We study the problem of batch verification for verifiable delay functions (VDFs), focusing on proofs of correct exponentiation (PoCE), which underlie recent VDF constructions. We show how to compile any PoCE into a batch PoCE, offering significant savings in both communication and verification time. Concretely, given any PoCE with communication complexity $c$, verification time $t$ and soundness error $\delta$, and any pseudorandom function with key length ${\sf k}_{\sf prf}$ and evaluation time $ t_{\sf prf}$, we construct: -- A batch PoCE for verifying $n$ instances with communication complexity $m\cdot c +{\sf k}_{\sf prf}$, verification time $m\cdot t + n\cdot m\cdot O(t_{\sf op} + t_{\sf prf})$ and soundness error $\delta + 2^{-m}$, where $\lambda$ is the security parameter, $m$ is an adjustable parameter that can take any integer value, and $t_{\sf op}$ is the time required to evaluate the group operation in the underlying group. This should be contrasted with the naive approach, in which the communication complexity and verification time are $n \cdot c$ and $n \cdot t$, respectively. The soundness of this compiler relies only on the soundness of the underlying PoCE and the existence of one-way functions. -- An improved batch PoCE based on the low order assumption. For verifying $n$ instances, the batch PoCE requires communication complexity $c +{\sf k}_{\sf prf}$ and verification time $t + n\cdot (t_{\sf prf} + \log(s)\cdot O(t_{\sf op}))$, and has soundness error $\delta + 1/s$. The parameter $s$ can take any integer value, as long as it is hard to find group elements of order less than $s$ in the underlying group. We discuss instantiations in which $s$ can be exponentially large in the security parameter $\lambda$. If the underlying PoCE is constant round and public coin (as is the case for existing protocols), then so are all of our batch PoCEs. This implies that they can be made non-interactive using the Fiat-Shamir transform. Additionally, for RSA groups with moduli which are the products of two safe primes, we show how to efficiently verify that certain elements are not of order $2$. This protocol, together with the second compiler above and any (single-instance) PoCE in these groups, yields an efficient batch PoCE in safe RSA groups. To complete the picture, we also show how to extend Pietrzak's protocol (which is statistically sound in the group $QR_N^+$ when $N$ is the product of two safe primes) to obtain a statistically-sound PoCE in safe RSA groups.

Belenios is an online voting system that provides a strong notion of election verifiability, where no single party has to be trusted, and security holds as soon as either the voting registrar or the voting server is honest. It was formally proved to be secure, making the assumption that no further ballots are cast on the bulletin board after voters verified their ballots. In practice, however, revoting is allowed and voters can verify their ballots anytime. This gap between formal proofs and use in practice leaves open space for attacks, as has been shown recently. In this paper we make two simple additions to Belenios and we formally prove that the new version satisfies the expected verifiability properties. Our proofs are automatically performed with the Tamarin prover, under the assumption that voters are allowed to vote at most four times.

Fully homomorphic encryption (FHE) enables a simple, attractive framework for secure search. Compared to other secure search systems, no costly setup procedure is necessary; it is sufficient for the client merely to upload the encrypted database to the server. Confidentiality is provided because the server works only on the encrypted query and records. While the search functionality is enabled by the full homomorphism of the encryption scheme. For this reason, researchers have been paying increasing attention to this problem. Since Akavia et al. (CCS 2018) presented a framework for secure search on FHE encrypted data and gave a working implementation called SPiRiT, several more efficient realizations have been proposed. In this paper, we identify the main bottlenecks of this framework and show how to significantly improve the performance of FHE-base secure search. In particular, 1. To retrieve $\ell$ matching items, the existing framework needs to repeat the protocol $\ell$ times sequentially. In our new framework, all matching items are retrieved in parallel in a single protocol execution. 2. The most recent work by Wren et al. (CCS 2020) requires $O(n)$ multiplications to compute the first matching index. Our solution requires no homomorphic multiplication, instead using only additions and scalar multiplications to encode all matching indices. 3. Our implementation and experiments show that to fetch 16 matching records, our system gives an 1800X speed-up over the state of the art in fetching the query results resulting in a 26X speed-up for the full search functionality.

We propose a new theoretical approach for building anonymous mixing mechanisms for cryptocurrencies. Rather than requiring a fully uniform permutation during mixing, we relax the requirement, insisting only that neighboring permutations are similarly likely. This is defined formally by borrowing from the definition of differential privacy. This relaxed privacy definition allows us to greatly reduce the amount of interaction and computation in the mixing protocol. Our construction achieves $O(n \cdot polylog(n))$ computation time for mixing $n$ addresses, whereas all other mixing schemes require $O(n^2)$ total computation across all parties. Additionally, we support a smooth tolerance of fail-stop adversaries and do not require any trusted setup. We analyze the security of our generic protocol under the UC framework, and under a stand-alone, game-based definition. We finally describe an instantiation using ring signatures and confidential transactions.

Distributed ledger are maintained through consensus protocols executed by mutually distrustful parties. However, these consensus protocols have inherent limitations thus resulting in scalability issues of the ledger. Layer-2 protocols operate on channels and allow parties to interact with another without going through the consensus protocol albeit relying on its security as fall-back. Prominent Layer-2 protocols are payment channels for Bitcoin that allow two parties to exchange coins, State Channels for Ethereum that allow two parties to execute a state machine, and Hydra heads [FC'21] for Cardano which allows multiple parties execution of Constraint Emitting Machines (CEM). Channels can be concatenated into networks using techniques such as Hashed Timelocked Contracts to execute payments or virtual state channels as introduced by Dziembowski et al. [CCS'18] to execute state machines. These constructions allow interaction between two parties across a channel network, i.e. the two endpoints of a path of channels. This is realized by utilizing intermediaries, which are the parties on the channel path which are in-between both endpoints, who have to pay collateral to ensure security of the constructions. While these approaches can be used with Hydra, they cannot be trivially extended to allow execution of CEMs between an arbitrary amount of parties across different Hydra heads. This work addresses this gap by introducing the Interhead construction that allows for the iterative creation of virtual Hydra heads. Of independent interest, our construction is the first that (1) supports channels with an arbitrary amount of parties and (2) allows for collateral to be paid by multiple intermediaries which allows to share this burden and thus improves practicality.

We advance the state-of-the art for zero-knowledge commit-and-prove SNARKs (CP-SNARKs). CP-SNARKs are an important class of SNARKs which, using commitments as ``glue'', allow to efficiently combine proof systems---e.g., general-purpose SNARKs (an efficient way to prove statements about circuits) and $\Sigma$-protocols (an efficient way to prove statements about group operations). Thus, CP-SNARKs allow to efficiently provide zero-knowledge proofs for composite statements such as $h=H(g^{x})$ for some hash-function $H$. Our main contribution is providing the first construction of CP-SNARKs where the proof size is succinct in the number of commitments. We achieve our result by providing a general technique to compile Algebraic Holographic Proofs (AHP) (an underlying abstraction used in many modern SNARKs) with special ``decomposition'' properties into an efficient CP-SNARK. We then show that some of the most efficient AHP constructions---Marlin, PLONK, and Sonic---satisfy our compilation requirements. Our resulting SNARKs achieve universal and updatable reference strings, which are highly desirable features as they greatly reduce the trust needed in the SNARK setup phase.

This work leverages on the framework of Karakostas et al. (SCN'20) by extending it to the realm of reputation and trust. At the best of our knowledge, it is the first to introduce reputation and trust to proof of stake systems. Namely, we show that their delegation framework can be repurposed to construct a trust layer over a proof of stake consensus protocol in addition to its original stake delegation application. Furthermore, we show that such extension yields a concrete reputation system satisfying the positive results of (1) Asharov et al. (Asiacrypt'13), therefore allowing the secure execution of multiparty protocols such as GMW (STOC' 87) and Damgard and Ishai (Crypto'05), and (2) Kleinrock et al. (Indocrypt'20), therefore allowing the construction of Reputation-fair Lottery and therefore Proof of Reputation. More concretely, our devised layer is used to construct a concrete reputation system based on arbitrary stake distribution. In this layer groups of users can freely ``assign their respective trust'' to members of a set of trustees, i.e., participants that offered themselves as receivers of such assignment. Furthermore, our work offers the advantage of providing a clear stake based criteria, verifiable in the ledger, and, therefore, naturally resistant to sybil attack, that the set of trustees indeed yields an honest majority. This setting provides a better situation than a simple assumption of honest majority, since it involves stake in a decentralized ledger, and the public verifiability of the reputation score via verification of the stake distribution.

We construct a concretely efficient Zero Knowledge (ZK) Oblivious RAM (ORAM) that consumes $2 \log n$ oblivious transfers (OTs) of length-$2\sigma$ secrets per access of an arithmetic value, for statistical security parameter $\sigma$ and array size $n$. This is an asymptotic and concrete improvement over previous best (concretely efficient) ZK ORAM Bub- bleRAM of Heath and Kolesnikov ([HK20a], CCS 2020), whose access cost is $1/2 \log^2 n$ OTs of length-$2\sigma$ secrets. ZK ORAM is essential for proving statements that are best expressed as RAM programs, rather than Boolean or arithmetic circuits. Our construction is private-coin ZK. We integrate it with [HK20a]’s ZK Proof (ZKP) protocol and prove the resulting ZKP system secure. We implemented PrORAM in C++. Compared to the state-of-the-art BubbleRAM, our PrORAM is $~10\times$ faster for arrays of size $2^{20}$ of $40$-bit values.

This paper presents HashWires, a hash-based range proof protocol that is applicable in settings for which there is a trusted third party (typically a credential issuer) that can generate commitments. We refer to these as "credential-based" range proofs (CBRPs). HashWires improves upon hashchain solutions that are typically restricted to micro-payments for small interval ranges, achieving an exponential speedup in proof generation and verification time. In terms of proof size and computational cost, we show that HashWires compares favorably against Bulletproofs for both 32- and 64-bit numeric values. Although CBRPs are inherently less flexible than general zero-knowledge range proofs, we provide a number of applications in which a credential issuer can leverage HashWires to provide range proofs for private values, without having to rely on heavyweight cryptographic tools and assumptions.

We propose a Dynamic Universal Accumulator in the Accumulator Manager setting for bilinear groups which extends Nguyen's positive accumulator and Au et al. and Damgård and Triandopoulos non-membership proof mechanism. The new features include support for batch addition and deletion operations as well as a privacy-friendly decentralized batch witness update protocol, where the witness update information is the same for all users. Together with a non-interactive zero-knowledge protocol, these make the proposed scheme suitable as an efficient and scalable Anonymous Credential System, accessible even by low-resource users. We show security of the proposed protocol in the Generic Group Model under a (new) generalized version of the t-SDH assumption and we demonstrate its practical relevance by providing and discussing an implementation realized using state-of-the-art libraries.

Zero-knowledge (ZK) proofs with an optimal memory footprint have attracted a lot of attention, because such protocols can easily prove very large computation with a small memory requirement. Such ZK protocol only needs O(M) memory for both parties, where M is the memory required to verify the statement in the clear. In this paper, we propose several new ZK protocols in this setting, which improve the concrete efficiency and, at the same time, enable sublinear amortized communication for circuits with some notion of relaxed uniformity. 1. In the circuit-based model, where the computation is represented as a circuit over a field, our ZK protocol achieves a communication complexity of 1 field element per non-linear gate for any field size while keeping the computation very cheap. We implemented our protocol, which shows extremely high efficiency and affordability. Compared to the previous best-known implementation, we achieve 6×–7× improvement in computation and 3×– 7× improvement in communication. When running on intro-level AWS instances, our protocol only needs one US dollar to prove one trillion AND gates (or 2.5 US dollars for one trillion multiplication gates over a 61-bit field). 2. In the setting where part of the computation can be represented as a set of polynomials, we can achieve communication sublinear to the polynomial size: the communication only depends on the input size and the highest degree of all polynomials, independent of the number of polynomials and the number of multiplications in the polynomials. Using the improved ZK protocol, we can prove matrix multiplication with communication proportional to the input size, rather than the number of multiplications. Proving the multiplication of two 1024 × 1024 matrices, our implementation, with one thread and 1 GB of memory, only needs 10 seconds and communicates 25 MB, 35× faster than the state-of-the-art protocol Virgo that would need more than 140 GB of memory for the same task.

