International Association
for Cryptologic Research

The constant-sized polynomial commitment scheme by Kate, Zaverucha, and Goldberg (Asiscrypt 2010), also known as the KZG commitment, is an essential component in designing bandwidth-efficient verifiable secret-sharing (VSS) protocols. We point out, however, that the KZG commitment is missing two important properties that are crucial for VSS protocols.

First, the KZG commitment has not been proven to be degree binding in the standard adversary model without idealized group assumptions. In other words, the committed polynomial is not guaranteed to have the claimed degree, which is supposed to be the reconstruction threshold of VSS. Without this property, shareholders in VSS may end up reconstructing different secrets depending on which shares are used.

Second, the KZG commitment does not support polynomials with different degrees at once with a single setup. If the reconstruction threshold of the underlying VSS protocol changes, the protocol must redo the setup, which involves an expensive multi-party computation known as the powers of tau setup.

In this work, we augment the KZG commitment to address both of these limitations. Our scheme is degree-binding in the standard model under the strong Diffie-Hellman (SDH) assumption. It supports any degree $0 < d \le m$ under a powers-of-tau common reference string with $m+1$ group elements generated by a one-time setup.

Constructing key-agreement protocols in the random oracle model (ROM) is a viable method to assess the feasibility of developing public-key cryptography within Minicrypt. Unfortunately, as shown by Impagliazzo and Rudich (STOC 1989) and Barak and Mahmoody (Crypto 2009), such protocols can only guarantee limited security: any $\ell$-query protocol can be attacked by an $O(\ell^2)$-query adversary. This quadratic gap matches the key-agreement protocol proposed by Merkle (CACM 78), known as Merkle's Puzzles.

Besides query complexity, the communication complexity of key-agreement protocols in the ROM is also an interesting question in the realm of find-grained cryptography, even though only limited security is achievable. Haitner et al. (ITCS 2019) first observed that in Merkle's Puzzles, to obtain secrecy against an eavesdropper with $O(\ell^2)$ queries, the honest parties must exchange $\Omega(\ell)$ bits. Therefore, they conjectured that high communication complexity is unavoidable, i.e., any $\ell$-query protocols with $c$ bits of communication could be attacked by an $O(c\cdot \ell)$-query adversary. This, if true, will suggest that Merkle's Puzzle is also optimal regarding communication complexity. Building upon techniques from communication complexity, Haitner et al. (ITCS 2019) confirmed this conjecture for two types of key agreement protocols with certain natural properties.

This work affirms the above conjecture for all non-adaptive protocols with perfect completeness. Our proof uses a novel idea called density increment argument. This method could be of independent interest as it differs from previous communication lower bounds techniques (and bypasses some technical barriers).

Publicly Verifiable Secret Sharing (PVSS) is a fundamental primitive that allows to share a secret $S$ among $n$ parties via a publicly verifiable transcript $T$. Existing (efficient) PVSS are only proven secure against static adversaries who must choose who to corrupt ahead of a protocol execution. As a result, any protocol (e.g., a distributed randomness beacon) that builds on top of such a PVSS scheme inherits this limitation. To overcome this barrier, we revisit the security of PVSS under adaptive corruptions and show that, surprisingly, many protocols from the literature already achieve it in a meaningful way:

- We propose a new security definition for aggregatable PVSS, i.e., schemes that allow to homomorphically combine multiple transcripts into one compact aggregate transcript $AT$ that shares the sum of their individual secrets. Our notion captures that if the secret shared by $AT$ contains at least one contribution from an honestly generated transcript, it should not be predictable. We then prove that several existing schemes satisfy this notion against adaptive corruptions in the algebraic group model.

- To motivate our new notion, we show that it implies the adaptive security of two recent random beacon protocols, SPURT (S&P '22) and OptRand (NDSS '23), who build on top of aggregatable PVSS schemes satisfying our notion of unpredictability. For a security parameter $\lambda$, our result improves the communication complexity of the best known adaptively secure random beacon protocols to $O(\lambda n^2)$ for synchronous networks with $t

Repeated modular squaring plays a crucial role in various time-based cryptographic primitives, such as Time-Lock Puzzles and Verifiable Delay Functions. At ACM CCS 2021, Thyagarajan et al. introduced “OpenSquare”, a decentralised protocol that lets a client delegate the computation of repeated modular squaring to third-party servers while ensuring that these servers are compensated only if they deliver valid results. In this work, we unveil a significant vulnerability in OpenSquare, which enables servers to receive payments without fulfilling the delegated task. To tackle this issue, we present a series of mitigation measures.

