## CryptoDB

### Papers from CRYPTO 2021

Year
Venue
Title
2021
CRYPTO
Subtractive Sets over Cyclotomic Rings: Limits of Schnorr-like Arguments over Lattices
We study when (dual) Vandermonde systems of the form V_T ⋅ z = s⋅w admit a solution z over a ring R, where V_T is the Vandermonde matrix defined by a set T and where the “slack” s is a measure of the quality of solutions. To this end, we propose the notion of (s,t)-subtractive sets over a ring R, with the property that if S is (s,t)-subtractive then the above (dual) Vandermonde systems defined by any t-subset T ⊆ S are solvable over R. The challenge is then to find large sets S while minimising (the norm of) s when given a ring R. By constructing families of (s,t)-subtractive sets S of size n = poly(λ) over cyclotomic rings R = ZZ[ζ_{p^ℓ}] for prime p, we construct Schnorr-like lattice-based proofs of knowledge for the SIS relation A ⋅ x = s ⋅ y mod q with O(1/n) knowledge error, and s=1 in case p = poly(λ). Our technique slots naturally into the lattice Bulletproof framework from Crypto’20, producing lattice-based succinct arguments for NP with better parameters. We then give matching impossibility results constraining n relative to s, which suggest that our Bulletproof-compatible protocols are optimal unless fundamentally new techniques are discovered. Noting that the knowledge error of lattice Bulletproofs is Ω(log k/n) for witnesses in R^k and subtractive set size n, our result represents a barrier to practically efficient lattice-based succinct arguments in the Bulletproof framework. Beyond these main results, the concept of (s,t)-subtractive sets bridges group-based threshold cryptography to the lattice settings, which we demonstrate by relating it to distributed pseudorandom functions.
2021
CRYPTO
Lower bounds on lattice sieving and information set decoding
In two of the main areas of post-quantum cryptography, based on lattices and codes, nearest neighbor techniques have been used to speed up state-of-the-art cryptanalytic algorithms, and to obtain the lowest asymptotic cost estimates to date [May--Ozerov, Eurocrypt'15; Becker--Ducas--Gama--Laarhoven, SODA'16]. These upper bounds are useful for assessing the security of cryptosystems against known attacks, but to guarantee long-term security one would like to have closely matching lower bounds, showing that improvements on the algorithmic side will not drastically reduce the security in the future. As existing lower bounds from the nearest neighbor literature do not apply to the nearest neighbor problems appearing in this context, one might wonder whether further speedups to these cryptanalytic algorithms can still be found by only improving the nearest neighbor subroutines. We derive new lower bounds on the costs of solving the nearest neighbor search problems appearing in these cryptanalytic settings. For the Euclidean metric we show that for random data sets on the sphere, the locality-sensitive filtering approach of [Becker--Ducas--Gama--Laarhoven, SODA 2016] using spherical caps is optimal, and hence within a broad class of lattice sieving algorithms covering almost all approaches to date, their asymptotic time complexity of $2^{0.292d + o(d)}$ is optimal. Similar conditional optimality results apply to lattice sieving variants, such as the $2^{0.265d + o(d)}$ complexity for quantum sieving [Laarhoven, PhD thesis 2016] and previously derived complexity estimates for tuple sieving [Herold--Kirshanova--Laarhoven, PKC 2018]. For the Hamming metric we derive new lower bounds for nearest neighbor searching which almost match the best upper bounds from the literature [May--Ozerov, Eurocrypt 2015]. As a consequence we derive conditional lower bounds on decoding attacks, showing that also here one should search for improvements elsewhere to significantly undermine security estimates from the literature.