Fair exchange protocols let two mutually distrusted parties exchange digital data in a way that neither can cheat. At CCS 2017, Campanelli et al. proposed two blockchain-based protocols for the fair exchange of digital coins and a certain service, i.e., “proofs of retrievability” (PoR), that take place between a buyer and seller. In this work, we identify two serious issues of these schemes; namely, (1) a malicious client can waste the seller’s resources, and (2) real-time leakage of information to non-participants in the exchange. To rectify the issues, we propose “recurring contingent PoR payment” (RC-PoR-P). It lets the fair exchange reoccur while ensuring that the seller’s resources are not wasted, and the parties’ privacy is preserved. We implemented the RC- PoR-P. Our cost analysis indicates that the RC-PoR-P is efficient. The RC-PoR-P is the first of its kind that offers all the above features.

Threshold Signatures allow n parties to share the power of issuing digital signatures so that any coalition of size at least (t+1) can sign, whereas groups of t or less players cannot. Over the last few years many schemes addressed the question of realizing efficient threshold variants for the specific case of EC-DSA signatures. In this paper we present new solutions to the problem that aim at reducing the overall bandwidth consumption. Our main contribution is a new variant of the Gennaro and Goldfeder protocol from ACM CCS 2018 that avoids all the required range proofs, while retaining provable security against malicious adver- saries in the dishonest majority setting. Our experiments show that – for all levels of security – our signing protocol reduces the bandwidth consumption of best previously known secure protocols for factors varying between 4.4 and 9, while key generation is consistently two times less expensive. Furthermore compared to these same protocols, our signature generation is faster for 192-bits of security and beyond.

Authenticated Key Exchange (AKE) protocols, by definition, guarantee both session key secrecy and entity authentication. Informally, session key secrecy means that only the legitimate parties learn the established key and mutual authentication means that one party can assure itself the session key is actually established with the other party. Today, an important application area for AKE is Internet of Things (IoT) systems, where an IoT device runs the protocol to establish a session key with a remote server. In this paper, we identify two additional security requirements for IoT-oriented AKE, namely Key Compromise Impersonation (KCI) resilience and Server Compromise Impersonation (SCI) resilience. These properties provide an additional layer of security when the IoT device and the server get compromised respectively. Inspired by Chan et al.'s bigdata-based unilateral authentication protocol, we propose a novel AKE protocol which achieves mutual authentication, session key secrecy (including perfect forward secrecy), and the above two resilience properties. To demonstrate its practicality, we implement our protocol and show that one execution costs about 15.19 ms (or, 84.73 ms) for the IoT device and 2.44 ms (or, 12.51 ms) for the server for security parameter λ =128 (or, λ =256). We finally propose an enhanced protocol to reduce the computational complexity on the end of IoT by outsourcing an exponentiation computation to the server. By instantiating the signature scheme with NIST's round three alternate candidate Picnic, we show that one protocol execution costs about 14.44 ms (or, 58.45 ms) for the IoT device and 12.78 ms (or, 46.34 ms) for the server for security parameter λ =128 (or, λ =256).

We introduce the concept of turn-based communication channel between two mutually distrustful parties with communication consistency, i.e. both parties have the same message history, and happens in sets of exchanged messages across a limited number of turns. Our construction leverages on timed primitives. Namely, we introduce a novel Delta-delay hash function definition in order to establish turns in the channel. Concretely, we introduce the one-way turn-based communication scheme and the two-way turn-based communication protocol and provide a concrete instantiation that achieves communication consistency.

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.

Standard hybrid encryption schemes based on the KEM-DEM framework are hard to implement efficiently in a distributed manner whilst maintaining the CCA security property of the scheme. This is because the DEM needs to be decrypted under the key encapsulated by the KEM, before the whole ciphertext is declared valid. In this paper we present a new variant of the KEM-DEM framework, closely related to Tag-KEMs, which sidesteps this issue. We then present a post-quantum KEM for this framework based on Learning-with-Rounding, which is designed specifically to have fast distributed decryption. Our combined construction of a hybrid encryption scheme with Learning-with-Rounding based KEM, called Gladius, is closely related to the NIST Round 3 candidate called Saber. Finally, we give a prototype distributed implementation that achieves a decapsulation time of 4.99 seconds for three parties.

Payment Channel Networks (PCNs) have given a huge boost to the scalability of blockchain-based cryptocurrencies: Beyond improving the transaction rate, PCNs enabled cheap cross-currency payments and atomic swaps. However, current PCNs proposals either heavily rely on special scripting features of the underlying blockchain (e.g. Hash Time Lock Contracts) or are tailored to a handful of digital signature schemes, such as Schnorr or ECDSA signatures. This leaves us in an unsatisfactory situation where many currencies that are being actively developed and use different signature schemes cannot enjoy the benefits of a PCN. In this work, we investigate whether we can construct PCNs assuming the minimal ability of a blockchain to verify a digital signature, for any signature scheme. In answering this question in the affirmative, we introduce the notion of lockable signatures, which constitutes the cornerstone of our PCN protocols. Our approach is generic and the PCN protocol is compatible with any digital signature scheme, thus inheriting all favorable properties of the underlying scheme that are not offered by Schnorr/ECDSA (e.g.\ aggregatable signatures or post-quantum security). While the usage of generic cryptographic machinery makes our generic protocol impractical, we view it as an important feasibility result as it may serve as the basis for constructing optimized protocols for specific signature schemes. To substantiate this claim, we design a highly efficient PCN protocol for the special case of Boneh-Lynn-Shacham (BLS) signatures. BLS signatures enjoy many unique features that make it a viable candidate for a blockchain, e.g. short, unique, and aggregatable signatures. Yet, prior to our work, no PCN was known to be compatible with it (without requiring an advanced scripting language). The cost of our PCN is dominated by a handful of calls to the BLS algorithms. Our concrete evaluation of these basic operations shows that users with commodity hardware can process payments with minimal overhead.

Individual verifiability remains one of the main practical challenges in e-voting systems and, despite the central importance of this property, countries that sought to implement it faced repeated security problems. In this note, we revisit this property in the context of the IVXV version of the Estonian voting system, which has been in used for the Estonian municipal elections of 2017 and for the Estonian and European parliamentary elections of 2019. We show that a compromised voter device can defeat the individual verifiability mechanism of the current Estonian voting system. Our attack takes advantage of the revoting option that is available in the Estonian voting system, and only requires compromise of the voting client application: it does not require compromising the mobile device verification app, or any server side component.

In this paper, we present a concretely efficient protocol for private set intersection (PSI) in the multi-party setting using oblivious pseudorandom function (OPRF). In fact, we generalize the approach used in the work of Chase and Miao [CRYPTO 2020] towards deploying a lightweight multi-point OPRF construction for two-party PSI. Our protocol only includes oblivious transfer (OT) extension and garbled Bloom filter as its main ingredients and avoids computationally expensive operations. From a communication pattern perspective, the protocol consists of two types of interactions. The first type is performed over a star-like communication graph in which one designated party interacts with all other parties via performing OTs as the sender. Besides, parties communicate through a path-like communication graph that involves sending a garbled Bloom filter from the first party to its neighboring party following the last one. This design makes our protocol to be highly scalable due to the independence of each party's complexity from the number of participating parties and thus causes a communication and computation complexities of $O(n\lambda k)$, where $n$ is the set size, $k$ is the number of hash functions, and $\lambda$ is the security parameter. Moreover, the asymptotic complexity of the designated party is $O(tn\lambda)$ which linearly scales with the number of parties $t$. We prove security of the proposed protocol against semi-honest adversaries.

We present Zerojoin, a privacy-enhancing protocol for UTXO blockchains. Like Zerocoin, our protocol uses zero-knowledge proofs and a pool of participants. However, unlike Zerocoin, our pool size is not monotonically increasing. Thus, our protocol overcomes the major drawback of Zerocoin. Our approach can also be considered a non-interactive variant of CoinJoin, where the interaction is replaced by a public transaction on the blockchain. The security of Zerojoin relies on the Decisional-Diffie-Hellman (DDH) assumption. We also present ErgoMix, a practical implementation of Zerojoin on top of Ergo, a smart contract platform based on Sigma protocols. While Zerojoin contains the key ideas, it leaves open the practical issue of handling fees. The key contribution of ErgoMix is a novel approach to handle fees in Zerojoin.

There has been recent exciting progress on building non-interactive non-malleable commitments from judicious assumptions. All proposed approaches proceed in two steps. First, obtain simple "base'' commitment schemes for very small tag/identity spaces based on a various sub-exponential hardness assumptions. Next, assuming sub-exponential non-interactive witness indistinguishable proofs (NIWIs), and variants of keyless collision resistant hash functions, construct non-interactive compilers that convert tag-based non-malleable commitments for a small tag space into tag-based non-malleable commitments for a larger tag space. We propose the first black-box construction of non-interactive non-malleable commitments. Our key technical contribution is a novel way of implementing the non-interactive proof of consistency required by the tag amplification process. Prior to our work, the only known approach to tag amplification without setup and with black-box use of the base scheme (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) added multiple rounds of interaction. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA (chosen commitment attack) security. In addition to being black-box, our approach dispenses with the need for sub-exponential NIWIs, that was common to all prior work. Instead of NIWIs, we rely on sub-exponential hinting PRGs which can be obtained based on a broad set of assumptions such as sub-exponential CDH or LWE.

It is well known that several cryptographic primitives cannot be achieved without a common reference string (CRS). Those include, for instance, non-interactive zero-knowledge for NP, or maliciously secure computation in fewer than four rounds. The security of those primitives heavily relies upon on the assumption that the trusted authority, who generates the CRS, does not misuse the randomness used in the CRS generation. However, we argue that there is no such thing as an unconditionally trusted authority and every authority must be held accountable for any trust to be well-founded. Indeed, a malicious authority can, for instance, recover private inputs of honest parties given transcripts of the protocols executed with respect to the CRS it has generated. While eliminating trust in the trusted authority may not be entirely feasible, can we at least move towards achieving some notion of accountability? We propose a new notion in which, if the CRS authority releases the private inputs of protocol executions to others, we can then provide a publicly-verifiable proof that certifies that the authority misbehaved. We study the feasibility of this notion in the context of non-interactive zero knowledge and two-round secure two-party computation.

In this short note we consider the scheme to share a bitstring secret among $n$ parties such that any $m$ of them, cooperating, can reconstruct it, but any $m - 1$ of them cannot (a so-called $(m,n)$-threshold scheme). The scheme is based on the sound ranging problem, which is to determine the unknown position of the source and the unknown instant when it emitted the sound from known instants when the sound wave reached known sensors. The features are 1) shadows are computed not so much by the secret dealer, but rather by environment where the sound propagates, so the amount of computations performed by the dealer is $O(1)$ instead of $O(n)$ as $n \rightarrow \infty$, and 2) the dealer does not need to establish separate secure channel with each party. There are severe inherent drawbacks though.

The Messaging Layer Security (MLS) project is an IETF effort aiming to establish an industry- wide standard for secure group messaging (SGM). Its development is supported by several major secure-messaging providers (with a combined user base in the billions) and a growing body of academic research. MLS has evolved over many iterations to become a complex, non-trivial, yet relatively ad-hoc cryptographic protocol. In an effort to tame its complexity and build confidence in its security, past analyses of MLS have restricted themselves to sub-protocols of MLS—most prominently a type of sub-protocol embodying so-called continuous group key agreement (CGKA). However, to date the task of proving or even defining the security of the full MLS protocol has been left open. In this work, we fill in this missing piece. First, we formally capture the security of SGM protocols by defining a corresponding security game, which is parametrized by a safety predicate that characterizes the exact level of security achieved by a construction. Then, we cast MLS as an SGM protocol, showing how to modularly build it from the following three main components (and some additional standard cryptographic primitives) in a black-box fashion: (a) CGKA, (b) forward-secure group AEAD (FS-GAEAD), which is a new primitive and roughly corresponds to an “epoch” of group messaging, and (c) a so-called PRF-PRNG, which is a two-input hash function that is a pseudorandom function (resp. generator with input) in its first (resp. second) input. Crucially, the security predicate for the SGM security of MLS can be expressed purely as a function of the security predicates of the underlying primitives, which allows to swap out any of the components and immediately obtain a security statement for the resulting SGM construction. Furthermore, we provide instantiations of all component primitives, in particular of CGKA with MLS’s TreeKEM sub-protocol (which we prove adaptively secure) and of FS-GAEAD with a novel construction (which has already been adopted by MLS). Along the way we introduce a collection of new techniques, primitives, and results with applications to other SGM protocols and beyond. For example, we extend the Generalized Selective Decryption proof technique (which is central in CGKA literature) and prove adaptive security for another (practical) more secure CGKA protocol called RTreeKEM (Alwen et al., CRYPTO ’20). The modularity of our approach immediately yields a corollary characterizing the security of an SGM construction using RTreeKEM.