Over the last decade, online reputation has become a central aspect of our digital lives. Most online services and communities assign a reputation score to users, based on feedback from other users about various criteria such as how reliable, helpful, or knowledgeable a person is. While many online services compute reputation based on the same set of such criteria, users currently do not have the ability to use their reputation scores across services. As a result, users face trouble establishing themselves on new services or trusting each other on services that do not support reputation tracking. Existing systems that aggregate reputation scores, unfortunately, provide no guarantee in terms of user privacy, and their use makes user accounts linkable. Such a lack of privacy may result in embarrassment, or worse, place users in danger.

In this paper, we present StreetRep, a practical system for aggregating user reputation scores in a privacy-preserving manner. StreetRep makes it possible for users to provide their aggregated scores over multiple services without revealing their respective identities on each service. We discuss our novel approach for tamper-proof privacy preserving score aggregation from multiple sources by combining existing techniques such as blind signatures, homomorphic signatures and private information retrieval. We discuss its practicality and resiliency against different types of attacks. We also built a prototype implementation of StreetRep. Our evaluation demonstrates that StreetRep (a) performs efficiently and (b) practically scales to a large user base.

How can a model owner prove they trained their model according to the correct specification? More importantly, how can they do so while preserving the privacy of the underlying dataset and the final model? We study this problem and formulate the notion of zero-knowledge proof of training (zkPoT), which formalizes rigorous security guarantees that should be achieved by a privacy-preserving proof of training. While it is theoretically possible to design zkPoT for any model using generic zero-knowledge proof systems, this approach results in extremely unpractical proof generation times. Towards designing a practical solution, we propose the idea of combining techniques from MPC-in-the-head and zkSNARKs literature to strike an appropriate trade-off between proof size and proof computation time. We instantiate this idea and propose a concretely efficient, novel zkPoT protocol for logistic regression.

Crucially, our protocol is streaming-friendly and does not require RAM proportional to the size of the circuit being trained and, hence, can be adapted to the requirements of available hardware. We expect the techniques developed in this paper to also generally be useful for designing efficient zkPoT protocols for other relatively more sophisticated ML models.

We implemented and benchmarked prover/verifier runtimes and proof sizes for training a logistic regression model using mini-batch gradient descent on a 4~GB dataset of 262,144 records with 1024 features. We divide our protocol into three phases: (1) data-independent offline phase (2) data-dependent phase that is independent of the model (3) online phase that depends both on the data and the model. The total proof size (across all three phases) is less than $10\%$ of the data set size ($<350$~MB). In the online phase, the prover and verifier times are under 10 minutes and half a minute respectively, whereas in the data-dependent phase, they are close to one hour and a few seconds respectively.

The Algorand consensus protocol is interesting both in theory and in practice. On the theoretical side, to achieve adaptive security, it introduces the novel idea of player replaceability, where each step of the protocol is executed by a different randomly selected committee whose members remain secret until they send their first and only message. The protocol provides consistency under arbitrary network conditions and liveness under intermittent network partitions. On the practical side, the protocol is used to secure the Algorand cryptocurrency, whose total value is approximately $850M at the time of writing.

The Algorand protocol in use differs substantially from the protocols described in the published literature on Algorand. Despite its significance, it lacks a formal analysis. In this work, we describe and analyze the Algorand consensus protocol as deployed today in Algorand’s ecosystem. We show that the overall protocol framework is sound by characterizing network conditions and parameter settings under which the protocol can be proven secure.

User privacy is becoming increasingly important in our digital society. Yet, many applications face legal requirements or regulations that prohibit unconditional anonymity guarantees, e.g., in electronic payments where surveillance is mandated to investigate suspected crimes.

As a result, many systems have no effective privacy protections at all, or have backdoors, e.g., stored at the operator side of the system, that can be used by authorities to disclose a user’s private information (e.g., lawful interception). The problem with such backdoors is that they also enable silent mass surveillance within the system. To prevent such misuse, various approaches have been suggested which limit possible abuse or ensure it can be detected. Many works consider auditability of surveillance actions but do not enforce that traces are left when backdoors are retrieved. A notable exception which offers retrospective and silent surveillance is the recent work on misuse-resistant surveillance by Green et al. (EUROCRYPT’21). However, their approach relies on extractable witness encryption, which is a very strong primitive with no known efficient and secure implementations.

