with potentially hundreds of parties. The protocols run a single message-independent interactive ephemeral randomness generation procedure (i.e., DKG) followed by \emph{non-interactive} signature generation for multiple messages, at a communication cost similar to one execution of a synchronous non-robust protocol in prior work (e.g., Gennaro et al.) and with a large number of parties (ranging from few tens to hundreds and more). Our protocols extend seamlessly to the dynamic/proactive setting where each run of the protocol uses a new committee with refreshed shares of the secret key; in particular, they support large committees periodically sampled from among the overall population of parties and the required secret state is transferred to the selected parties. The protocols work over a broadcast channel and are robust (provide guaranteed output delivery) even over asynchronous networks. The combination of these features makes our protocols a good match for implementing a signature service over a public blockchain with many validators, where guaranteed output delivery is an absolute must. In that setting, there is a system-wide public key, where the corresponding secret signature key is distributed among the validators. Clients can submit messages (under suitable controls, e.g. smart contracts), and authorized messages are signed relative to the global public key. Asymptotically, when running with committees of $n$ parties, our protocols can generate $\Omega(n^2)$ signatures per run, while providing resilience against $\Omega(n)$ corrupted nodes and broadcasting only $O(n^2)$ group elements and scalars (hence $O(1)$ elements per signature). We prove the security of our protocols via a reduction to the hardness of the discrete logarithm problem in the random oracle model.

Addition of $n$ inputs is often the easiest nontrivial function to compute securely. Motivated by several open questions, we ask what can be computed securely given only an oracle that computes the sum. Namely, what functions can be computed in a model where parties can only encode their input locally, then sum up the encodings over some Abelian group $\G$, and decode the result to get the function output. An {\em additive randomized encoding} (ARE) of a function $f(x_1,\ldots,x_n)$ maps every input $x_i$ independently into a randomized encoding $\hat x_i$, such that $\sum_{i=1}^n$ $\hat x_i$ reveals $f(x_1,\ldots,x_n)$ and nothing else about the inputs. In a {\em robust} ARE, the sum of {\em any subset} of the $\hat x_i$ only reveals the {\em residual function} obtained by restricting the corresponding inputs. We obtain positive and negative results on ARE. In particular: \begin{itemize} \item {\em Information-theoretic ARE.} We fully characterize the 2-party functions $f:X_1\times X_2\to\{0,1\}$ admitting a perfectly secure ARE. For $n\ge 3$ parties, we show a useful ``capped sum'' function that separates statistical security from perfect security. \item {\em Computational ARE.} We present a general feasibility result, showing that \emph{all functions} can be computed in this model, under a standard hardness assumption in bilinear groups. We also describe a heuristic lattice-based construction. \item {\em Robust ARE.} We present a similar feasibility result for {\em robust} computational ARE based on ideal obfuscation along with standard cryptographic assumptions. \end{itemize} We then describe several applications of ARE and the above results. \begin{itemize} \item Under a standard cryptographic assumption, our computational ARE schemes imply the feasibility of general non-interactive secure computation in the {\em shuffle model}, where messages from different parties are shuffled. This implies a general utility-preserving compiler from differential privacy in the central model to computational differential privacy in the (non-robust) shuffle model. \item The existence of information-theoretic {\em robust} ARE implies ``best-possible'' information-theoretic MPC protocols (Halevi et al., TCC 2018) and degree-2 multiparty randomized encodings (Applebaum et al., TCC 2018). This yields new positive results for specific functions in the former model, as well as a simple unifying barrier for obtaining negative results in both models. \end{itemize}