Proof of reserves protocols enable cryptocurrency exchanges to prove solvency, i.e. prove that they have enough reserves to meet their liabilities towards their customers. MProve (EuroS&PW, 2019) was the first proof of reserves protocol for Monero which provided some privacy to the exchanges’ addresses. As the key images and the addresses are inherently linked in the MProve proof, an observer could easily recognize the exchange-owned address when a transaction spending from it appears on the blockchain. This is detrimental for an exchange’s privacy and becomes a natural reason for exchanges to not adopt MProve. To this end, we propose MProve+, a Bulletproofs- based (S&P, 2018) NIZK protocol, which unlinks the key images and the addresses, thus alleviating the drawback of MProve. Furthermore, MProve+ presents a promising alternative to MProve due to an order of magnitude smaller proof sizes along with practical proof generation and verification times.

The BeleniosVS electronic voting scheme offers an attractive mix of verifiability and privacy properties. Moreover, using the ProVerif protocol-verification tool, BeleniosVS has automatic machine-aided analysis of (end-to-end) verifiability in 96 different threat models with the machine-aided analysis finding proofs in 22 cases and finding attacks in the remaining 74 cases. The high number of threat models covered by ProVerif delivers a much richer security analysis than the norm. We revisit the BeleniosVS scheme and propose several refinements to the ProVerif security model and scheme which increase the number of threat models in which the scheme has verifiability from 22 to 28. Our new ProVerif security model also implies end-to-end verifiability but the requirements are easier to satisfy. Interestingly, in all six improvements, both the changes to the security model and one or more changes to the scheme are necessary to prove verifiability.

We construct a simple public-coin zero-knowledge proof system solely based on symmetric primitives, from which we can apply the Fiat-Shamir heuristic to make it non-interactive. Our construction can be regarded as a simplified cut-and-choose-based malicious secure twoparty computation for the zero-knowledge functionality. Our protocol is suitable for pedagogical purpose for its simplicity (code is only 728 lines).

The increasing adoption of machine learning inference in applications has led to a corresponding increase in concerns surrounding the privacy guarantees offered by existing mechanisms for inference. Such concerns have motivated the construction of efficient secure inference protocols that allow parties to perform inference without revealing their sensitive information. Recently, there has been a proliferation of such proposals, rapidly improving efficiency. However, most of these protocols assume that the client is semi-honest, that is, the client does not deviate from the protocol; yet in practice, clients are many, have varying incentives, and can behave arbitrarily. To demonstrate that a malicious client can completely break the security of semi-honest protocols, we first develop a new model-extraction attack against many state-of-the-art secure inference protocols. Our attack enables a malicious client to learn model weights with 22x-312x fewer queries than the best black-box model-extraction attack and scales to much deeper networks. Motivated by the severity of our attack, we design and implement MUSE, an efficient two-party secure inference protocol resilient to malicious clients. MUSE introduces a novel cryptographic protocol for conditional disclosure of secrets to switch between authenticated additive secret shares and garbled circuit labels, and an improved Beaver's triple generation procedure which is 8x-12.5x faster than existing techniques. These protocols allow MUSE to push a majority of its cryptographic overhead into a preprocessing phase: compared to the equivalent semi-honest protocol (which is close to state-of-the-art), MUSE's online phase is only 1.7x-2.2x slower and uses 1.4x more communication. Overall, MUSE is 13.4x-21x faster and uses 2x-3.6x less communication than existing secure inference protocols which defend against malicious clients.

We introduce Checkable Subspace Sampling Arguments, a new information theoretic interactive proof system in which the prover shows that a vector has been sampled in a subspace according to the verifier's coins. We show that this primitive provides a unifying view that explains the technical core of most of the constructions of universal and updatable pairing-based (zk)SNARKs. This characterization is extended to a fully algebraic framework for designing such SNARKs in a modular way. We propose new constructions of CSS arguments that lead to SNARKs with different performance trade-offs. Our most efficient construction, Basilisk, seems to have the smallest proof size in the literature, although it pays a price in terms of structure reference string for the number of multiplicative gates whose fan-out exceeds a certain bound.

We propose and evaluate a secure-multiparty-computation (MPC) solution in the semi-honest model with dishonest majority that is based on multiparty homomorphic encryption (MHE). To support our solution, we introduce a multiparty version of the Brakerski-Fan-Vercauteren homomorphic cryptosystem and implement it in an open-source library. MHE-based MPC solutions have several advantages: Their transcript is public, their offline phase is compact, and their circuit-evaluation procedure is non-interactive. By exploiting these properties, the communication complexity of MPC tasks is reduced from quadratic to linear in the number of parties, thus enabling secure computation among potentially thousands of parties and in a broad variety of computing paradigms, from the traditional peer-to-peer setting to cloud-outsourcing and smart-contract technologies. MHE-based approaches can also outperform the state-of-the-art solutions, even for a small number of parties. We demonstrate this for three circuits: private input selection with application to private-information retrieval, component-wise vector multiplication with application to private-set intersection, and Beaver multiplication triples generation. For the first circuit, privately selecting one input among eight thousand parties' (of 32 KB each) requires only 1.31 MB of communication per party and completes in 61.7 seconds. For the second circuit with eight parties, our approach is 8.6 times faster and requires 39.3 times less communication than the current methods. For the third circuit and ten parties, our approach generates 20 times more triples per second while requiring 136 times less communication per-triple than an approach based on oblivious transfer. We implemented our scheme in the Lattigo library and open-sourced the code at https://github.com/ldsec/lattigo.

We present the first homomorphic secret sharing (HSS) construction that simultaneously (1) has negligible correctness error, (2) supports integers from an exponentially large range, and (3) relies on an assumption not known to imply FHE --- specifically, the Decisional Composite Residuosity (DCR) assumption. This resolves an open question posed by Boyle, Gilboa, and Ishai (Crypto 2016). Homomorphic secret sharing is analogous to fully-homomorphic encryption, except the ciphertexts are shared across two non-colluding evaluators. Previous constructions of HSS either had non-negligible correctness error and polynomial-size plaintext space or were based on the stronger LWE assumption. We also present two applications of our technique: a multi-server ORAM with constant bandwidth overhead, and a rate-1 trapdoor hash function with negligible error rate.

Polynomial commitment schemes (PCS) have recently been in the spotlight for their key role in building SNARKs. A PCS provides the ability to commit to a polynomial over a finite field and prove its evaluation at points. A succinct PCS has commitment and evaluation proof size sublinear in the degree of the polynomial. An efficient PCS has sublinear proof verification. Any efficient and succinct PCS can be used to construct a SNARK with similar security and efficiency characteristics (in the random oracle model). Proof-carrying data (PCD) enables a set of parties to carry out an indefinitely long distributed computation where every step along the way is accompanied by a proof of correctness. It generalizes incrementally verifiable computation and can even be used to construct SNARKs. Until recently, however, the only known method for constructing PCD required expensive SNARK recursion. A system called Halo first demonstrated a new methodology for building PCD without SNARKs, exploiting an aggregation property of the Bulletproofs inner-product argument. The construction was heuristic because it makes non-black-box use of a concrete instantiation of the Fiat-Shamir transform. We expand upon this methodology to show that PCD can be (heuristically) built from any homomorphic polynomial commitment scheme (PCS), even if the PCS evaluation proofs are neither succinct nor efficient. In fact, the Halo methodology extends to any PCS that has an even more general property, namely the ability to aggregate linear combinations of commitments into a new succinct commitment that can later be opened to this linear combination. Our results thus imply new constructions of SNARKs and PCD that were not previously described in the literature and serve as a blueprint for future constructions as well.

Schnorr's signature scheme permits an elegant threshold signing protocol due to its linear signing equation. However each new signature consumes fresh randomness, which can be a major attack vector in practice. Sources of randomness in deployments are frequently either unreliable, or require state continuity, i.e. reliable fresh state resilient to rollbacks. State continuity is a notoriously difficult guarantee to achieve in practice, due to system crashes caused by software errors, malicious actors, or power supply interruptions (Parno et al., S&P '11). This is a non-issue for Schnorr variants such as EdDSA, which is specified to derive nonces deterministically as a function of the message and the secret key. However, it is challenging to translate these benefits to the threshold setting, specifically to construct a threshold Schnorr scheme where signing neither requires parties to consume fresh randomness nor update long-term secret state. In this work, we construct a dishonest majority threshold Schnorr protocol that enables such stateless deterministic nonce derivation using standardized block ciphers. Our core technical ingredients are new tools for the zero-knowledge from garbled circuits (ZKGC) paradigm to aid in verifying correct nonce derivation: - A mechanism based on UC Commitments that allows a prover to commit once to a witness, and prove an unbounded number of statements online with only cheap symmetric key operations. - A garbling gadget to translate intermediate garbled circuit wire labels to arithmetic encodings. Our scheme prioritizes computation cost, with each proof requiring only a small constant number of exponentiations.

In the last decades, several signcryption schemes have been proposed for different privacy-enhancing purposes. In this paper, we propose a new privacy-enhancing group signcryption scheme that provides: unforgeability, confidentiality, ciphertext and sender anonymity, traceability, unlinkability, exculpability, coalition-resistance, and unforgeable tracing verification. It is important to notice that the proposed scheme allows a signer to anonymously signcryt a message on the group's behalf (i.e., sender's anonymity). Security analysis of the scheme is also provided. Our proposal is proven to be strongly existentially unforgeable under an adaptive chosen message attack, indistinguishable under an adaptive chosen ciphertext attack, and to provide ciphertext anonymity under an adaptive chosen ciphertext attack. Furthermore, the scheme is extended to work in a multi-receiver scenario, where an authorized group of receivers is able to unsigncrypt the ciphertext. The experimental results show that our scheme is efficient even on computationally restricted devices and can be therefore used in many IoT applications. Signcrypt protocol on smart cards takes less than 1~s (including communication overhead). The time of Unsigncrypt protocol on current ARM devices is negligible (less than 40 ms).

We construct the first constant-round protocols for secure quantum computation in the two-party (2PQC) and multi-party (MPQC) settings with security against malicious adversaries. Our protocols are in the common random string (CRS) model. - Assuming two-message oblivious transfer (OT), we obtain (i) three-message 2PQC, and (ii) five-round MPQC with only three rounds of online (input-dependent) communication; such OT is known from quantum-hard Learning with Errors (QLWE). - Assuming sub-exponential hardness of QLWE, we obtain (i) three-round 2PQC with two online rounds and (ii) four-round MPQC with two online rounds. - When only one (out of two) parties receives output, we achieve minimal interaction (two messages) from two-message OT; classically, such protocols are known as non-interactive secure computation (NISC), and our result constitutes the first maliciously-secure quantum NISC. Additionally assuming reusable malicious designated-verifier NIZK arguments for NP (MDV-NIZKs), we give the first MDV-NIZK for QMA that only requires one copy of the quantum witness. Finally, we perform a preliminary investigation into two-round secure quantum computation where each party must obtain output. On the negative side, we identify a broad class of simulation strategies that suffice for classical two-round secure computation that are unlikely to work in the quantum setting. Next, as a proof-of-concept, we show that two-round secure quantum computation exists with respect to a quantum oracle.

We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Crépeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT.

In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field $\mathbb{F}$ and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over $\mathbb{F}_{p}$ to a secret sharing ``in the exponent'' can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves. We include the following practical applications originating from our framework: First we show how to securely realize the Pointcheval-Sanders signature scheme (CT-RSA 2016) in MPC. Second we present a construction for dynamic proactive secret-sharing which outperforms the current state of the art from CCS 2019. Third we present a construction for MPC input certification using digital signatures that we show experimentally to outperform the previous best solution in this area.

In this work we introduce a novel four-party honest-majority MPC protocol with active security that achieves comparable efficiency to equivalent protocols in the same setting, while having a much simpler design and not relying on function-dependent preprocessing. Our initial protocol satisfies security with abort, but we present some extensions to achieve guaranteed output delivery. Unlike previous works, we do not achieve this by delegating the computation to one single party that is identified to be honest, which is likely to hinder the adoption of these technologies as it centralizes sensitive data. Instead, our novel approach guarantees termination of the protocol while ensuring that no single party (honest or corrupt) learns anything beyond the output. We implement our four-party protocol with abort in the MP-SPDZ framework for multiparty computation and benchmark multiple applications like MNIST classification training and ImageNet inference. Our results show that our four-party protocol performs similarly to an efficient honest-majority three-party protocol that only provides semi-honest/passive security, which suggest that adding a fourth party can be an effective method to achieve active security without harming performance.