2021
CRYPTO
Non-Interactive Secure Multiparty Computation for Symmetric Functions, Revisited: More Efficient Constructions and Extensions
Non-interactive secure multiparty computation (NIMPC) is a variant of secure computation which allows each of $n$ players to send only a single message depending on his input and correlated randomness. Abelian programs, which can realize any symmetric function, are defined as functions on the sum of the players' inputs over an abelian group and provide useful functionalities for real-world applications. We improve and extend the previous results in the following ways: \begin{itemize} \item We present NIMPC protocols for abelian programs that improve the best known communication complexity. If inputs take any value of an abelian group $\mathbb{G}$, our protocol achieves the communication complexity $O(|\mathbb{G}|(\log|\mathbb{G}|)^2)$ improving $O(|\mathbb{G}|^2n^2)$ of Beimel et al. (Crypto 2014). If players are limited to inputs from subsets of size at most $d$, our protocol achieves $|\mathbb{G}|(\log|\mathbb{G}|)^2(\max\{n,d\})^{(1+o(1))t}$ where $t$ is a corruption threshold. This result improves $|\mathbb{G}|^3(nd)^{(1+o(1))t}$ of Beimel et al. (Crypto 2014), and even $|\mathbb{G}|^{\log n+O(1)}n$ of Benhamouda et al. (Crypto 2017) if $t=o(\log n)$ and $|\mathbb{G}|=n^{\Theta(1)}$. \item We propose for the first time NIMPC protocols for linear classifiers that are more efficient than those obtained from the generic construction. \item We revisit a known transformation of Benhamouda et al. (Crypto 2017) from Private Simultaneous Messages (PSM) to NIMPC, which we repeatedly use in the above results. We reveal that a sub-protocol used in the transformation does not satisfy the specified security. We also fix their protocol with only constant overhead in the communication complexity. As a byproduct, we obtain an NIMPC protocol for indicator functions with asymptotically optimal communication complexity with respect to the input length. \end{itemize}
2021
CRYPTO
Linear Cryptanalysis of FF3-1 and FEA
Improved attacks on generic small-domain Feistel ciphers with alternating round tweaks are obtained using linear cryptanalysis. This results in practical distinguishing and message-recovery attacks on the United States format-preserving encryption standard FF3-1 and the South-Korean standards FEA-1 and FEA-2. The data-complexity of the proposed attacks on FF3-1 and FEA-1 is $O(N^{r/2 - 1.5})$, where $N^2$ is the domain size and $r$ is the number of rounds. For example, FF3-1 with $N = 10^3$ can be distinguished from an ideal tweakable block cipher with advantage $\ge 1/10$ using $2^{23}$ encryption queries. Recovering the left half of a message with similar advantage requires $2^{24}$ data. The analysis of FF3-1 serves as an interesting real-world application of (generalized) linear cryptanalysis over the group $\mathbb{Z}/N\mathbb{Z}$.
2021
CRYPTO
Cryptanalysis of Full LowMC and LowMC-M with Algebraic Techniques
In this paper, we revisit the difference enumeration technique for LowMC and develop new algebraic techniques to achieve efficient key-recovery attacks. In the original difference enumeration attack framework, an inevitable step is to precompute and store a set of intermediate state differences for efficient checking via the binary search. Our first observation is that Bar-On et al.'s general algebraic technique developed for SPNs with partial nonlinear layers can be utilized to fulfill the same task, which can make the memory complexity negligible as there is no need to store a huge set of state differences any more. Benefiting from this technique, we could significantly improve the attacks on LowMC when the block size is much larger than the key size and even break LowMC with such a kind of parameter. On the other hand, with our new key-recovery technique, we could significantly improve the time to retrieve the full key if given only a single pair of input and output messages together with the difference trail that they take, which was stated as an interesting question by Rechberger et al. at ToSC 2018. Combining both techniques, with only 2 chosen plaintexts, we could break 4 rounds of LowMC adopting a full S-Box layer with block size of 129, 192 and 255 bits, respectively, which are the 3 recommended parameters for Picnic3, an alternative third-round candidate in NIST's Post-Quantum Cryptography competition. We have to emphasize that our attacks do not indicate that Picnic3 is broken as the Picnic use-case is very different and an attacker cannot even freely choose 2 plaintexts to encrypt for a concrete LowMC instance. However, such parameters are deemed as secure in the latest LowMC. Moreover, much more rounds of seven instances of the backdoor cipher LowMC-M as proposed by Peyrin and Wang in CRYPTO 2020 can be broken without finding the backdoor by making full use of the allowed $2^{64}$ data. The above mentioned attacks are all achieved with negligible memory.