In this work, we develop a building block for auditable surveillance. In our protocol, backdoors or escrow secrets of users are protected in multiple ways: (1) Backdoors are short-term and user-specific; (2) they are shared between trustworthy parties to avoid a single point of failure; and (3) backdoor access is given conditionally. Moreover (4) there are audit trails and public statistics for every (granted) backdoor request; and (5) surveillance remains silent, i.e., users do not know they are surveilled. Concretely, we present an abstract UC-functionality which can be used to augment applications with auditable surveillance capabilities. Our realization makes use of threshold encryption to protect user secrets, and is concretely built in a blockchain context with committee-based YOSO MPC. As a consequence, the committee can verify that the conditions for backdoor access are given, e.g., that law enforcement is in possession of a valid surveillance warrant (via a zero-knowledge proof). Moreover, access leaves an audit trail on the ledger, which allows an auditor to retrospectively examine surveillance decisions.

As a toy example, we present an Auditably Sender-Traceable Encryption scheme, a PKE scheme where the sender can be deanonymized by law enforcement. We observe and solve problems posed by retrospective surveillance via a special non-interactive non-committing encryption scheme which allows zero-knowledge proofs over message, sender identity and (escrow) secrets.

Cryptographic proof systems provide integrity, fairness, and privacy in applications that outsource data processing tasks. However, general-purpose proof systems do not scale well to large inputs. At the same time, ad-hoc solutions for concrete applications - e.g., machine learning or image processing - are more efficient but lack modularity, hence they are hard to extend or to compose with other tools of a data-processing pipeline.

In this paper, we combine the performance of tailored solutions with the versatility of general-purpose proof systems. We do so by introducing a modular framework for verifiable computation of sequential operations. The main tool of our framework is a new information-theoretic primitive called Verifiable Evaluation Scheme on Fingerprinted Data (VE) that captures the properties of diverse sumcheck-based interactive proofs, including the well-established GKR protocol. Thus, we show how to compose VEs for specific functions to obtain verifiability of a data-processing pipeline.

We propose a novel VE for convolution operations that can handle multiple input-output channels and batching, and we use it in our framework to build proofs for (convolutional) neural networks and image processing. We realize a prototype implementation of our proof systems, and show that we achieve up to $5 \times$ faster proving time and $10 \times$ shorter proofs compared to the state-of-the-art, in addition to asymptotic improvements.

Physical attacks are well-known threats to cryptographic implementations. While countermeasures against passive Side-Channel Analysis (SCA) and active Fault Injection Analysis (FIA) exist individually, protecting against their combination remains a significant challenge. A recent attempt at achieving joint security has been published at CCS 2022 under the name CINI-MINIS. The authors introduce relevant security notions and aim to construct arbitrary-order gadgets that remain trivially composable in the presence of a combined adversary. Yet, we show that all CINI-MINIS gadgets at any order are susceptible to a devastating attack with only a single fault and probe due to a lack of error correction modules in the compression. We explain the details of the attack, pinpoint the underlying problem in the constructions, propose an additional design principle, and provide new (fixed) provably secure and composable gadgets for arbitrary order. Luckily, the changes in the compression stage help us to save correction modules and registers elsewhere, making the resulting Combined Private Circuits (CPC) more secure and more efficient than the original ones. We also explain why the discovered flaws have been missed by the associated formal verification tool VERICA (TCHES 2022) and propose fixes to remove its blind spot. Finally, we explore alternative avenues to repair the compression stage without additional corrections based on non-completeness, i.e., constructing a compression that never recombines any secret. Yet, while this approach could have merit for low-order gadgets, it is, for now, hard to generalize and scales poorly to higher orders. We conclude that our refurbished arbitrary order CINI gadgets provide a solid foundation for further research.

In the context of post-quantum secure algorithms like CRYSTALS-Kyber, the importance of protecting sensitive polynomial coefficients from side-channel attacks is increasingly recognized. Our research introduces two alternative masking methods to enhance the security of the compression function in Kyber through masking. Prior to this, the topic had been addressed by only one other research study. The "Double and Check" method integrates arithmetic sharing and symmetry adjustments, introducing a layer of obfuscation by determining coefficient values based on modular overflows. In contrast, the Look-Up-Table (LUT) integration method employs arithmetic-to-Boolean conversions, augmented by a pre-computed table for efficient value verifications. Furthermore, by leveraging the alternative prime 7681, we propose a novel masked compression function. This prime, 7681, is also notable as the smallest prime suitable for fast NTT multiplication. While both algorithms prioritize data protection and streamlined processing, they also underscore the inherent challenges of balancing computational speed with the potential vulnerabilities to side-channel attacks.