Time-based primitives like time-lock puzzles (TLP) are finding widespread use in practical protocols, partially due to the surge of interest in the blockchain space where TLPs and related primitives are perceived to solve many problems. Unfortunately, the security claims are often shaky or plainly wrong since these primitives are used under composition. One reason is that TLPs are inherently not UC secure and time is tricky to model and use in the UC model. On the other hand, just specifying standalone notions of the intended task, left alone correctly using standalone notions like non-malleable TLPs only, might be hard or impossible for the given task. And even when possible a standalone secure primitive is harder to apply securely in practice afterwards as its behavior under composition is unclear. The ideal solution would be a model of TLPs in the UC framework to allow simple modular proofs. In this paper we provide a foundation for proving composable security of practical protocols using time-lock puzzles and related timed primitives in the UC model. We construct UC-secure TLPs based on random oracles and show that using random oracles is necessary. In order to prove security, we provide a simple and abstract way to reason about time in UC protocols. Finally, we demonstrate the usefulness of this foundation by constructing applications that are interesting in their own right, such as UC-secure two-party computation with output-independent abort.

We construct the first efficient MPC protocol that only requires black-box access to a non-commutative ring $R$. Previous results in the same setting were efficient only either for a constant number of corruptions or when computing branching programs and formulas. Our techniques are based on a generalization of Shamir's secret sharing to non-commutative rings, which we derive from the work on Reed Solomon codes by Quintin, Barbier and Chabot (IEEE Transactions on Information Theory, 2013). When the center of the ring contains a set $A = \{\alpha_0, \ldots, \alpha_n\}$ such that $\forall i \neq j, \alpha_i - \alpha_j \in R^*$, the resulting secret sharing scheme is strongly multiplicative and we can generalize existing constructions over finite fields without much trouble. Most of our work is devoted to the case where the elements of $A$ do not commute with all of $R$, but they just commute with each other. For such rings, the secret sharing scheme cannot be linear ``on both sides" and furthermore it is not multiplicative. Nevertheless, we are still able to build MPC protocols with a concretely efficient online phase and black-box access to $R$. As an example we consider the ring $\mathcal{M}_{m\times m}(\mathbb{Z}/2^k\mathbb{Z})$, for which when $m > \log(n+1)$, we obtain protocols that require around $\lceil\log(n+1)\rceil/2$ less communication and $2\lceil\log(n+1)\rceil$ less computation than the state of the art protocol based on Circuit Amortization Friendly Encodings (Dalskov, Lee and Soria-Vazquez, ASIACRYPT 2020). In this setting with a ``less commutative" $A$, our black-box preprocessing phase has a less practical complexity of $\poly(n)$. Due to this, we additionally provide specialized, concretely efficient preprocessing protocols for $R = \mathcal{M}_{m\times m}(\mathbb{Z}/2^k\mathbb{Z})$ that exploit the structure of the matrix ring.

Payment is an essential part of e-commerce. Merchants usually rely on third-parties, so-called payment processors, who take care of transferring the payment from the customer to the merchant. How a payment processor interacts with the customer and the merchant varies a lot. Each payment processor typically invents its own protocol that has to be integrated into the merchant’s application and provides the user with a new, potentially unknown and confusing user experience. Pushed by major companies, including Apple, Google, Mastercard, and Visa, the W3C is currently developing a new set of standards to unify the online checkout process and “streamline the user’s payment experience”. The main idea is to integrate payment as a native functionality into web browsers, referred to as the Web Payment APIs. While this new checkout process will indeed be simple and convenient from an end-user perspective, the technical realization requires rather significant changes to browsers. Many major browsers, such as Chrome, Firefox, Edge, Safari, and Opera, already implement these new standards, and many payment processors, such as Google Pay, Apple Pay, or Stripe, support the use of Web Payment APIs for payments. The ecosystem is constantly growing, meaning that the Web Payment APIs will likely be used by millions of people worldwide. So far, there has been no in-depth security analysis of these new standards. In this paper, we present the first such analysis of the Web Payment APIs standards, a rigorous formal analysis. It is based on the Web Infrastructure Model (WIM), the most comprehensive model of the web infrastructure to date, which, among others, we extend to integrate the new payment functionality into the generic browser model. Our analysis reveals two new critical vulnerabilities that allow a malicious merchant to over-charge an unsuspecting customer. We have verified our attacks using the Chrome implementation and reported these problems to the W3C as well as the Chrome developers, who have acknowledged these problems. Moreover, we propose fixes to the standard, which by now have been adopted by the W3C and Chrome, and prove that the fixed Web Payment APIs indeed satisfy strong security properties.

A Multi-Client Functional Encryption (MCFE) scheme for set intersection is a cryptographic primitive that enables an evaluator to learn the intersection from all sets of a pre-determined number of clients, without need to learn the plaintext set of each individual client. In this paper, we propose a flexible version of the MCFE schemes for the set intersection, called Flexible Multi-Client Functional Encryption for Set Intersection (FMCFE). In our FMCFE scheme, the evaluator can learn the intersection from any flexible choice of sets (instead of all sets). In this regard, we redefine syntax and security notions of the MCFE schemes for the FMCFE schemes. In the literature, solving multi-client set intersection problem in polynomial time, such that only the intersection result is revealed (without additional information), is an open problem. In this paper, we propose a relaxed solution using FMCFE schemes to solve secure set intersection in polynomial time. We analyze that for practical use of secure multi-client set intersection, this relaxation is necessary. We also show that our scheme has the adaptive indistinguishability-based security under passive corruption. Our proof relies on the Symmetric eXternal Diffie-Hellman (SXDH) assumption in the standard model.

Private Set Intersection protocols (PSIs) allow parties to compute the intersection of their private sets, such that nothing about the sets’ elements beyond the intersection is revealed. PSIs have a variety of applications, primarily in efficiently supporting data sharing in a privacy-preserving manner. At Eurocrypt 2019, Ghosh and Nilges pro- posed three efficient PSIs based on the polynomial representation of sets and proved their security against active adversaries. In this work, we show that these three PSIs are susceptible to several serious attacks. The attacks let an adversary (1) learn the correct intersection while making its victim believe that the intersection is empty, (2) learn a certain element of its victim’s set beyond the intersection, and (3) delete multiple elements of its victim’s input set. We explain why the proofs did not identify these attacks and propose a set of mitigations

This paper presents Checklist, a system for private blocklist lookups. In Checklist, a client can determine whether a particular string appears on a server-held blocklist of strings, without leaking its string to the server. Checklist is the first blocklist-lookup system that (1) leaks no information about the client's string to the server, (2) does not require the client to store the blocklist in its entirety, and (3) allows the server to respond to the client's query in time sublinear in the blocklist size. To make this possible, we construct a new two-server private-information-retrieval protocol that is both asymptotically and concretely faster, in terms of server-side time, than those of prior work. We evaluate Checklist in the context of Google's “Safe Browsing” blocklist, which all major browsers use to prevent web clients from visiting malware-hosting URLs. Today, lookups to this blocklist leak partial hashes of a subset of clients' visited URLs to Google's servers. We have modified Firefox to perform Safe-Browsing blocklist lookups via Checklist servers, which eliminates the leakage of partial URL hashes from the Firefox client to the blocklist servers. This privacy gain comes at the cost of increasing communication by a factor of 3.3×, and the server-side compute costs by 9.8×. Checklist reduces end-to-end server-side costs by 6.7×, compared to what would be possible with prior state-of-the-art two-server private information retrieval.

In this work, we examine the efficiency of protocols for secure evaluation of basic mathematical functions ($\mathtt{sqrt}, \mathtt{sin}, \mathtt{arcsin}$, amongst others), essential to various application domains. e.g., Artificial Intelligence. Furthermore, we have incorporated our code in state-of-the-art Multiparty Computation (MPC) software, so we can focus on the algorithms to be used as opposed to the underlying MPC system. We make use of practical approaches that, although, some of them, theoretically can be regarded as less efficient, can, nonetheless, be implemented in such software libraries without further adaptation. We focus on basic scientific operations, and introduce a series of data-oblivious protocols based on fixed point representation techniques. Our protocols do not reveal intermediate values and do not need special adaptations from the underlying MPC protocols. We include extensive computational experimentation under various settings and MPC protocols.

We introduce MatRiCT+, a practical private blockchain payment protocol based on ``post-quantum'' lattice assumptions. MatRiCT+ builds on MatRiCT due to Esgin et al. (ACM CCS'19) and, in general, follows the Ring Confidential Transactions (RingCT) approach used in Monero, the largest privacy-preserving cryptocurrency. In terms of the practical aspects, MatRiCT+ has 2-18x shorter proofs (depending on the number of input accounts, M) and runs 3-11x faster (for a typical transaction) in comparison to MatRiCT. A significant advantage of MatRiCT+ is that the proof length's dependence on M is very minimal (only O(log M)), while MatRiCT has a proof length linear in M. To support its efficiency, we devise several novel techniques in our design of MatRiCT+ to achieve compact lattice-based zero-knowledge proof systems, exploiting the algebraic properties of power-of-2 cyclotomic rings commonly used in practical lattice-based cryptography. Along the way, we design a family of ``optimal'' challenge spaces, using a technique we call partition-and-sample, with minimal $\ell_1$-norm and invertible challenge differences (with overwhelming probability), while supporting highly-splitting power-of-2 cyclotomic rings. We believe all these results to be widely applicable and of independent interest.

Existing models for non-interactive MPC cannot provide full privacy for inputs, because they inherently leak the residual function (i.e., the output of the function on the honest parties’ input together with all possible values of the adversarial inputs). For example, in any non-interactive sealed-bid auction, the last bidder can figure out what was the highest previous bid. We present a new MPC model which avoids this privacy leak. To achieve this, we utilize a blockchain in a novel way, incorporating smart contracts and arbitrary parties that can be incentivized to perform computation (“bounty hunters,” akin to miners). Security is maintained under a monetary assumption about the parties: an honest party can temporarily supply a recoverable collateral of value higher than the computational cost an adversary can expend. We thus construct non-interactive MPC protocols with strong security guarantees (full security, no residual leakage) in the short term. Over time, as the adversary can invest more and more computational resources, the security guarantee decays. Thus, our model, which we call Gage MPC, is suitable for secure computation with limited-time secrecy, such as auctions. A key ingredient in our protocols is a primitive we call “Gage Time Capsules” (GaTC): a time capsule that allows a party to commit to a value that others are able to reveal but only at a designated computational cost. A GaTC allows a party to commit to a value together with a monetary collateral. If the original party properly opens the GaTC, it can recover the collateral. Otherwise, the collateral is used to incentivize bounty hunters to open the GaTC. This primitive is used to ensure completion of Gage MPC protocols on the desired inputs. As a requisite tool (of independent interest), we present a generalization of garbled circuit that are more robust: they can tolerate exposure of extra input labels. This is in contrast to Yao’s garbled circuits, whose secrecy breaks down if even a single extra label is exposed. Finally, we present a proof-of-concept implementation of a special case of our construction, yielding an auction functionality over an Ethereum-like blockchain.

The TLS 1.3 session resumption handshakes enables a client and a server to resume a previous connection via a shared secret, which was established during a previous session. In practice, this is often done via session tickets, where the server provides a "self-encrypted" ticket containing the shared secret to its clients. A client may resume its session by sending the ticket to the server, which allows the server to retrieve the shared secret stored within the ticket. Usually, a ticket is only accepted by the server that issued the ticket. However, in practice, servers that share the same hostname, often share the same key material for ticket encryption. The concept of a server accepting a ticket, which was issued by a different server, is known as session resumption across hostnames (SRAH). In 2020, Sy et al. showed in an empirical analysis that, by using SRAH, the time to load a webpage can be reduced by up to 31% when visiting the page for the very first time. Despite its performance advantages, the TLS 1.3 specification currently discourages the use of SRAH. In this work, we formally investigate which security guarantees can be achieved when using SRAH. To this end, we provide the first formalization of SRAH and analyze its security in the multi-stage key exchange model (Dowling et al.; JoC 2021), which proved useful in previous analyses of TLS handshakes. We find that an adversary can break authentication if clients do not specify the intended receiver of their first protocol message. However, if the intended receiver is specified by the client, we prove that SRAH is secure in the multi-stage key exchange model.

Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice. We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called Mac'n'Cheese, with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of $m$ statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in $m$). These disjunctions can further be nested, allowing efficient proofs about complex statements with many levels of disjunctions. We also show how to make Mac'n'Cheese non-interactive (after a preprocessing phase) using the Fiat-Shamir transform, and with only a small degradation in soundness. We have implemented the online phase of Mac'n'Cheese and achieve a runtime of 144 ns per AND gate and 1.5 $\mu$s per multiplication gate in $\mathbb{F}_{2^{61}-1}$ when run over a network with a 95 ms latency and a bandwidth of 31.5 Mbps. In addition, we show that the disjunction optimization improves communication as expected: when proving a boolean circuit with eight branches and each branch containing roughly 1 billion multiplications, Mac'n'Cheese requires only 75 more bytes to communicate than in the single branch case.

We propose a framework for building Nakamoto-style proof-of-work blockchains where blocks are treated differently in the ``longest chain rule''. The crucial parameter is a weight function assigning different weights to blocks according to their hash value. Our framework enables the analysis of different weight functions while proving all statements at the appropriate level of abstraction. This allows us to quickly derive protocol guarantees for different weight functions. We exemplify the usefulness of our framework by capturing the classical Bitcoin protocol as well as exponentially growing functions as special cases. We show the typical properties---chain growth, chain quality and common prefix---for both, and further show that the latter provide an additional guarantee, namely a weak form of optimistic responsiveness. More precisely, we prove for a certain class of exponentially growing weight functions that in periods without corruption, the confirmation time only depends on the unknown actual network delay instead of the known upper bound.

While the practicality of secure multi-party computation (MPC) has been extensively analyzed and improved over the past decade, we are hitting the limits of efficiency with the traditional approaches of representing the computed functionalities as generic arithmetic or Boolean circuits. This work follows the design principle of identifying and constructing fast and provably-secure MPC protocols to evaluate useful high-level algebraic abstractions; thus, improving the efficiency of all applications relying on them. We present Polymath, a constant-round secure computation protocol suite for the secure evaluation of (multi-variate) polynomials of scalars and matrices, functionalities essential to numerous data-processing applications. Using precise natural precomputation and high-degree of parallelism prevalent in the modern computing environments, Polymath can make latency of secure polynomial evaluations of scalars and matrices independent of polynomial degree and matrix dimensions. We implement our protocols over the HoneyBadgerMPC library and apply them to two prominent secure computation tasks: privacy-preserving evaluation of decision trees and privacy-preserving evaluation of Markov processes. For the decision tree evaluation problem, we demonstrate the feasibility of evaluating high-depth decision tree models in a general n-party setting. For the Markov process application, we demonstrate that Polymath can compute large powers of transition matrices with better online time and less communication.

BUG REPORT: In early 2021 we were made aware of a bug in Lemma 9.1 by Carmit Hazay, Muthu Venkitasubramaniam, Laasya Bangalore, and Rishabh Bhadauria. The bug does not have an easy fix and we are currently exploring whether a different proof can be found. Until then the results of this paper should not be considered proven and in particular the protocols should not be considered secure. We will later either update the e-print version with a new proof or withdraw the paper. ORIGINAL ABSTRACT: In this work we consider the problem of oblivious linear function evaluation (OLE). OLE is a special case of oblivious polynomial evaluation (OPE) and deals with the oblivious evaluation of a linear function $f(x)=ax+b$. This problem is non-trivial in the sense that the sender chooses $a,b$ and the receiver $x$, but the receiver may only learn $f(x)$. We present a highly efficient and UC-secure construction of OLE in the OT-hybrid model that requires only $O(1)$ OTs per OLE. The construction is based on noisy encodings introduced by Naor and Pinkas (STOC'99). Our main technical contribution solves a problem left open in their work, namely we show in a generic way how to achieve full simulation-based security from noisy encodings. All previous constructions using noisy encodings achieve only passive security. Our result requires novel techniques that might be of independent interest. Using our highly efficient OLE as a black box, we obtain a direct construction of an OPE protocol that simultaneously achieves UC-security and requires only $O(d)$ OTs, where $d$ is the degree of the polynomial that shall be evaluated.

An indistinguishability obfuscator is a probabilistic polynomial-time algorithm that takes a circuit as input and outputs a new circuit that has the same functionality as the input circuit, such that for any two circuits of the same size that compute the same function, the outputs of the indistinguishability obfuscator are indistinguishable. Here, we study schemes for indistinguishability obfuscation for quantum circuits. We present two definitions for indistinguishability obfuscation: in our first definition (qiO) the outputs of the obfuscator are required to be indistinguishable if the input circuits are perfectly equivalent, while in our second definition (qiOD), the outputs are required to be indistinguishable as long as the input circuits are approximately equivalent with respect to a pseudo-distance D. Our main results provide (1) a computationally-secure scheme for qiO where the size of the output of the obfuscator is exponential in the number of non-Clifford (T gates), which means that the construction is efficient as long as the number of T gates is logarithmic in the circuit size and (2)a statistically-secure qiOD, for circuits that are close to the kth level of the Gottesman-Chuang hierarchy (with respect to D); this construction is efficient as long as k is small and fixed.

Smart contracts present a uniform approach for deploying distributed computation and have become a popular means to develop security critical applications. A major barrier to adoption for many applications is the public nature of existing systems, such as Ethereum. Several systems satisfying various definitions of privacy and requiring various trust assumptions have been proposed; however, none achieved the universality and uniformity that Ethereum achieved for non-private contracts: One unified method to construct most contracts. We provide a unified security model for private smart contracts which is based on the Universal Composition (UC) model and propose a novel core protocol, Kachina, for deploying privacy-preserving smart contracts, which encompasses previous systems. We demonstrate the Kachina method of smart contract development, using it to construct a contract that implements privacy-preserving payments, along the lines of Zerocash, which is provably secure in the UC setting and facilitates concurrency.

In this work, we show how to garble arithmetic circuits with full active security in the general multiparty setting, secure in the full-threshold setting (that is, when only one party is assumed honest). Our solution allows interfacing Boolean garbled circuits with arithmetic garbled circuits. Previous works in the arithmetic circuit domain focused on the 2-party setting, or on semi-honest security and assuming an honest majority -- notably, the work of Ben-Efraim (Asiacrypt 2018) in the semi-honest, honest majority security model, which we adapt and extend. As an additional contribution, we improve on Ben-Efraim's selector gate. A selector gate is a gate that given two arithmetic inputs and one binary input, outputs one of the arithmetic inputs, based on the value of the selection bit input. Our new construction for the selector gate reduces the communication cost to almost half of that of Ben-Efraim's gate. This result applies both to the semi-honest and to the active security model.

Searchable symmetric encryption (SSE) enables clients to search encrypted data. Curtmola et al. (ACM CCS 2006) formalized a model and security notions of SSE and proposed two concrete constructions called SSE-1 and SSE-2. After the seminal work by Curtmola et al., SSE becomes an active area of encrypted search. In this paper, we focus on two unnoticed problems in the seminal paper by Curtmola et al. First, we show that SSE-2 does not appropriately implement Curtmola et al.'s construction idea for dummy addition. We refine SSE-2's (and its variants') dummy-adding procedure to keep the number of dummies sufficiently many but as small as possible. We then show how to extend it to the dynamic setting while keeping the dummy-adding procedure work well and implement our scheme to show its practical efficiency. Second, we point out that the SSE-1 can cause a search error when a searched keyword is not contained in any document file stored at a server and show how to fix it.

In this work we introduce a new (circuit-dependent) homomorphic secret sharing (HSS) scheme for any $\log/\log\log$-local circuit, with communication proportional only to the width of the circuit and polynomial computation, which is secure assuming the super-polynomial hardness of learning parity with noise (LPN). At the heart of our new construction is a pseudorandom correlation generator (PCG) which allows two parties to locally stretch short seeds into pseudorandom instances of an arbitrary $\log/\log\log$-local additive correlation. Our main application, and the motivation behind this work, is a generic two-party secure computation protocol for every layered (boolean or arithmetic) circuit of size $s$ with total communication $O(s/\log\log s)$ and polynomial computation, assuming the super-polynomial hardness of the standard learning parity with noise assumption (a circuit is layered if its nodes can be partitioned in layers, such that any wire connects adjacent layers). This expands the set of assumptions under which the `circuit-size barrier' can be broken, for a large class of circuits. The strength of the underlying assumption is tied to the sublinearity factor: we achieve communication $O(s/k(s))$ under the $s^{2^{k(s)}}$-hardness of LPN, for any $k(s) \leq (\log\log s) / 4$. Previously, the set of assumptions known to imply a PCG for correlations of degree $\omega(1)$ or generic secure computation protocols with sublinear communication was restricted to LWE, DDH, and a circularly secure variant of DCR.

This work concerns secure protocols in the massively parallel computation (MPC) model, which is one of the most widely-accepted models for capturing the challenges of writing protocols for the types of parallel computing clusters which have become commonplace today (MapReduce, Hadoop, Spark, etc.). Recently, the work of Chan et al. (ITCS '20) initiated this study, giving a way to compile any MPC protocol into a secure one in the common random string model, achieving the standard secure multi-party computation definition of security with up to 1/3 of the parties being corrupt. We are interested in achieving security for much more than 1/3 corruptions. To that end, we give two compilers for MPC protocols, which assume a simple public-key infrastructure, and achieve semi-honest security for all-but-one corruptions. Our first compiler assumes hardness of the learning-with-errors (LWE) problem, and works for any MPC protocol with ``short'' output---that is, where the output of the protocol can fit into the storage space of one machine, for instance protocols that output a trained machine learning model. Our second compiler works for any MPC protocol (even ones with a long output, such as sorting) but assumes, in addition to LWE, indistinguishability obfuscation and a circular secure variant of threshold FHE. Both protocols allow the attacker to choose corrupted parties based on the trusted setup, an improvement over Chan et al., whose protocol requires that the CRS is chosen independently of the attacker's choices.

Direct Anonymous Attestation (DAA) is an anonymous signature scheme, which allows the Trusted Platform Module (TPM), a small chip embedded in a host computer, to attest to the state of the host system, while preserving the privacy of the user. DAA provides two signature modes: fully anonymous signatures and pseudonymous signatures. One main goal of designing DAA schemes is to reduce the TPM signing workload as much as possible, as the TPM has only limited resources. In an optimal DAA scheme, the signing workload on the TPM will be no more than that required for a normal signature like ECSchnorr. To date, no scheme has achieved the optimal signing efficiency for both signature modes. In this paper, we propose the first DAA scheme which achieves the optimal TPM signing efficiency for both signature modes. In this scheme, the TPM takes only a single exponentiation to generate a signature, and this single exponentiation can be pre-computed. Our scheme can be implemented using the existing TPM 2.0 commands, and thus is compatible with the TPM 2.0 specification. We benchmarked the TPM 2.0 commands needed for three DAA use cases on an Infineon TPM 2.0 chip, and also implemented the host signing and verification algorithm for our scheme on a laptop with 1.80GHz Intel Core i7-8550U CPU. Our experimental results show that our DAA scheme obtains a total signing time of about 144 ms for either of two signature modes (compared to an online signing time of about 65 ms). Based on our benchmark results for the pseudonymous signature mode, our scheme is roughly 2x (resp., 5x) faster than the existing DAA schemes supported by TPM 2.0 in terms of total (resp., online) signing efficiency. In addition, our DAA scheme supports selective attribute disclosure, which can satisfy more application require- ments. We also extend our DAA scheme to support signature-based revocation and to guarantee privacy against subverted TPMs. The two extended DAA schemes keep the TPM signing efficiency optimal for both of two signa- ture modes, and outperform existing related schemes in terms of signing performance.