2021
CRYPTO
Multi-Input Quadratic Functional Encryption from Pairings
We construct the first multi-input functional encryption (MIFE) scheme for quadratic functions from pairings. Our construction supports polynomial number of users, where user $i$, for $i \in [n]$, encrypts input $\bfx_i \in \mbZ^m$ to obtain ciphertext $\ct_i$, the key generator provides a key $\sk_\bfc$ for vector $\bfc \in \mbZ^{({mn})^2}$ and decryption, given $\ct_1,\ldots,\ct_n$ and $\sk_\bfc$, recovers $\ip{\bfc}{\bfx \otimes \bfx}$ and nothing else. We achieve indistinguishability-based (selective) security against unbounded collusions under the standard bilateral matrix Diffie-Hellman assumption. All previous MIFE schemes either support only inner products (linear functions) or rely on strong cryptographic assumptions such as indistinguishability obfuscation or multi-linear maps.
2021
CRYPTO
Deniable Fully Homomorphic Encryption from Learning With Errors
We define and construct {\it Deniable Fully Homomorphic Encryption} based on the Learning With Errors (LWE) polynomial hardness assumption. Deniable FHE enables storing encrypted data in the cloud to be processed securely without decryption, maintaining deniability of the encrypted data, as well the prevention of vote-buying in electronic voting schemes where encrypted votes can be tallied without decryption. Our constructions achieve {\it compactness} independently of the level of deniability- both the size of the public key and the size of the ciphertexts are bounded by a fixed polynomial, independent of the faking probability achieved by the scheme. This is in contrast to all previous constructions of deniable encryption schemes (even without requiring homomorphisms) which are based on polynomial hardness assumptions, originating with the seminal work of Canetti, Dwork, Naor and Ostrovsky (CRYPTO 1997) in which the ciphertext size grows with the inverse of the faking probability. Canetti {\it et al.} argued that this dependence seems inherent'', but our constructions illustrate this is not the case. We note that the Sahai-Waters (STOC13) construction of deniable encryption from indistinguishability-obfuscation achieves compactness and can be easily modified to achieve deniable FHE as well, but it requires multiple, stronger sub-exponential hardness assumptions, which are furthermore not post-quantum secure. In contrast, our constructions rely only on the LWE polynomial hardness assumption, as currently required for FHE even without deniability. The running time of our encryption algorithm depends on the inverse of the faking probability, thus the scheme falls short of achieving simultaneously compactness, negligible deniability probability {\it and} polynomial encryption time. Yet, we believe that achieving compactness is a fundamental step on the way to achieving all properties simultaneously as has been the historical journey for other primitives such as functional encryption. Interestingly, we note that our constructions support large message spaces, whereas previous constructions were bit by bit, and can be run in online-offline model of encryption, where the bulk of computation is independent of the message and may be performed in an offline pre-processing phase. The running time of the online phase, is independent of the faking probability, whereas the offline encryption run-time grows with the inverse of the faking probability. At the heart of our constructions is a new way to use bootstrapping to obliviously generate FHE ciphertexts so that it supports faking under coercion.
2021
CRYPTO
Revisiting the Security of DbHtS MACs: Beyond-Birthday-Bound in the Multi-User Setting
Double-block Hash-then-Sum (\textsf{DbHtS}) MACs are a class of MACs that aim for achieving beyond-birthday-bound security, including \textsf{SUM-ECBC}, \textsf{PMAC\_Plus}, \textsf{3kf9} and \textsf{LightMAC\_Plus}. Recently Datta et al. (FSE'19), and then Kim et al. (Eurocrypt'20) prove that \textsf{DbHtS} constructions are secure beyond the birthday bound in the single-user setting. However, by a generic reduction, their results degrade to (or even worse than) the birthday bound in the multi-user setting. In this work, we revisit the security of \textsf{DbHtS} MACs in the multi-user setting. We propose a generic framework to prove beyond-birthday-bound security for \textsf{DbHtS} constructions. We demonstrate the usability of this framework with applications to key-reduced variants of \textsf{DbHtS} MACs, including \textsf{2k-SUM-ECBC}, \textsf{2k-PMAC\_Plus} and \textsf{2k-LightMAC\_Plus}. Our results show that the security of these constructions will not degrade as the number of users grows. On the other hand, our results also indicate that these constructions are secure beyond the birthday bound in both single-user and multi-user setting without additional domain separation, which is used in the prior work to simplify the analysis. Moreover, we find a critical flaw in \textsf{2kf9}, which is proved to be secure beyond the birthday bound by Datta et al. (FSE'19). We can successfully forge a tag with probability 1 without making any queries. We go further to show attacks with birthday-bound complexity on several variants of \textsf{2kf9}.
