Multi-Source Non-Malleable Extractors and Applications

We introduce a natural generalization of two-source non-malleable extractors (Cheragachi and Guruswami, TCC 2014) called as \textit{multi-source non-malleable extractors}. Multi-source non-malleable extractors are special independent source extractors which satisfy an additional non-malleability property. This property requires that the output of the extractor remains close to uniform even conditioned on its output generated by tampering {\it several sources together}. We formally define this primitive, give a construction that is secure against a wide class of tampering functions, and provide applications. More specifically, we obtain the following results: \begin{itemize} \item For any $s \geq 2$, we give an explicit construction of a $s$-source non-malleable extractor for min-entropy $\Omega(n)$ and error $2^{-n^{\Omega(1)}}$ in the {\it overlapping joint tampering model}. This means that each tampered source could depend on any strict subset of all the sources and the sets corresponding to each tampered source could be overlapping in a way that we define. Prior to our work, there were no known explicit constructions that were secure even against disjoint tampering (where the sets are required to be disjoint without any overlap). %Our extractor is pre-image sampleable and hence, gives rise to non-malleable codes against the same tampering family. % \item We show how to efficiently preimage sample given the output of (a variant of) our extractor and this immediately gives rise to a $s$-state non-malleable code secure in the overlapping joint tampering model (via a generalization of the result by Cheragachi and Guruswami). \item We adapt the techniques used in the above construction to give a $t$-out-of-$n$ non-malleable secret sharing scheme (Goyal and Kumar, STOC 2018) for any $t \leq n$ in the \emph{disjoint tampering model}. This is the first general construction of a threshold non-malleable secret sharing (NMSS) scheme in the disjoint tampering model. All prior constructions had a restriction that the size of the tampered subsets could not be equal. \item We further adapt the techniques used in the above construction to give a $t$-out-of-$n$ non-malleable secret sharing scheme (Goyal and Kumar, STOC 2018) for any $t \leq n$ in the \emph{overlapping joint tampering model}. This is the first construction of a threshold NMSS in the overlapping joint tampering model. \item We show that a stronger notion of $s$-source non-malleable extractor that is multi-tamperable against disjoint tampering functions gives a single round network extractor protocol (Kalai et al., FOCS 2008) with attractive features. Plugging in with a new construction of multi-tamperable, 2-source non-malleable extractors provided in our work, we get a network extractor protocol for min-entropy $\Omega(n)$ that tolerates an {\it optimum} number ($t = p-2$) of faulty processors and extracts random bits for {\it every} honest processor. The prior network extractor protocols could only tolerate $t = \Omega(p)$ faulty processors and failed to extract uniform random bits for a fraction of the honest processors. \end{itemize

Stronger Leakage-Resilient and Non-Malleable Secret-Sharing Schemes for General Access Structures

In this work we present a collection of compilers that take secret sharing schemes for an arbitrary access structures as input and produce either leakage-resilient or non-malleable secret sharing schemes for the same access structure. A leakage-resilient secret sharing scheme hides the secret from an adversary, who has access to an unqualified set of shares, even if the adversary additionally obtains some size-bounded leakage from all other secret shares. A non-malleable secret sharing scheme guarantees that a secret that is reconstructed from a set of tampered shares is either equal to the original secret or completely unrelated. To the best of our knowledge we present the first generic compiler for leakage-resilient secret sharing for general access structures. In the case of non-malleable secret sharing, we strengthen previous definitions, provide separations between them, and construct a non-malleable secret sharing scheme for general access structures that fulfills the strongest definition with respect to independent share tampering functions. More precisely, our scheme is secure against concurrent tampering: The adversary is allowed to (non-adaptively) tamper the shares multiple times, and in each tampering attempt can freely choose the qualified set of shares to be used by the reconstruction algorithm to re-construct the tampered secret. This is a strong analogue of the multiple-tampering setting for split-state non-malleable codes and extractors. We show how to use leakage-resilient and non-malleable secret sharing schemes to construct leakage-resilient and non-malleable threshold signatures. Classical threshold signatures allow to distribute the secret key of a signature scheme among a set of parties, such that certain qualified subsets can sign messages. We construct threshold signature schemes that remain secure even if an adversary leaks from or tampers with all secret shares

List Oblivious Transfer and Applications to Round-Optimal Black-Box Multiparty Coin Tossing

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that, assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys. In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries. Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party