Oblivious Transfer (OT) is a fundamental primitive in cryptography, supporting protocols such as Multi-Party Computation and Private Set Intersection (PSI), that are used in applications like contact discovery, remote diagnosis and contact tracing. Due to its fundamental nature, it is utterly important that its execution is secure even if arbitrarily composed with other instances of the same, or other protocols. This property can be guaranteed by proving its security under the Universal Composability model. Herein, a 3-round Random Oblivious Transfer (ROT) protocol is proposed, which achieves high computational efficiency, in the Random Oracle Model. The security of the protocol is based on the Ring Learning With Errors assumption (for which no quantum solver is known). ROT is the basis for OT extensions and, thus, achieves wide applicability, without the overhead of compiling ROTs from OTs. Finally, the protocol is implemented in a server-class Intel processor and four application-class ARM processors, all with different architectures. The usage of vector instructions provides on average a 40% speedup. The implementation shows that our proposal is at least one order of magnitude faster than the state-of-the-art, and is suitable for a wide range of applications in embedded systems, IoT, desktop, and servers. From a memory footprint perspective, there is a small increase (16%) when compared to the state-of-the-art. This increase is marginal and should not prevent the usage of the proposed protocol in a multitude of devices. In sum, the proposal achieves up to 37k ROTs/s in an Intel server-class processor and up to 5k ROTs/s in an ARM application-class processor. A PSI application, using the proposed ROT, is up to 6.6 times faster than related art.

A succinct functional commitment (SFC) scheme for a circuit class $\mathbf{CC}$ enables, for any circuit $\mathcal{C} \in \mathbf{CC}$, the committer to first succinctly commit to a vector $\vec{\alpha}$, and later succinctly open the commitment to $\mathcal{C} (\vec{\alpha}, \vec{\beta})$, where the verifier chooses $\vec{\beta}$ at the time of opening. Unfortunately, SFC commitment schemes are known only for severely limited function classes like the class of inner products. By making non-black-box use of SNARK-construction techniques, we propose an SFC scheme for the large class of semi-sparse polynomials. The new SFC scheme can be used to, say, efficiently (1) implement sparse polynomials, and (2) aggregate various interesting SFC (e.g., vector commitment and polynomial commitment) schemes. The new scheme is evaluation-binding under a new instantiation of the computational uber-assumption. We provide a thorough analysis of the new assumption.

Dijk et al. presents Remote Attestation (RA) for secure processor technology which is secure in the presence of an All Digital State Observing (ADSO) adversary. The scheme uses a combination of hardware security primitives and design principles together with a new cryptographic primitive called a Public Key Session based One-Time Signature Scheme with Secret Key Exposure (OTS-SKE). Dijk et al. show a hash based realization of OTS-SKE which is post quantum secure but suffers long $8.704$ KB signatures for 128-bit quantum security or 256-bit classical security. From a classical cryptographic perspective we complete the picture by introducing a bilinear map based OTS-SKE with short $0.125$ KB signatures, $65$ times shorter, and for which the security reduces to the Computational Diffie-Hellman Problem (CDHP) -- at the cost of a $9\times$ longer initialization phase in the RA scheme if implemented in software (this can be improved with appropriate elliptic curve hardware acceleration). Signing takes 560 ms at most $60\%$ of the $>936$ ms needed for the hash based scheme.

Roughly four decades ago, Taher ElGamal put forward what is today one of the most widely known and best understood public key encryption schemes. ElGamal encryption has been used in many different contexts, chiefly among them by the OpenPGP standard. Despite its simplicity, or perhaps because of it, in reality there is a large degree of ambiguity on several key aspects of the cipher. Each library in the OpenPGP ecosystem seems to have implemented a slightly different "flavour" of ElGamal encryption. While --taken in isolation-- each implementation may be secure, we reveal that in the interoperable world of OpenPGP, unforeseen cross-configuration attacks become possible. Concretely, we propose different such attacks and show their practical efficacy by recovering plaintexts and even secret keys.

In response to ongoing discussions about data usage by companies and governments, and its implications for privacy, there is a growing demand for secure communication techniques. While during their advent, most messenger apps focused on features rather than security, this has changed in the recent years: Since then, many have adapted end-to-end encryption as a standard feature. One of the most popular solutions is the Signal messenger, which aims to guarantee forward secrecy (i.e. security of previous communications in case of leakage of long-term secrets) and future secrecy (i.e. security of future communications in case of leakage of short-term secrets). If every user uses exactly one device, it is known that Signal achieves forward secrecy and even post-compromise security (i.e. security of future communications in case of leakage of long-term secrets). But the Signal protocol also allows for the use of multiple devices via the Sesame protocol. This multi-device setting is typically ignored in the security analysis of Signal. In this work, we discuss the security of the Signal messenger in this multi-device setting. We show that the current implementation of the device registration allows an attacker to register an own, malicious device, which gives them unrestricted access to all future communication of their victim, and even allows full impersonation. This directly shows that the current Signal implementation does not guarantee post-compromise security. We discuss several countermeasures, both simple ones aiming to increase detectability of our attack, as well as a broader approach that seeks to solve the root issue, namely the weak device registration flow.

Programmers are used to the rounding and error properties of IEEE double precision arithmetic, however in secure computing paradigms, such as provided by Multi-Party Computation (MPC), usually a different form of approximation is provided for real number arithmetic. We compare the two standard variants using for LSSS-based MPC, with an implementation of IEEE compliant double precision using binary circuit-based MPC. We compare the relative performance, and conclude that the addition cost of IEEE compliance maybe too great for some applications. Thus in the secure domain standards bodies may wish to examine a different form of real number approximations.

Symmetric Searchable Encryption (SSE) allows users to outsource encrypted data to a possibly untrusted remote location while simultaneously being able to perform keyword search directly through the stored ciphertexts. An ideal SSE scheme should reveal no information about the content of the encrypted information nor about the searched keywords and their mapping to the stored files. However, most of the existing SSE schemes fail to fulfill this property since in every search query, some information potentially valuable to a malicious adversary is leaked. The leakage becomes even bigger if the underlying SSE scheme is dynamic. In this paper, we minimize the leaked information by proposing a forward and backward private SSE scheme in a multi-client setting. Our construction achieves optimal search and update costs. In contrast to many recent works, each search query only requires one round of interaction between a user and the cloud service provider. In order to guarantee the security and privacy of the scheme and support the multi-client model (i.e. synchronization between users), we exploit the functionality offered by AMD's Secure Encrypted Virtualization (SEV).

Apple's file-sharing service AirDrop leaks phone numbers and email addresses by exchanging vulnerable hash values of the user's own contact identifiers during the authentication handshake with nearby devices. In a paper presented at USENIX Security'21, we theoretically describe two attacks to exploit these vulnerabilities and propose "PrivateDrop" as a privacy-preserving drop-in replacement for Apple's AirDrop protocol based on private set intersection. In this demo, we show how these vulnerabilities are efficiently exploitable via Wi-Fi and physical proximity to a target. Privacy and security implications include the possibility of conducting advanced spear phishing attacks or deploying multiple "collector" devices in order to build databases that map contact identifiers to specific locations. For our proof-of-concept, we leverage a custom rainbow table construction to reverse SHA-256 hashes of phone numbers in a matter of milliseconds. We discuss the trade-off between success rate and storage requirements of the rainbow table and, after following responsible disclosure with Apple, we publish our proof-of-concept implementation as "AirCollect" on GitHub.

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are $\delta$-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are $\delta$-close to the property. In particular, no set in the collection has roughly half of its members $\delta$-close to the property and the others $\delta$-far from it. We show that the collection of affine spaces displays a proximity gap with respect to Reed--Solomon (RS) codes, even over small fields, of size polynomial in the dimension of the code, and the gap applies to any $\delta$ smaller than the Johnson/Guruswami-Sudan list-decoding bound of the RS code. We also show near-optimal gap results, over fields of (at least) linear size in the RS code dimension, for $\delta$ smaller than the unique decoding radius. Concretely, if $\delta$ is smaller than half the minimal distance of an RS code $V\subset {\mathbb F}_q^n$, every affine space is either entirely $\delta$-close to the code, or alternatively at most an $(n/q)$-fraction of it is $\delta$-close to the code. Finally, we discuss several applications of our proximity gap results to distributed storage, multi-party cryptographic protocols, and concretely efficient proof systems. We prove the proximity gap results by analyzing the execution of classical algebraic decoding algorithms for Reed--Solomon codes (due to Berlekamp-Welch and Guruswami-Sudan) on a formal element of an affine space. This involves working with Reed-Solomon codes whose base field is an (infinite) rational function field. Our proofs are obtained by developing an extension (to function fields) of a strategy of Arora and Sudan for analyzing low-degree tests.

Reducing interaction in Multiparty Computation (MPC) is a highly desirable goal in cryptography. It is known that 2-round MPC can be based on the minimal assumption of 2-round Oblivious Transfer (OT) [Benhamouda and Lin, Garg and Srinivasan, EC 2018], and 1-round MPC is impossible in general. In this work, we propose a natural ``hybrid'' model, called \textbf{multiparty reusable Non-Interactive Secure Computation Market (mrNISC)}. In this model, parties publish encodings of their private inputs $x_i$ at the beginning, once and for all. Later, any subset $I$ of them can compute \emph{on-the-fly} a function $f$ on their inputs $\vec x_I = {\{x_i\}}_{i \in I}$ by just sending a single message to a stateless evaluator, conveying the result $f(\vec x_I)$ and nothing else. Importantly, the input encodings can be \emph{reused} in any number of on-the-fly computations, and the same classical simulation security guaranteed by multi-round MPC, is achieved. In short, mrNISC has minimal yet ``tractable'' interaction pattern. We initiate the study of mrNISC on several fronts. First, we formalize the security of mrNISC protocols in both a UC definition and a game-based definition. Second, we construct mrNISC protocols in the plain model with semi-honest and semi-malicious security based on bilinear groups. Third, we demonstrate the power of mrNISC by showing two applications: non-interactive MPC (NIMPC) with reusable setup and a distributed version of program obfuscation. In addition, at the core of our construction of mrNISC is a witness encryption scheme for a special language that verifies Non-Interactive Zero-Knowledge (NIZK) proofs of the validity of computations over committed values, which we believe is of independent interest.

Modern secure messaging protocols can offer strong security guarantees such as Post-Compromise Security (PCS), which enables participants to heal after compromise. The core PCS mechanism in protocols like Signal is designed for pairwise communication, making it inefficient for large groups, while recently proposed designs for secure group messaging, ART, IETF's MLS Draft-11/TreeKEM, use group keys derived from tree structures to efficiently provide PCS to large groups. Until now, research on PCS designs only considered healing behaviour within a single group. In this work we provide the first analysis of the healing behaviour when a user participates in multiple groups. Our analysis reveals that the currently proposed protocols based on group keys, such as ART and TreeKEM/MLS Draft-11, provide significantly weaker PCS guarantees than group protocols based on pairwise PCS channels. In fact, we show that if new users can be created dynamically, ART, TreeKEM, and MLS Draft-11 never fully heal authentication. We map the design space of healing mechanisms, analyzing security and overhead of possible solutions. This leads us to a promising solution based on (i) global updates that affect all current and future groups, and (ii) post-compromise secure signatures. Our solution allows group messaging protocols such ART and MLS to achieve substantially stronger PCS guarantees. We provide a security definition for post-compromise secure signatures and an instantiation.

Expanding graphs are known due to their remarkable applications to Computer Science. We are looking for their applications to Post Quantum Cryptography. One of them is postquantum analog of Diffie-Hellman protocol in the area of intersection of Noncommutative and Multivariate Cryptographies .This graph based protocol allows correspondents to elaborate collision cubic transformations of affine space Kn defined over finite commutative ring K. Security of this protocol rests on the complexity of decomposition problem of nonlinear polynomial map into given generators. We show that expanding graphs allow to use such output as a ‘’seed’’ for secure construction of infinite sequence of cubic transformation of affine spaces of increasing dimension. Correspondents can use the sequence of maps for extracting passwords for one time pads in alphabet K and other symmetric or asymmetric algorithms. We show that cubic polynomial maps of affine spaces of prescribed dimension can be used for transition of quadratic public keys of Multivariate Cryptography into the shadow of private areas.

Secure Multiparty Computation (MPC) is an invaluable tool for training machine learning models when the training data cannot be directly accessed by the model trainer. Unfortunately, complex algorithms, such as deep learning models, have their computational complexities increased by orders of magnitude when performed using MPC protocols. In this contribution, we study how to efficiently train an important class of machine learning problems by using MPC where features are known by one of the computing parties and only the labels are private. We propose new protocols combining differential privacy (DP) and MPC in order to privately and efficiently train a deep learning model in such scenario. More specifically, we release differentially private information during the MPC computation to dramatically reduce the training time. All released information does not compromise the privacy of the labels at the individual level. Our protocols can have running times that are orders of magnitude better than a straightforward use of MPC at a moderate cost in model accuracy.