This paper presents the first protocols for Proactive Secret Sharing (PSS) that only require constant (in the number of parties, n) communication per party per epoch. By harnessing the power of expander graphs, we are able to obtain strong guarantees about the security of the system. We present the following PSS protocols: – A PSS protocol that provides privacy (but no robustness) against an adversary controlling O(n) parties per epoch. – A PSS protocol that provides robustness (but no privacy) against an adversary controlling O(n) parties per epoch. – A PSS protocol that provides privacy against an adversary controlling O(n^a) ) parties per epoch and provides robustness against an adversary controlling O(n^(1−a)) parties per epoch, for any constant 0 ≤ a ≤ 1. Instantiating this with a = 1/2 gives a PSS protocol that is proactively secure (private and robust) against an adversary controlling O(√n) parties per epoch. Additionally, we discuss how secure channels, whose existence is usually assumed by PSS protocols, are challenging to create in the mobile adversary setting, and we present a method to instantiate them from a weaker assumption.

The inherent difficulty of maintaining stateful environments over long periods of time gave rise to the paradigm of serverless computing, where mostly-stateless components are deployed on demand to handle computation tasks, and are teared down once their task is complete. Serverless architecture could offer the added benefit of improved resistance to targeted denial-of-service attacks, by hiding from the attacker the physical machines involved in the protocol until after they complete their work. Realizing such protection, however, requires that the protocol only uses stateless parties, where each party sends only one message and never needs to speaks again. Perhaps the most famous example of this style of protocols is the Nakamoto consensus protocol used in Bitcoin: A peer can win the right to produce the next block by running a local lottery (mining), all while staying covert. Once the right has been won, it is executed by sending a single message. After that, the physical entity never needs to send more messages. We refer to this as the You-Only-Speak-Once (YOSO) property, and initiate the formal study of it within a new model that we call the YOSO model. Our model is centered around the notion of roles, which are stateless parties that can only send a single message. Crucially, our modelling separates the protocol design, that only uses roles, from the role-assignment mechanism, that assigns roles to actual physical entities. This separation enables studying these two aspects separately, and our YOSO model in this work only deals with the protocol-design aspect. We describe several techniques for achieving YOSO MPC; both computational and information theoretic. Our protocols are synchronous and provide guaranteed output delivery (which is important for application domains such as blockchains), assuming honest majority of roles in every time step. We describe a practically efficient computationally-secure protocol, as well as a proof-of-concept information theoretically secure protocol.

We consider the following basic question: to what extent are standard secret sharing schemes and protocols for secure multiparty computation that build on them resilient to leakage? We focus on a simple local leakage model, where the adversary can apply an arbitrary function of a bounded output length to the secret state of each party, but cannot otherwise learn joint information about the states. We show that additive secret sharing schemes and high-threshold instances of Shamir’s secret sharing scheme are secure under local leakage attacks when the underlying field is of a large prime order and the number of parties is sufficiently large. This should be contrasted with the fact that any linear secret sharing scheme over a small characteristic field is clearly insecure under local leakage attacks, regardless of the number of parties. Our results are obtained via tools from Fourier analysis and additive combinatorics. We present two types of applications of the above results and techniques. As a positive application, we show that the “GMW protocol” for honest-but-curious parties, when implemented using shared products of random field elements (so-called “Beaver Triples”), is resilient in the local leakage model for sufficiently many parties and over certain fields. This holds even when the adversary has full access to a constant fraction of the views. As a negative application, we rule out multiparty variants of the share conversion scheme used in the 2-party homomorphic secret sharing scheme of Boyle et al. (in: Crypto, 2016).

Blockchains are gaining traction and acceptance, not just for cryptocurrencies, but increasingly as an architecture for distributed computing. In this work we seek solutions that allow a \emph{public} blockchain to act as a trusted long-term repository of secret information: Our goal is to deposit a secret with the blockchain, specify how it is to be used (e.g., the conditions under which it is released), and have the blockchain keep the secret and use it only in the specified manner (e.g., release only it once the conditions are met). This simple functionality enables many powerful applications, including signing statements on behalf of the blockchain, using it as the control plane for a storage system, performing decentralized program-obfuscation-as-a-service, and many more. Using proactive secret sharing techniques, we present a scalable solution for implementing this functionality on a public blockchain, in the presence of a mobile adversary controlling a small minority of the participants. The main challenge is that, on the one hand, scalability requires that we use small committees to represent the entire system, but, on the other hand, a mobile adversary may be able to corrupt the entire committee if it is small. For this reason, existing proactive secret sharing solutions are either non-scalable or insecure in our setting. We approach this challenge via "player replaceability", which ensures the committee is anonymous until after it performs its actions. Our main technical contribution is a system that allows sharing and re-sharing of secrets among the members of small dynamic committees, without knowing who they are until after they perform their actions and erase their secrets. Our solution handles a fully mobile adversary corrupting roughly 1/4 of the participants at any time, and is scalable in terms of both the number of parties and the number of time intervals.

