International Association
for Cryptologic Research

A {\em leakage-resilient circuit} for $f:\{0,1\}^n\to\{0,1\}^m$ is a randomized Boolean circuit $C$ mapping a randomized encoding of an input $x$ to an encoding of $y=f(x)$, such that applying any leakage function $L\in \cal L$ to the wires of $C$ reveals essentially nothing about $x$. A {\em leakage-tolerant circuit} achieves the stronger guarantee that even when $x$ and $y$ are not protected by any encoding, the output of $L$ can be simulated by applying some $L'\in \cal L$ to $x$ and $y$ alone. Thus, $C$ is as secure as an ideal hardware implementation of $f$ with respect to leakage from $\cal L$. Leakage-resilient circuits were constructed for low-complexity classes $\cal L$, including (length-$t$ output) $\mathcal{AC}0$ functions, parities, and functions with bounded communication complexity. In contrast, leakage-{\em tolerant} circuits were only known for the simple case of {\em probing} leakage, where $L$ outputs the values of $t$ wires in $C$. We initiate a systematic study of leakage-tolerant circuits for natural classes $\cal L$ of {\em global} leakage functions, obtaining the following main results. \begin{itemize} \item {\bf Leakage-tolerant circuits for depth-1 leakage.} Every circuit $C_f$ for $f$ can be efficiently compiled into an $\cal L$-tolerant circuit $C$ for $f$, where $\cal L$ includes all leakage functions $L$ that output either $t$ {\em parities} or $t$ {\em disjunctions} (alternatively, conjunctions) of any number of wires or their negations. In the case of parities, our simulator runs in $2^{O(t)}$ time. We provide partial evidence that this may be inherent. \item {\bf Application to stateful leakage-resilient circuits.} Using a general transformation from leakage-tolerant circuits, we obtain the first construction of {\em stateful} $t$-leakage-resilient circuits that tolerate a {\em continuous} parity leakage, and the first such construction for disjunction/conjunction leakage in which the circuit size grows sub-quadratically with $t$. Interestingly, here we can obtain $\poly(t)$-time simulation even in the case of parities. \end{itemize}

In this work we present a novel actively secure dishonest majority MPC protocol, \textsc{SuperPack}, whose efficiency improves as the number of \emph{honest} parties increases. Concretely, let $0<\epsilon<1/2$ and consider an adversary that corrupts $t<n(1-\epsilon)$ out of $n$ parties. \textsc{SuperPack} requires $6/\epsilon$ field elements of online communication per multiplication gate across all parties, assuming circuit-dependent preprocessing, and $10/\epsilon$ assuming circuit-independent preprocessing. In contrast, most of previous works such as SPDZ (Damg\aa rd \emph{et al}, ESORICS 2013) and its derivatives perform the same regardless of whether there is only one honest party, or a constant (non-majority) fraction of honest parties. The only exception is due to Goyal \emph{et al} (CRYPTO 2022), which achieves $58/\epsilon + 96/\epsilon^2$ field elements assuming circuit-independent preprocessing. Our work improves this result substantially by a factor of at least $25$ in the circuit-independent preprocessing model. Practically, we also compare our work with the best concretely efficient online protocol Turbospeedz (Ben-Efraim \emph{et al}, ACNS 2019), which achieves $2(1-\epsilon)n$ field elements per multiplication gate among all parties. Our online protocol improves over Turbospeedz as $n$ grows, and as $\epsilon$ approaches $1/2$. For example, if there are $90\%$ corruptions ($\epsilon=0.1$), with $n=50$ our online protocol is $1.5\times$ better than Turbospeedz and with $n=100$ this factor is $3\times$, but for $70\%$ corruptions ($\epsilon=0.3$) with $n=50$ our online protocol is $3.5\times$ better, and for $n=100$ this factor is $7\times$. Our circuit-dependent preprocessing can be instantiated from OLE/VOLE. The amount of OLE/VOLE correlations required in our work is a factor of $\approx \epsilon n/2$ smaller than these required by Le Mans (Rachuri and Scholl, CRYPTO 2022) leveraged to instantiate the proprocesing of Turbospeedz. Our dishonest majority protocol relies on packed secret-sharing and leverages ideas from the honest majority \textsc{TurboPack} (Escudero \emph{et al}, CCS 2022) protocol to achieve concrete efficiency for any circuit topology, not only SIMD. We implement both \textsc{SuperPack} and Turbospeedz and verify with experimental results that our approach indeed leads to more competitive runtimes in distributed environments with a moderately large number of parties.