2021
CRYPTO
Pushing the Limits of Valiant's Universal Circuits: Simpler, Tighter and More Compact
A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size $n$). Valiant provides a $k$-way recursive construction of UCs (STOC 1976), where $k$ tunes the complexity of the recursion. More concretely, Valiant gives theoretical constructions of 2-way and 4-way UCs of asymptotic (multiplicative) sizes $5n\log n$ and $4.75 n\log n$ respectively, which matches the asymptotic lower bound $\Omega(n\log n)$ up to some constant factor. Motivated by various privacy-preserving cryptographic applications, Kiss et al. (Eurocrypt 2016) validated the practicality of $2$-way universal circuits by giving example implementations for private function evaluation. G{\"{u}}nther et al. (Asiacrypt 2017) and Alhassan et al. (J. Cryptology 2020) implemented the 2-way/4-way hybrid UCs with various optimizations in place towards making universal circuits more practical. Zhao et al. (Asiacrypt 2019) optimized Valiant's 4-way UC to asymptotic size $4.5 n\log n$ and proved a lower bound $3.64 n\log n$ for UCs under the Valiant framework. As the scale of computation goes beyond 10-million-gate ($n=10^7$) or even billion-gate level ($n=10^9$), the constant factor in UCs size plays an increasingly important role in application performance. In this work, we investigate Valiant's universal circuits and present an improved framework for constructing universal circuits with the following advantages. [Simplicity.] Parameterization is no longer needed. In contrast to that previous implementations resorted to a hybrid construction combining $k=2$ and $k=4$ for a tradeoff between fine granularity and asymptotic size-efficiency, our construction gets the best of both worlds when configured at the lowest complexity (i.e., $k=2$). [Compactness.] Our universal circuits have asymptotic size $3n\log n$, improving upon the best previously known $4.5n\log n$ by 33\% and beating the $3.64n\log n$ lower bound for UCs constructed under Valiant's framework (Zhao et al., Asiacrypt 2019). [Tightness.] We show that under our new framework the UCs size is lower bounded by $2.95 n\log n$, which almost matches the $3n\log n$ circuit size of our $2$-way construction. We implement the 2-way universal circuits and evaluate its performance with other implementations, which confirms our theoretical analysis.
2021
CRYPTO
Smoothing Out Binary Linear Codes and Worst-case Sub-exponential Hardness for LPN
Learning parity with noise (LPN) is a notorious (average-case) hard problem that has been well studied in learning theory, coding theory and cryptography since the early 90's. It further inspires the Learning with Errors (LWE) problem [Regev, STOC 2005], which has become one of the central building blocks for post-quantum cryptography and advanced cryptographic. Unlike LWE whose hardness can be reducible from worst-case lattice problems, no corresponding worst-case hardness results were known for LPN until very recently. At Eurocrypt 2019, Brakerski et al. [BLVW19] established the first feasibility result that the worst-case hardness of nearest codeword problem (NCP) (on balanced linear code) at the extremely low noise rate $\frac{\log^2 n}{n}$ implies the quasi-polynomial hardness of LPN at the extremely high noise rate $1/2-1/\poly(n)$. It remained open whether a worst-case to average-case reduction can be established for standard (constant-noise) LPN, ideally with sub-exponential hardness. We start with a simple observation that the hardness of high-noise LPN over large fields is implied by that of the LWE of the same modulus, and is thus reducible from worst-case hardness of lattice problems. We then revisit [BLVW19], which is the main focus of this work. We first expand the underlying binary linear codes (of the NCP) to not only the balanced code considered in [BLVW19] but also to another code (in some sense dual to balanced code). At the core of our reduction is a new variant of smoothing lemma (for both binary codes) that circumvents the barriers (inherent in the underlying worst-case randomness extraction) and admits tradeoffs for a wider spectrum of parameter choices. In addition to the worst-case hardness result obtained in [BLVW19], we show that for any constant $0<c<1$ the constant-noise LPN problem is ($T=2^{\Omega(n^{1-c})},\epsilon=2^{-\Omega(n^{\min(c,1-c)})},q=2^{\Omega(n^{\min(c,1-c)})}$)-hard assuming that the NCP at the low-noise rate $\tau=n^{-c}$ is ($T'={2^{\Omega(\tau n)}}$, $\epsilon'={2^{-\Omega(\tau n)}}$,$m={2^{\Omega(\tau n)}}$)-hard in the worst case, where $T$, $\epsilon$, $q$ and $m$ are time complexity, success rate, sample complexity, and codeword length respectively. Moreover, refuting the worst-case hardness assumption would imply arbitrary polynomial speedups over the current state-of-the-art algorithms for solving the NCP (and LPN), which is a win-win result. Unfortunately, public-key encryptions and collision resistant hash functions need constant-noise LPN with ($T={2^{\omega(\sqrt{n})}}$, $\epsilon'={2^{-\omega(\sqrt{n})}}$,$q={2^{\sqrt{n}}}$)-hardness (Yu et al., CRYPTO 2016 \& ASIACRYPT 2019), which is almost (up to an arbitrary $\omega(1)$ factor in the exponent) what is reducible from the worst-case NCP when $c= 0.5$. We leave it as an open problem whether the gap can be closed or there is a separation in place.
2021
CRYPTO
A New Simple Technique to Bootstrap Various Lattice Zero-Knowledge Proofs to QROM Secure NIZKs
Many of the recent advanced lattice-based Sigma-/public-coin honest verifier (HVZK) interactive protocols based on the techniques developed by Lyubashevsky (Asiacrypt'09, Eurocrypt'12) can be transformed into a non-interactive zero-knowledge (NIZK) proof in the random oracle model (ROM) using the Fiat-Shamir transform. Unfortunately, although they are known to be secure in the __classical__ ROM, existing proof techniques are incapable of proving them secure in the __quantum__ ROM (QROM). Alternatively, while we could instead rely on the Unruh transform (Eurocrypt'15), the resulting QROM secure NIZK will incur a large overhead compared to the underlying interactive protocol. In this paper, we present a new simple semi-generic transform that compiles many existing lattice-based Sigma-/public-coin HVZK interactive protocols into QROM secure NIZKs. Our transform builds on a new primitive called __extractable linear homomorphic commitment__ protocol. The resulting NIZK has several appealing features: it is not only a proof of knowledge but also straight-line extractable; the proof overhead is smaller compared to the Unruh transform; it enjoys a relatively small reduction loss; and it requires minimal background on quantum computation. To illustrate the generality of our technique, we show how to transform the recent Bootle et al.'s 5-round protocol with an exact sound proof (Crypto'19) into a QROM secure NIZK by increasing the proof size by a factor of 2.6. This compares favorably to the Unruh transform that requires a factor of more than 50.
2021
CRYPTO
Subquadratic SNARGs in the Random Oracle Model
In a seminal work, Micali (FOCS 1994) gave the first succinct non-interactive argument (SNARG) in the random oracle model (ROM). The construction combines a PCP and a cryptographic commitment, and has several attractive features: it is plausibly post-quantum; it can be heuristically instantiated via lightweight cryptography; and it has a transparent (public-coin) parameter setup. However, it also has a significant drawback: a large argument size. In this work, we provide a new construction that achieves a smaller argument size. This is the first progress on the Micali construction since it was introduced over 25 years ago. A SNARG in the ROM is (t,ε)-secure if every t-query malicious prover can convince the verifier of a false statement with probability at most ε. For (t,ε)-security, the argument size of all known SNARGs in the ROM (including Micali's) is Õ((log (t/ε))^2) bits, *even* if one were to rely on conjectured probabilistic proofs well beyond current techniques. In practice, these costs lead to SNARGs that are much larger than constructions based on other (pre-quantum and costly) tools. This has led many to believe that SNARGs in the ROM are inherently quadratic. We show that this is not the case. We present a SNARG in the ROM with a sub-quadratic argument size: Õ(log (t/ε) * log t). Our construction relies on a strong soundness notion for PCPs and a weak binding notion for commitments. We hope that our work paves the way for understanding if a linear argument size, that is O(log (t/ε)), is achievable in the ROM.