The idea of smart contracts has been around for a long time. The introduction of Ethereum has taken the concept of smart contracts to new heights because of its integration with Blockchain technology. As a result, the applications of smart contracts have also surged in areas such as e-Voting, Insurance, Crowdfunding, etc. In this paper, we aim to present the construction of a “Fully Anonymous e-Voting” protocol using the concepts of zkHawk and Zcash. zkHawk is a novel smart contract protocol designed during this Ph.D. that improves upon the Hawk protocol by solving the underlying anonymity problem of a trusted manager. We will leverage the concept of zk-SNARKs in Zcash to carry out the voting phase of the election and the zkHawk smart contract protocol to tally the results of the election. The voting phase employing Zcash will be initially designed with Non-Universal zk-SNARKs and improved upon with Universal zk-SNARKs.

The Signal protocol is used in many messaging applications today. While it is an active research topic to design a post-quantum variant of the protocol, no such variant is currently realized in the real world. In the following document we describe a hybrid version of the Signal protocol, that will be implemented to achieve post-quantum security for Tutanota’s end-to-end encrypted e-mails.

OPAQUE [Jarecki et al., Eurocrypt 2018] is an asymmetric password authenticated key exchange (aPAKE) protocol that is being developed as an Internet standard and for use within TLS 1.3. OPAQUE combines an Oblivious PRF (OPRF) with an authenticated key exchange to provide strong security properties, including security against pre-computation attacks (called saPAKE security). However, the security of OPAQUE relies crucially on the security of the OPRF. If the latter breaks (by cryptanalysis, quantum attacks or security compromise), the user's password is exposed to an offline dictionary attack. To address this weakness, we present KHAPE, a variant of OPAQUE that does not require the use of an OPRF to achieve aPAKE security, resulting in improved resilience and near-optimal computational performance. An OPRF can be optionally added to KHAPE, for enhanced saPAKE security, but without opening the password to an offline dictionary attack upon OPRF compromise. In addition to resilience to OPRF compromise, a DH-based implementation of KHAPE (using HMQV) offers the best performance among aPAKE protocols in terms of exponentiations with less than the cost of an exponentiation on top of an UNauthenticated Diffie-Hellman exchange. KHAPE uses three messages if the server initiates the exchange or four when the client does (one more than OPAQUE in the latter case). All results in the paper are proven within the UC framework in the ideal cipher model. Of independent interest is our treatment of key-hiding AKE which KHAPE uses as a main component as well as our UC proofs of AKE security for protocols 3DH (a basis of Signal), HMQV and SKEME, that we use as efficient instantiations of KHAPE.

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 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.

Secure computation enables two or more parties to jointly evaluate a function without revealing to each other their private input. G-module is an abelian group M, where the group G acts compatibly with the abelian group structure on M. In this work, we present several secure computation protocols for G-module operations in the online/offline mode. We then show how to instantiate those protocols to implement many widely used secure computation primitives in privacy-preserving machine learning and data mining, such as oblivious cyclic shift, one-round shared OT, oblivious permutation, oblivious shuffle, secure comparison, oblivious selection, DReLU, and ReLU, etc. All the proposed protocols are constant-round, and they are 2X - 10X more efficient than the-state-of-the-art constant-round protocols in terms of communication complexity.

A recent result by Dulek et al. (EUROCRYPT 2020) showed a secure protocol for computing any quantum circuit even without the presence of an honest majority. Their protocol, however, is susceptible to a ``denial of service'' attack and allows even a single corrupted party to force an abort. We propose the first quantum protocol that admits security-with-identifiable-abort, which allows the honest parties to agree on the identity of a corrupted party in case of an abort. Additionally, our protocol is the first to have the property that the number of rounds where quantum communication is required is independent of the circuit complexity. Furthermore, if there exists a post-quantum secure classical protocol whose round complexity is independent of the circuit complexity, then our protocol has this property as well. Our protocol is secure under the assumption that classical quantum-resistant fully homomorphic encryption schemes with decryption circuit of logarithmic depth exist. Interestingly, our construction also admits a reduction from quantum fair secure computation to classical fair secure computation.

With the development of side-channel attacks, a necessity arises to invent authenticated key exchange protocols in a leakage-resilient manner. Constructing authenticated key exchange protocols using existing cryptographic schemes is an effective method, as such construction can be instantiated with any appropriate scheme in a way that the formal security argument remains valid. In parallel, constructing authenticated key exchange protocols that are proven to be secure in the standard model is more preferred as they rely on real-world assumptions. In this paper, we present a Diffie-Hellman-style construction of a leakage-resilient authenticated key exchange protocol, that can be instantiated with any CCLA2-secure public-key encryption scheme and a function from the pseudo-random function family. Our protocol is proven to be secure in the standard model assuming the hardness of the decisional Diffie-Hellman problem. Furthermore, it is resilient to continuous partial leakage of long-term secret keys, that happens even after the session key is established, while satisfying the security features defined by the eCK security model.

Post-quantum cryptography (PQC) is nowadays a very active research field [1]. We follow a non-standard way to achieve it, taking any common protocol and replacing arithmetic with GF(2^8) field operations, a procedure defined as R-Propping [2-7]. The resulting protocol security relies on the intractability of a generalized discrete log problem, combined with the power sets of algebraic ring extension tensors and resilience to quantum and algebraic attacks. Oblivious Transfer (OT) is a keystone for Secure Multiparty Computing (SMPC) [8], one of the most pursued cryptographic areas. It is a critical issue to develop a fast OT solution because of its intensive use in many protocols. Here, we adopt the simple OT protocol developed by Chou and Orlandi [9] as the base model to be propped. Our solution is fully scalable to achieve quantum and classical security levels as needed. We present a step-by-step numerical example of the proposed protocol.

We present a novel framework for asynchronous permissioned blockchain with high performance and post-quantum security for the first time. Specifically, our framework contains two asynchronous Byzantine fault tolerance (aBFT) protocols SodsBC and SodsBC++. We leverage concurrently preprocessing to accelerate the preparation of three cryptographic objects for the repeated consensus procedure, including common random coins as the needed randomness, secret shares of symmetric encryption keys for censorship resilience, and nested hash values for external validation predicates. All preprocessed objects utilize proved or commonly believed to be post-quantum cryptographic tools to resist an adversary equipped with quantum computation capabilities. The evaluation in AWS shows that SodsBC and SodsBC++ reduce the latency of two state-of-the-art but quantum-sensitive competitors Honeybadger and Dumbo by $53\%$ and $6\%$, respectively in the setting that the number of participants is $100$ and each block part has $20,000$ transactions.

Cryptocurrencies have received a lot of research attention in recent years following the release of the first cryptocurrency Bitcoin. With the rise in cryptocurrency transactions, the need for smart contracts has also increased. Smart contracts, in a nutshell, are digitally executed contracts wherein some parties execute a common goal. The main problem with most of the current smart contracts is that there is no privacy for a party's input to the contract from either the blockchain or the other parties. Our research builds on the Hawk project that provides transaction privacy along with support for smart contracts. However, Hawk relies on a special trusted party known as a manager, which must be trusted not to leak each party's input to the smart contract. In this paper, we present a practical private smart contract protocol that replaces the manager with an MPC protocol such that the function to be executed by the MPC protocol is relatively lightweight, involving little overhead added to the smart contract function, and uses practical sigma protocols and homomorphic commitments to prove to the blockchain that the sum of the incoming balances to the smart contract matches the sum of the outgoing balances.

Suppose that $n$ players want to elect a random leader and they communicate by posting messages to a common broadcast channel. This problem is called leader election, and it is fundamental to the distributed systems and cryptography literature. Recently, it has attracted renewed interests due to its promised applications in decentralized environments. In a game theoretically fair leader election protocol, roughly speaking, we want that even majority coalitions cannot increase its own chance of getting elected, nor hurt the chance of any honest individual. The folklore tournament-tree protocol, which completes in logarithmically many rounds, can easily be shown to satisfy game theoretic security. To the best of our knowledge, no sub-logarithmic round protocol was known in the setting that we consider. We show that by adopting an appropriate notion of approximate game-theoretic fairness, and under standard cryptographic assumption, we can achieve $(1-1/2^{\Theta(r)})$-fairness in $r$ rounds for $\Theta(\log \log n) \leq r \leq \Theta(\log n)$, where $n$ denotes the number of players. In particular, this means that we can approximately match the fairness of the tournament tree protocol using as few as $O(\log \log n)$ rounds. We also prove a lower bound showing that logarithmically many rounds is necessary if we restrict ourselves to ``perfect'' game-theoretic fairness and protocols that are ``very similar in structure'' to the tournament-tree protocol. Although leader election is a well-studied problem in other contexts in distributed computing, our work is the first exploration of the round complexity of {\it game-theoretically fair} leader election in the presence of a possibly majority coalition. As a by-product of our exploration, we suggest a new, approximate game-theoretic fairness notion, called ``approximate sequential fairness'', which provides a more desirable solution concept than some previously studied approximate fairness notions.

Imagine one or more non-colluding servers each holding a large public database, e.g., the repository of DNS entries. Clients would like to access entries in this database without disclosing their queries to the servers. Classical private information retrieval (PIR) schemes achieve polylogarithmic bandwidth per query, but require the server to perform linear computation per query, which is a significant barrier towards deployment. Several recent works showed, however, that by introducing a one-time, per-client, off-line preprocessing phase, an \emph{unbounded} number of client queries can be subsequently served with sublinear online computation time per query (and the cost of the preprocessing can be amortized over the unboundedly many queries). Existing preprocessing PIR schemes (supporting unbounded queries), unfortunately, make undesirable tradeoffs to achieve sublinear online computation: they are either significantly non-optimal in online time or bandwidth, %they either require %$\sqrt{n}$ or more bandwidth per query, which is asymptotically %worse than classical PIR schemes, or require the servers to store a linear amount of state per client or even per query, or require polylogarithmically many non-colluding servers. We propose a novel 2-server preprocessing PIR scheme that achieves $\widetilde{O}(\sqrt{n})$ online computation per query and $\widetilde{O}(\sqrt{n})$ client storage, while preserving the polylogarithmic online bandwidth of classical PIR schemes. Both the online bandwidth and computation are optimal up to a poly-logarithmic factor. In our construction, each server stores only the original database and nothing extra, and each online query is served within a single round trip. Our construction relies on the standard LWE assumption. As an important stepping stone, we propose new, more generalized definitions for a cryptographic object called a Privately Puncturable Pseudorandom Set, and give novel constructions that depart significantly from prior approaches.

We introduce a new technique for indexing joins in encrypted SQL databases called partially precomputed joins which achieves lower leakage and bandwidth than those used in prior constructions. These techniques are incorporated into state-of-the-art structured encryption schemes for SQL data, yielding a hybrid indexing scheme with both partially and fully precomputed join indexes. We then introduce the idea of leakage-aware query planning by giving a heuristic that helps the client decide, at query time, which index to use so as to minimize leakage and stay below a given bandwidth budget. We conclude by simulating our constructions on real datasets, showing that our heuristic is accurate and that partially-precomputed joins perform well in practice.

In the wake of the global COVID-19 pandemic, video conference systems have become essential for not only business purposes, but also private, academic, and educational uses. Among the various systems, Zoom is the most widely deployed video conference system. In October 2020, Zoom Video Communications rolled out their end-to-end encryption (E2EE) to protect conversations in a meeting from even insiders, namely, the service provider Zoom. In this study, we conduct thorough security evaluations of the E2EE of Zoom (version 2.3.1) by analyzing their cryptographic protocols. We discover several attacks more powerful than those expected by Zoom according to their whitepaper. Specifically, if insiders collude with meeting participants, they can impersonate any Zoom user in target meetings, whereas Zoom indicates that they can impersonate only the current meeting participants. Besides, even without relying on malicious participants, insiders can impersonate any Zoom user in target meetings though they cannot decrypt meeting streams. In addition, we demonstrate several impersonation attacks by meeting participants or insiders colluding with meeting participants. Although these attacks may be beyond the scope of the security claims made by Zoom or may be already mentioned in the whitepaper, we reveal the details of the attack procedures and their feasibility in the real-world setting and propose effective countermeasures in this paper. Our findings are not an immediate threat to the E2EE of Zoom; however, we believe that these security evaluations are of value for deeply understanding the security of E2EE of Zoom.