Web3 applications based on blockchains regularly need access to randomness that is unbiased, unpredictable, and publicly verifiable. For Web3 gaming applications, this becomes a crucial selling point to attract more users by providing credibility to the "random reward" distribution feature. A verifiable random function (VRF) protocol satisfies these requirements naturally, and there is a tremendous rise in the use of VRF services. As most blockchains cannot maintain the secret keys required for VRFs, Web3 applications interact with external VRF services via a smart contract where a VRF output is exchanged for a fee. While this smart contract-based plain-text exchange offers the much-needed public verifiability immediately, it severely limits the way the requester can employ the VRF service: the requests cannot be made in advance, and the output cannot be reused. This introduces significant latency and monetary overhead.

This work overcomes this crucial limitation of the VRF service by introducing a novel privacy primitive Output Private VRF ( Pri-VRF) and thereby adds significantly more flexibility to the Web3-based VRF services. We call our framework FlexiRand. While maintaining the pseudo-randomness and public verifiability properties of VRFs, FlexiRand ensures that the requester alone can observe the VRF output. The smart contract and anybody else can only observe a blinded-yet-verifiable version of the output. We formally define Pri-VRF, put forward a practically efficient design, and provide provable security analysis in the universal composability (UC) framework (in the random oracle model) using a variant of one-more Diffie-Hellman assumption over bilinear groups.

As the VRF service, with its ownership of the secret key, be- comes a single point of failure, it is realized as a distributed VRF with the key secret-shared across distinct nodes in our framework. We develop our distributed Pri-VRF construction by combining approaches from Distributed VRF and Distributed Oblivious PRF literature. We provide provable security analysis (in UC), implement it and compare its performance with existing distributed VRF schemes. Our distributed Pri-VRF only introduces a minimal computation and communication overhead for the VRF service, the requester, and the contract.

We introduce Lanturn: a general purpose adaptive learning-based framework for measuring the cryptoeconomic security of composed decentralized-finance (DeFi) smart contracts. Lanturn discovers strategies comprising of concrete transactions for extracting economic value from smart contracts interacting with a particular transaction environment. We formulate the strategy discovery as a black-box optimization problem and leverage a novel adaptive learning-based algorithm to address it. Lanturn features three key properties. First, it needs no contract-specific heuristics or reasoning, due to our black-box formulation of cryptoeconomic security. Second, it utilizes a simulation framework that operates natively on blockchain state and smart contract machine code, such that transactions returned by Lanturn’s learning-based optimization engine can be executed on-chain without modification. Finally, Lanturn is scalable in that it can explore strategies comprising a large number of transactions that can be reordered or subject to insertion of new transactions. We evaluate Lanturn on the historical data of the biggest and most active DeFi Applications: Sushiswap, UniswapV2, UniswapV3, and AaveV2. Our results show that Lanturn not only rediscovers existing, well-known strategies for extracting value from smart contracts, but also discovers new strategies that are previously undocumented. Lanturn also consistently discovers higher value than evidenced in the wild, surpassing a natural baseline computed using value extracted by bots and other strategic agents.

When modelling how public key encryption can enable secure communication, we should acknowledge that secret information, such as private keys or the randomness used for encryption, could become compromised. Intuitively, one would expect unrelated communication to remain secure, yet formalizing this intuition has proven challenging. Several security notions have appeared that aim to capture said scenario, ranging from the multi-user setting with corruptions, via selective opening attacks (SOA), to non-committing encryption (NCE). Remarkably, how the different approaches compare has not yet been systematically explored.

We provide a novel framework that maps each approach to an underlying philosophy of confidentiality: indistinguishability versus simulatability based, each with an a priori versus an a posteriori variant, leading to four distinct philosophies. In the absence of corruptions, these notions are largely equivalent; yet, in the presence of corruptions, they fall into a hierarchy of relative strengths, from IND-CPA and IND-CCA at the bottom, via indistinguishability SOA and simulatability SOA, to NCE at the top.

We provide a concrete treatment for the four notions, discuss subtleties in their definitions and asymptotic interpretations and identify limitations of each. Furthermore, we re-cast the main implications of the hierarchy in a concrete security framework, summarize and contextualize other known relations, identify open problems, and close a few gaps.

We end on a survey of constructions known to achieve the various notions. We identify and name a generic random-oracle construction that has appeared in various guises to prove security in seemingly different contexts. It hails back to Bellare and Rogaway's seminal work on random oracles (CCS'93) and, as previously shown, suffices to meet one of the strongest notions of our hierarchy (single-user NCE with bi-openings).