2021
CRYPTO
Lattice Reduction with Approximate Enumeration Oracles: Practical Algorithms and Concrete Performance
This work provides a systematic investigation of the use of approximate enumeration oracles in BKZ, building on recent technical progress on speeding-up lattice enumeration: relaxing (the search radius of) enumeration and extended preprocessing which preprocesses in a larger rank than the enumeration rank. First, we heuristically justify that relaxing enumeration with certain extreme pruning asymptotically achieves an exponential speed-up for reaching the same root Hermite factor (RHF). Second, we perform simulations/experiments to validate this and the performance for relaxed enumeration with numerically optimised pruning for both regular and extended preprocessing. Upgrading BKZ with such approximate enumeration oracles gives rise to our main result, namely a practical and faster (compared to previous work) polynomial-space lattice reduction algorithm for reaching the same RHF in practical and cryptographic parameter ranges. We assess its concrete time/quality performance with extensive simulations and experiments. As a consequence, we update the extrapolation of the crossover rank between a square-root cost estimate for quantum enumeration using our algorithm and the Core-SVP cost estimate for quantum sieving to 547.
2021
CRYPTO
Secure Wire Shuffling in the Probing Model
In this paper we describe the first improvement of the wire shuffling countermeasure against side-channel attacks described by Ishai, Sahai and Wagner at Crypto 2003. More precisely, we show how to get worst case statistical security against t probes with running time O(t) instead of O(t log t); our construction is also much simpler. Recall that the classical masking countermeasure achieves perfect security but with running time O(t^2). We also describe a practical implementation for AES that outperforms the masking countermeasure for t ≥ 6 000.
2021
CRYPTO
SSE and SSD: Page-Efficient Searchable Symmetric Encryption
Searchable Symmetric Encryption (SSE) enables a client to outsource a database to an untrusted server, while retaining the ability to securely search the data. The performance bottleneck of classic SSE schemes typically does not come from their fast, symmetric cryptographic operations, but rather from the cost of memory accesses. To address this issue, many works in the literature have considered the notion of locality, a simple design criterion that helps capture the cost of memory accesses in traditional storage media, such as Hard Disk Drives. A common thread among many SSE schemes aiming to improve locality is that they are built on top of new memory allocation schemes, which form the technical core of the constructions. The starting observation of this work is that for newer storage media such as Solid State Drives (SSDs), which have become increasingly common, locality is not a good predictor of practical performance. Instead, SSD performance mainly depends on page efficiency, that is, reading as few pages as possible. We define this notion, and identify a simple allocation problem, Data-Independent Packing, that captures the main technical challenge required to build page-efficient SSE. As our main result, we build a page-efficient and storage-efficient data-independent packing scheme, and deduce an SSE scheme with the same properties. The technical core of the result is a new generalization of cuckoo hashing to items of variable size. Practical experiments show that this approach achieves excellent performance.
2021
CRYPTO
Two-Round Trip Schnorr Multi-Signatures via Delinearized Witnesses
We construct a two-round Schnorr-based signature scheme (DWMS) by delinearizing two pre-witnesses supplied by each signer. DWMS is a secure signature scheme in the algebraic group model (AGM) and the random oracle model (ROM) under the assumption of the hardness of the one-more discrete logarithm problem and the 2-entwined sum problem that we introduce in this paper. Our new m-entwined sum problem tweaks the k-sum problem in a scalar field using the associated group. We prove the hardness of our new problem in the AGM assuming the hardness of the discrete logarithm problem in the associated group. We believe that our new problem simplifies the security proofs of multi-signature schemes that use the delinearization of witnesses.
2021
CRYPTO
ATLAS: Efficient and Scalable MPC in the Honest Majority Setting
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%.
2021
CRYPTO
Unconditional Communication-Efficient MPC via Hall's Marriage Theorem
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.