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is a complete Paillier (in: EUROCRYPT, pp 223–238, 1999) threshold encryption scheme in the two-party setting with security against malicious attacks. We further describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation protocol is comprised of the following subprotocols: (i) a distributed protocol for generation of an RSA composite and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite for the public key and is comprised of the following subprotocols: (i) a distributed generation of the corresponding secret key shares and (ii) a distributed decryption protocol for decrypting according to Paillier.

We study the possibility of achieving full security, with guaranteed output delivery, for secure multiparty computation of functionalities where only one party receives output, to which we refer as solitary functionalities. In the standard setting where all parties receive an output, full security typically requires an honest majority; otherwise even just achieving fairness is impossible. However, for solitary functionalities, fairness is clearly not an issue. This raises the following question: Is full security with no honest majority possible for all solitary functionalities?We give a negative answer to this question, by showing the existence of solitary functionalities that cannot be computed with full security. While such a result cannot be proved using fairness-based arguments, our proof builds on the classical proof technique of Cleve (STOC 1986) for ruling out fair coin-tossing and extends it in a nontrivial way.On the positive side, we show that full security against any number of malicious parties is achievable for many natural and useful solitary functionalities, including ones for which the multi-output version cannot be realized with full security.

We consider the following basic question: to what extent are standard secret sharing schemes and protocols for secure multiparty computation that build on them resilient to leakage? We focus on a simple local leakage model, where the adversary can apply an arbitrary function of a bounded output length to the secret state of each party, but cannot otherwise learn joint information about the states.We show that additive secret sharing schemes and high-threshold instances of Shamir’s secret sharing scheme are secure under local leakage attacks when the underlying field is of a large prime order and the number of parties is sufficiently large. This should be contrasted with the fact that any linear secret sharing scheme over a small characteristic field is clearly insecure under local leakage attacks, regardless of the number of parties. Our results are obtained via tools from Fourier analysis and additive combinatorics.We present two types of applications of the above results and techniques. As a positive application, we show that the “GMW protocol” for honest-but-curious parties, when implemented using shared products of random field elements (so-called “Beaver Triples”), is resilient in the local leakage model for sufficiently many parties and over certain fields. This holds even when the adversary has full access to a constant fraction of the views. As a negative application, we rule out multi-party variants of the share conversion scheme used in the 2-party homomorphic secret sharing scheme of Boyle et al. (Crypto 2016).

We reconsider the security guarantee that can be achieved by general protocols for secure multiparty computation in the most basic of settings: information-theoretic security against a semi-honest adversary. Since the 1980s, we have elegant solutions to this problem that offer full security, as long as the adversary controls a minority of the parties, but fail completely when that threshold is crossed. In this work, we revisit this problem, questioning the optimality of the standard notion of security. We put forward a new notion of information-theoretic security which is strictly stronger than the standard one, and which we argue to be “best possible.” This notion still requires full security against dishonest minority in the usual sense, and adds a meaningful notion of information-theoretic security even against dishonest majority.We present protocols for useful classes of functions that satisfy this new notion of security. Our protocols have the unique feature of combining the efficiency benefits of protocols for an honest majority and (most of) the security benefits of protocols for dishonest majority. We further extend some of the solutions to the malicious setting.