A secret sharing scheme enables one party to distribute shares of a secret to n parties and ensures that an adversary in control of t out of n parties will learn no information about the secret. However, traditional secret sharing schemes are often insufficient, especially for applications in which the set of parties who hold the secret shares might change over time. To achieve security in this setting, dynamic proactive secret sharing (DPSS) is used. DPSS schemes proactively update the secret shares held by the parties and allow changes to the set of parties holding the secrets. We propose FaB-DPSS (FAst Batched DPSS) -- a new and highly optimized batched DPSS scheme. While previous work on batched DPSS focuses on a single client submitting a batch of secrets and does not allow storing and releasing secrets independently, we allow multiple different clients to dynamically share and release secrets. FaB-DPSS is the most efficient robust DPSS scheme that supports the highest possible adversarial threshold of 1/2. We prove FaB-DPSS secure and implement it. All operations complete in seconds, and we outperform a prior state-of-the-art DPSS scheme by over 6 times. Additionally, we propose new applications of DPSS in the context of blockchains. Specifically, we propose a protocol that uses blockchains and FaB-DPSS to provide conditional secret storage. The protocol allows parties to store secrets along with a release condition, and once a (possibly different) party satisfies this release condition, the secret is privately released to that party. This functionality is similar to extractable witness encryption. While there are numerous compelling applications (e.g., time-lock encryption, one-time programs, and fair multi-party computation) which rely on extractable witness encryption, there are no known efficient constructions (or even constructions based on any well-studied assumptions) of extractable witness encryption. However, by utilizing blockchains and FaB-DPSS, we can easily build all those applications. We provide an implementation of our conditional secret storage protocol as well as several applications building on top of it.

A {\em $t$-private} circuit for a function $f$ is a randomized Boolean circuit $C$ that maps a randomized encoding of an input $x$ to an encoding of the output $f(x)$, such that probing $t$ wires anywhere in $C$ reveals nothing about $x$. Private circuits can be used to protect embedded devices against side-channel attacks. Motivated by the high cost of generating fresh randomness in such devices, several works have studied the question of minimizing the randomness complexity of private circuits. The best known upper bound, due to Coron et al. (Eurocrypt 2020), is $O(t^2\cdot\log s)$ random bits, where $s$ is the circuit size of $f$. We improve this to $O(t\cdot \log s)$, including the randomness used by the input encoder, and extend this bound to the stateful variant of private circuits. Our constructions are semi-explicit in the sense that there is an efficient randomized algorithm that generates the private circuit $C$ from a circuit for $f$ with negligible failure probability.

We revisit the question of minimizing the randomness complexity of protocols for secure multiparty computation (MPC) in the setting of perfect information-theoretic security. Kushilevitz and Mansour (SIAM J. Discret. Math., 1997) studied the case of n-party semi-honest MPC for the XOR function with security threshold t<n, showing that O(t^2 * log(n/t)) random bits are sufficient and \Omega(t) random bits are necessary. Their positive result was obtained via a non-explicit protocol, whose existence was proved using the probabilistic method. We essentially close the question by proving an \Omega(t^2) lower bound on the randomness complexity of XOR, matching the previous upper bound up to a logarithmic factor (or constant factor when t=\Omega(n)). We also obtain an explicit protocol that uses O(t^2 * \log^2n) random bits, matching our lower bound up to a polylogarithmic factor. We extend these results from XOR to general symmetric Boolean functions and to addition over a finite Abelian group, showing how to amortize the randomness complexity over multiple additions. Finally, combining our techniques with recent randomness-efficient constructions of private circuits, we obtain an explicit protocol for evaluating a general circuit C using only O(t^2 * \log |C|) random bits, by employing additional ``helper parties'' who do not contribute any inputs. This upper bound too matches our lower bound up to a logarithmic factor.