From June 2019 to March 2020, IETF conducted a selection process to choose password authenticated key exchange (PAKE) protocols for standardization. Similar standardization efforts were conducted before by IEEE (P1362.2) and ISO/IEC (11770-4). An important hallmark for this IETF selection process is its openness: anyone can nominate any candidate; all reviews are public; all email discussions on the IETF mailing lists are archived and publicly readable. However, despite the openness, it is unclear whether this IETF selection process has presented a successful model. Several important questions that were raised during the selection process had remained unaddressed even after the two winners (CPace and OPAQUE) were announced. We reflect on the IETF PAKE selection process as a case study, and summarize lessons in a set of principles with the hope to improve security standardization in the future.

Well-known authentication mechanisms such as Public-key Infrastructure (PKI) and Identity-based Public-key Certificates (ID-PKC) are not suitable to integrate with the peer-to-peer (P2P) network environment. The reason is the difficulty in maintaining a centralized authority to manage the certificates. The authentication becomes even harder in an anonymous environment. We present three authentication protocols such that the users can authenticate themselves in an anonymous P2P network, without revealing their identities. Firstly, we propose a way to use existing ring signature schemes to obtain anonymous authentication. Secondly, we propose an anonymous authentication scheme utilizing secret sharing schemes. Finally, we propose a zero-knowledge-based anonymous authentication protocol. We provide security justifications of the three protocols in terms of anonymity, completeness, soundness, resilience to impersonation attacks, and resilience to replay attacks.

General-purpose zero-knowledge proofs for all \textsf{NP} languages greatly simplify secure protocol design. However, they inherently require the code of the underlying relation. If the relation contains black-box calls to a cryptographic function, the code of that function must be known to use the ZK proof, even if both the relation and the proof require only black-box access to the function. Rosulek (Crypto'12) shows that non-trivial proofs for even simple statements, such as membership in the range of a one-way function, require non-black-box access. We propose an alternative approach to bypass Rosulek's impossibility result. Instead of asking for a ZK proof directly for the given one-way function $f$, we seek to construct a \textit{new} one-way function $F$ given only black-box access to $f$, \textit{and} an associated ZK protocol for proving non-trivial statements, such as range membership, over its output. We say that $F$, along with its proof system, is a \textit{proof-based} one-way function. We similarly define proof-based versions of other primitives, specifically pseudo-random generators and collision-resistant hash functions. We show how to construct proof-based versions of each of the primitives mentioned above from their ordinary counterparts under mild but necessary restrictions over the input. More specifically, - We first show that if the prover entirely chooses the input, then proof-based pseudo-random generators cannot be constructed from ordinary ones in a black-box manner, thus establishing that some restrictions over the input are necessary. - We next present black-box constructions handling inputs of the form $(x,r)$ where $r$ is chosen uniformly by the verifier. This is similar to the restrictions in the widely used Goldreich-Levin theorem. The associated ZK proofs support range membership over the output as well as arbitrary predicates over prefixes of the input. Our results open up the possibility that general-purpose ZK proofs for relations that require black-box access to the primitives above may be possible in the future without violating their black-box nature by instantiating them using proof-based primitives instead of ordinary ones.

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%.

Updatable encryption schemes allow for key rotation on ciphertexts. A client outsourcing storage of encrypted data to a cloud server can change its encryption key. The cloud server can update the stored ciphertexts to the new key using only a token provided by the client. This paper solves two open problems in updatable encryption, that of uni-directional vs. bi-directional updates, and post-quantum security. The main result in this paper is to analyze the security notions based on uni- and bi-directional updates. Surprisingly, we prove that uni- and bi-directional variants of each security notion are equivalent. The second result in this paper is to provide a new and efficient updatable encryption scheme based on the Decisional Learning with Error assumption. This gives us post-quantum security. Our scheme is bi-directional, but because of our main result, this is sufficient.

We apply multiparty computation (MPC) techniques to show, given a database that is secret-shared among multiple mutually distrustful parties, how the parties may obliviously construct a decision tree based on the secret data. We consider data with continuous attributes (i.e., coming from a large domain), and develop a secure version of a learning algorithm similar to the C4.5 or CART algorithms. Previous MPC-based work only focused on decision tree learning with discrete attributes (De Hoogh et al. 2014). Our starting point is to apply an existing generic MPC protocol to a standard decision tree learning algorithm, which we then optimize in several ways. We exploit the fact that even if we allow the data to have continuous values, which a priori might require fixed or floating point representations, the output of the tree learning algorithm only depends on the relative ordering of the data. By obliviously sorting the data we reduce the number of comparisons needed per node to $O(N \log^2 N)$ from the naive $O(N^2)$, where $N$ is the number of training records in the dataset, thus making the algorithm feasible for larger datasets. This does however introduce a problem when duplicate values occur in the dataset, but we manage to overcome this problem with a relatively cheap subprotocol. We show a procedure to convert a sorting network into a permutation network of smaller complexity, resulting in a round complexity of $O(\log N)$ per layer in the tree. We implement our algorithm in the MP-SPDZ framework and benchmark our implementation for both passive and active three-party computation using arithmetic modulo $2^{64}$. We apply our implementation to a large scale medical dataset of $\approx 290\,000$ rows using random forests, and thus demonstrate practical feasibility of using MPC for privacy-preserving machine learning based on decision trees for large datasets.

The J-PAKE protocol is a Password Authenticated Key Establishment protocol whose security rests on Diffie-Hellman key establishment and Non-Interactive Zero Knowledge proofs. It has seen widespread deployment and has previously been proven secure, including forward secrecy, in a game-based model. In this paper we show that this earlier proof can be re-cast in the Universal Composability framework, thus yielding a stronger result. We also investigate the extension of such proofs to a significantly more efficient variant of the original J-PAKE, that drops the second round Non-Interactive Zero-Knowledge proofs, that we call sJ-PAKE. Adapting the proofs to this light-weight variant proves highly-non trivial, and requires novel proof strategies and the introduction of the algebraic group model. This means that J-PAKE implementations can be made more efficient by simply deleting parts of the code while retaining security under stronger assumptions. We also investigate the security of two further new variants that combine the efficiency gains of dropping the second round NIZK proofs with the gains achieved by two earlier, lightweight variants: RO-J-PAKE and CRS-J-PAKE. The earlier variants replaced the second Diffie-Hellman terms from each party by either a hash term or a CRS term, thus removing the need for half of the NIZK proofs in the first round. The efficiency and security assumptions of these variants are compared.

We study the problem of privacy-preserving approximate kNN search in an outsourced environment — the client sends the encrypted data to an untrusted server and later can perform secure approximate kNN search and updates. We design a security model and propose a generic construction based on locality-sensitive hashing, symmetric encryption, and an oblivious map. The construction provides very strong security guarantees, not only hiding the information about the data, but also the access, query, and volume patterns. We implement, evaluate efficiency, and compare the performance of two concrete schemes based on an oblivious AVL tree and an oblivious BSkiplist.

Minimizing the round complexity of Byzantine Agreement (BA) protocols is a fundamental problem in distributed computing. The typical approach to achieve round efficient (randomized) BA is to have a weak form of BA, called graded consensus (GC), followed by a distributed coin, and to repeat this process until some termination condition is met---as introduced by Feldman and Micali (STOC'88). In this work, we revisit the question of building BA from GC, or, more precisely, from generalizations of GC. Concretely, for Monte Carlo style BA, where the protocol is run for a fixed number of rounds in function of the security parameter (in contrast to protocols with probabilistic termination), we demonstrate that this generalization helps to considerably reduce the round complexity of BA. In particular, assuming a setup for threshold signatures among the parties and corruption threshold $t<n/3$, we improve over the round complexity of the best known protocol by a factor of $1/2$, asymptotically; this is achieved by applying one single Feldman-Micali iteration consisting of one (generalized) GC instance and one round of coin tossing. Our technique also applies to the dishonest-minority case ($t<n/2$), yielding an improvement by a factor of $1/4$ (asymptotically) over the round complexity of the best known fixed-round protocol.

Fully homomorphic encryption (FHE) is an encryption scheme which enables computation on encrypted data without revealing the underlying data. While there have been many advances in the field of FHE, developing programs using FHE still requires expertise in cryptography. In this white paper, we present a fully homomorphic encryption transpiler that allows developers to convert high-level code (e.g., C++) that works on unencrypted data into high-level code that operates on encrypted data. Thus, our transpiler makes transformations possible on encrypted data. Our transpiler builds on Google's open-source XLS SDK (https://github.com/google/xls) and uses an off-the-shelf FHE library, TFHE (https://tfhe.github.io/tfhe/), to perform low-level FHE operations. The transpiler design is modular, which means the underlying FHE library as well as the high-level input and output languages can vary. This modularity will help accelerate FHE research by providing an easy way to compare arbitrary programs in different FHE schemes side-by-side. We hope this lays the groundwork for eventual easy adoption of FHE by software developers. As a proof-of-concept, we are releasing an experimental transpiler (https://github.com/google/fully-homomorphic-encryption/tree/main/transpiler) as open-source software.

In this work we show that an adversary can attack the integrity of contact tracing systems based on Google-Apple Exposure Notications (GAEN) by leveraging blockchain technology. We show that through smart contracts there can be an on-line market where infected individuals interested in monetizing their status can upload to the servers of the GAEN-based systems some keys (i.e., TEKs) chosen by a non-infected adversary. In particular, the infected individual can anonymously and digitally trade the upload of TEKs without a mediator and without running risks of being cheated. This vulnerability can therefore be exploited to generate large-scale fake exposure notifications of at-risk contacts with serious consequences (e.g., jeopardizing parts of the health system, affecting results of elections, imposing the closure of schools, hotels or factories). As main contribution, we design a smart contract with two collateral deposits that works, in general, on GAEN-based systems. We then also suggest the design of a more sophisticated smart contract, using DECO, that could be used to attack in a different way GAEN-based systems (i.e., this second smart contract can succeed even in case GAEN systems are repaired making ineffective the first smart contract). Our work shows how to realize with GAEN-based systems (in particular with Immuni and SwissCovid), the terrorist attack to decentralized contact tracing systems envisioned by Vaudenay.

We introduce and study a simple kind of proof system called line-point zero knowledge (LPZK). In an LPZK proof, the prover encodes the witness as an affine line $\mathbf{v}(t) := \mathbf{a}t + \mathbf{b}$ in a vector space $\mathbb{F}^n$, and the verifier queries the line at a single random point $t=\alpha$. LPZK is motivated by recent practical protocols for vector oblivious linear evaluation (VOLE), which can be used to compile LPZK proof systems into lightweight designated-verifier NIZK protocols. We construct LPZK systems for proving satisfiability of arithmetic circuits with attractive efficiency features. These give rise to designated-verifier NIZK protocols that require only 2-5 times the computation of evaluating the circuit in the clear (following an input-independent preprocessing phase), and where the prover communicates roughly 2 field elements per multiplication gate, or roughly 1 element in the random oracle model with a modestly higher computation cost. On the theoretical side, our LPZK systems give rise to the first linear interactive proofs (Bitansky et al., TCC 2013) that are zero knowledge against a malicious verifier. We then apply LPZK towards simplifying and improving recent constructions of reusable non-interactive secure computation (NISC) from VOLE (Chase et al., Crypto 2019). As an application, we give concretely efficient and reusable NISC protocols over VOLE for bounded inner product, where the sender's input vector should have a bounded $L_2$-norm.

We study when (dual) Vandermonde systems of the form ${V}_T^{{(\intercal)}} \cdot \vec{z} = s\cdot \vec{w}$ admit a solution $\vec{z}$ over a ring $\mathcal{R}$, 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 $\mathcal{R}$, with the property that if $S$ is $(s,t)$-subtractive then the above (dual) Vandermonde systems defined by any $t$-subset $T \subseteq S$ are solvable over $\mathcal{R}$. The challenge is then to find large sets $S$ while minimising (the norm of) $s$ when given a ring $\mathcal{R}$. By constructing families of $(s,t)$-subtractive sets $S$ of size $n = $ poly over cyclotomic rings $\mathcal{R} = \mathbb{Z}[\zeta_{p^\ell}]$ for prime $p$, we construct Schnorr-like lattice-based proofs of knowledge for the SIS relation ${A} \cdot \vec{x} = s \cdot \vec{y} \bmod q$ with $O(1/n)$ knowledge error, and $s = 1$ in case $p = $ poly. 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 \(\Omega(\log k/n)\) for witnesses in \(\mathcal{R}^k\) 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 lattice settings, which we demonstrate by relating it to distributed pseudorandom functions.