We introduce the first practical protocols for fully decentralized sealed-bid auctions using timed commitments. Timed commitments ensure that the auction is finalized fairly even if all participants drop out after posting bids or if $n-1$ bidders collude to try to learn the $n^{th}$ bidder’s bid value. Our protocols rely on a novel non-malleable timed commitment scheme which efficiently supports range proofs to establish that bidders have sufficient funds to cover a hidden bid value. This allows us to penalize users who abandon bids for exactly the bid value, while supporting simultaneous bidding in multiple auctions with a shared collateral pool. Our protocols are concretely efficient and we have implemented them in an Ethereum- compatible smart contract which automatically enforces payment and delivery of an auctioned digital asset.

In this paper, we introduce a novel trapdoor generation technique for Prest's hybrid sampler over NTRU lattices. Prest's sampler is used in particular in the recently proposed Mitaka signature scheme (Eurocrypt 2022), a variant of the Falcon signature scheme, one of the candidates selected by NIST for standardization. Mitaka was introduced to address Falcon's main drawback, namely the fact that the lattice Gaussian sampler used in its signature generation is highly complex, difficult to implement correctly, to parallelize or protect against side-channels, and to instantiate over rings of dimension not a power of two to reach intermediate security levels. Prest's sampler is considerably simpler and solves these various issues, but when applying the same trapdoor generation approach as Falcon, the resulting signatures have far lower security in equal dimension. The Mitaka paper showed how certain randomness-recycling techniques could be used to mitigate this security loss, but the resulting scheme is still substantially less secure by Falcon (by around 20 to 50 bits of CoreSVP security depending on the parameters), and has much slower key generation.

Our new trapdoor generation techniques solves all of those issues satisfactorily: it gives rise to a much simpler and faster key generation algorithm than Mitaka's (achieving similar speeds to Falcon), and is able to comfortably generate trapdoors reaching the same NIST security levels as Falcon as well. It can also be easily adapted to rings of intermediate dimensions, in order to support the same versatility as Mitaka in terms of parameter selection. All in all, this new technique combines all the advantages of both Falcon and Mitaka (and more) with none of the drawbacks.

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman assumption, which generalizes the work of Liu et al. (PKC 2023), and ``almost'' tightly with lattice-based assumptions, which tightens the security loss of the work of Beguinet et al. (ACNS 2023) and allows more efficient practical implementation with Kyber. Beyond these, it opens an opportunity of constructing tight PAKE based on various assumptions.

The use of random seeds to a deterministic random bit generator to generate uniform random sampling has been applied multiple times in post-quantum algorithms. The finalists Dilithium and Kyber use SHAKE and AES to generate the random sequence at multiple stages of the algorithm. Here we characterize one of the sampleing techniques available in Dilithium for a random sequence of length 256 with the help of the neutrosophic Boolean function. The idea of the neutrosophic Boolean function came from the theory of neutrosophy and it is useful to study any ternary distributions. We present the non-existence of neutrobalanced bent functions specifically with respect to the sampling named SampleInBall in Dilithium.

Location tracking accessories (or ``tracking tags'') such as those sold by Apple, Samsung, and Tile, allow owners to track the location of their property and devices via offline tracking networks. The tracking protocols have been designed to ensure some level of user privacy against surveillance by the vendor. Such privacy mechanisms, however, seem to be at odds with the phenomenon of tracker-based stalking, where attackers use these very tags to monitor a target's movements. Numerous such criminal incidents have been reported, and in response, manufacturers have chosen to weaken privacy guarantees in order to allow users to detect malicious stalker tags.

In this work we show how to achieve an improved trade-off between user privacy and stalker detection within the constraints of existing tracking protocols. We implement our new protocol using families of list-decodable error-correcting codes, and give efficient algorithms for stalker detection under realistic conditions.

Consider a cloud server that owns a key-value store and provides a private query service to its clients. Preserving client privacy in this setting is difficult because the key-value store is public, and a client cannot encrypt or modify it. Therefore, privacy in this context implies hiding the access pattern of a client. Pantheon is a system that cryptographically allows a client to retrieve the value corresponding to a key from a public key-value store without allowing the server or any adversary to know any information about the key or value accessed. Pantheon devises a single-round retrieval protocol which reduces server-side latency by refining its cryptographic machinery and massively parallelizing the query execution workload. Using these novel techniques, Pantheon achieves a $93\times$ improvement for server-side latency over a state-of-the-art solution.