In the last few years, the efficiency of secure multi-party computation (MPC) in the dishonest majority setting has increased by several orders of magnitudes starting with the SPDZ protocol family which offers a speedy information-theoretic online phase in the prepossessing model. However, state-of-the-art n-party MPC protocols in the dishonest majority setting incur online communication complexity per multiplication gate which is linear in the number of parties, i.e. O(n), per gate across all parties. In this work, we construct the first MPC protocols in the preprocessing model for dishonest majority with sublinear communication complexity per gate in the number of parties n. To achieve our results, we extend the use of packed secret sharing to the dishonest majority setting. For a constant fraction of corrupted parties (i.e. if 99 percent of the parties are corrupt), we can achieve a communication complexity of O(1) field elements per multiplication gate across all parties. At the crux of our techniques lies a new technique called sharing transformation. The sharing transformation technique allows us to transform shares under one type of linear secret sharing scheme into another, and even perform arbitrary linear maps on the secrets of (packed) secret sharing schemes with optimal communication complexity. This technique can be of independent interest since transferring shares from one type of scheme into another (e.g., for degree reduction) is ubiquitous in MPC. Furthermore, we introduce what we call sparsely packed Shamir sharing which allows us to address the issue of network routing efficiently, and packed Beaver triples which is an extension of the widely used technique of Beaver triples for packed secret sharing (for dishonest majority).

We propose to use blockchains to achieve MPC which does not require the participating parties to be online simultaneously or interact with each other. Parties who contribute inputs but do not wish to receive outputs can go offline after submitting a single message. In addition to our main result, we study combined communication- and state-complexity in MPC, as it has implications for the communication complexity of our main construction. Finally, we provide a variation of our main protocol which additionally provides guaranteed output delivery.

We study the communication complexity of unconditionally secure multiparty computation (MPC) protocols in the honest majority setting. Despite tremendous efforts in achieving efficient protocols for binary fields under computational assumptions, there are no efficient unconditional MPC protocols in this setting. In particular, there are no n party protocols with constant overhead admitting communication complexity of O(n) bits per gate. Cascudo, Cramer, Xing and Yuan (CRYPTO 2018) were the first ones to achieve such an overhead in the amortized setting by evaluating O(log n) copies of the same circuit in the binary field in parallel. In this work, we construct the first unconditional MPC protocol secure against a malicious adversary in the honest majority setting evaluating just a single boolean circuit with amortized communication complexity of O(n) bits per gate.

In this work, we address communication, computation, and round efficiency of unconditionally secure multi-party computation for arithmetic circuits in the honest majority setting. We achieve both algorithmic and practical improvements: - The best known result in the semi-honest setting has been due to Damgard and Nielsen (CRYPTO 2007). Over the last decade, their construction has played an important role in the progress of efficient secure computation. However despite a number of follow-up works, any significant improvements to the basic semi-honest protocol have been hard to come by. We show 33% improvement in communication complexity of this protocol. We show how to generalize this result to the malicious setting, leading to the best known unconditional honest majority MPC with malicious security. - We focus on the round complexity of the Damgard and Nielsen protocol and improve it by a factor of 2. Our improvement relies on a novel observation relating to an interplay between Damgard and Nielsen multiplication and Beaver triple multiplication. An implementation of our constructions shows an execution run time improvement compared to the state of the art ranging from 30% to 50%.

The best known n party unconditional multiparty computation protocols with an optimal corruption threshold communicates O(n) field elements per gate. This has been the case even in the semi-honest setting despite over a decade of research on communication complexity in this setting. Going to the slightly sub-optimal corruption setting, the work of Damgard, Ishai, and Kroigaard (EUROCRYPT 2010) provided the first protocol for a single circuit achieving communication complexity of O(log |C|) elements per gate. While a number of works have improved upon this result, obtaining a protocol with O(1) field elements per gate has been an open problem. In this work, we construct the first unconditional multi-party computation protocol evaluating a single arithmetic circuit with amortized communication complexity of O(1) elements per gate.

Consider a scenario where Alice stores some secret data $s$ on $n$ servers using a $t$-out-of-$n$ secret sharing scheme. Trudy (the collector) is interested in the secret data of Alice and is willing to pay for it. Trudy publishes an advertisement on the internet which describes an elaborate cryptographic scheme to collect the shares from the $n$ servers. Each server who decides to submit its share is paid a hefty monetary reward and is guaranteed ``immunity" from being caught or prosecuted in a court for violating its service agreement with Alice. Bob is one of the servers and sees this advertisement. On examining the collection scheme closely, Bob concludes that there is no way for Alice to prove anything in a court that he submitted his share. Indeed, if Bob is rational, he might use the cryptographic scheme in the advertisement and submit his share since there are no penalties and no fear of being caught and prosecuted. Can we design a secret sharing scheme which Alice can use to avoid such a scenario? We introduce a new primitive called as \textit{Traceable Secret Sharing} to tackle this problem. In particular, a traceable secret sharing scheme guarantees that a cheating server always runs the risk of getting traced and prosecuted by providing a valid evidence (which can be examined in a court of law) implicating its dishonest behavior. We explore various definitional aspects and show how they are highly non-trivial to construct (even ignoring efficiency aspects). We then give an efficient construction of traceable secret sharing assuming the existence of a secure two-party computation protocol. We also show an application of this primitive in constructing traceable protocols for multi-server delegation of computation.

We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold t < n/2, assuming the existence of a public broadcast channel. We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive until now. We also focus on the concrete communication complexity of evaluating each multiplication gate. We resolve the above question in the affirmative by providing an MPC with communication complexity O(Cn\phi) bits (ignoring fixed terms which are independent of the circuit) where \phi is the length of an element in the field, C is the size of the (arithmetic) circuit, n is the number of parties. This is the first construction where the asymptotic communication complexity matches the best-known semi-honest protocol. This represents a strict improvement over the previously best-known communication complexity of O(C(n\phi + \kappa) + D_Mn^2\kappa) bits, where \kappa is the security parameter and D_M is the multiplicative depth of the circuit. Furthermore, the concrete communication complexity per multiplication gate is 5.5 field elements per party in the best case and 7.5 field elements in the worst case when one or more corrupted parties have been identified. This also roughly matches the best-known semi-honest protocol, which requires 5.5 field elements per gate. The above also yields the first secure-with-abort MPC protocol with the same cost per multiplication gate as the best-known semi-honest protocol. Our main result is obtained by compiling the secure-with-abort MPC protocol into a fully secure one.

In this paper, we consider the setting where a party uses correlated random tapes across multiple executions of a cryptographic algorithm. We ask if the security properties could still be preserved in such a setting. As examples, we introduce the notion of correlated-tape zero knowledge, and, correlated-tape multi-party computation, where, the zero-knowledge property, and, the ideal/real model security must still be preserved even if a party uses correlated random tapes in multiple executions.Our constructions are based on a new type of randomness extractor which we call correlated-source extractors. Correlated-source extractors can be seen as a dual of non-malleable extractors, and, allow an adversary to choose several tampering functions which are applied to the randomness source. Correlated-source extractors guarantee that even given the output of the extractor on the tampered sources, the output on the original source is still uniformly random. Given (seeded) correlated-source extractors, and, resettably-secure computation protocols, we show how to directly get a positive result for both correlated-tape zero-knowledge and correlated-tape multi-party computation in the CRS model. This is tight considering the known impossibility results on cryptography with imperfect randomness.Our main technical contribution is an explicit construction of a correlated-source extractor where the length of the seed is independent of the number of tamperings. Additionally, we also provide a (non-explicit) existential result for correlated source extractors with almost optimal parameters.

We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold $$t < n/3$$ . We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive for over a decade.We resolve the above question in the affirmative by providing an MPC with communication complexity $$O(Cn\kappa + n^3\kappa )$$ where $$\kappa $$ is the size of an element in the field, C is the size of the (arithmetic) circuit, and, n is the number of parties. This represents a strict improvement over the previously best known communication complexity of $$O(Cn\kappa +D_Mn^2\kappa +n^3\kappa )$$ where $$D_M$$ is the multiplicative depth of the circuit. To obtain this result, we introduce a novel technique called 4-consistent tuples of sharings which we believe to be of independent interest.