International Association
for Cryptologic Research

We observe that most fixed-party distributed protocols can be rewritten by replacing a party with a ledger (such as a blockchain system) and the authenticated channel communication between parties with cross-chain relayers. This transform is useful because blockchain systems are always online and have battle-tested security assumptions. We provide a definitional framework that captures this analogy. We model the transform formally, and posit and prove a generic metatheorem that allows translating all theorems from the party setting into theorems in the emulated setting, while preserving analogies between party honesty and ledger security. In the heart of our proof lies a reduction-based simulation argument. As an example, our metatheorem can be used to construct a consensus protocol on top of other blockchains, creating a reliable rollup that assumes only the majority of the underlying layer-1s are secure.

Typical results in multi-party computation (in short, MPC) capture faulty parties by assuming a threshold adversary corrupting parties actively and/or fail-corrupting. These corruption types are, however, inadequate for capturing correct parties that might suffer temporary network failures and/or localized faults - these are particularly relevant for MPC over large, global scale networks. Omission faults and general adversary structures have been proposed as more suitable alternatives. However, to date, there is no characterization of the feasibility landscape combining the above ramifications of fault types and patterns. In this work we provide a tight characterization of feasibility of MPC in the presence of general adversaries - characterized by an adversary structure - that combine omission and active corruption. To this front we first provide a tight characterization of feasibility for Byzantine agreement (BA), a key tool in MPC protocols - this BA result can be of its own separate significance. Subsequently, we demonstrate that the common techniques employed in the threshold MPC literature to deal with omission corruptions do not work in the general adversary setting, not even for proving bounds that would appear straightforward, e.g, sufficiency of the well known $Q^3$ condition on omission-only general adversaries. Nevertheless we provide a new protocol that implements general adversary MPC under a surprisingly complex, yet tight as we prove, bound. As a contribution of independent interest, our work puts forth, for the first time, a formal treatment of general-adversary MPC with (active and) omission corruptions in Canetti's universal composition framework.

In this work, we introduce a family of asymmetric cryptographic functions based on dynamic number theoretic transformations with multiple rounds of modular arithmetic to enhance diffusion and difficulty of inversion. This function acts as a basic cryptographic building block for a novel communication-efficient zero-knowledge crypto-system. The system as defined exhibits partial homomorphism and behaves as an additive positive accumulator. By using a novel technique to constructively embed lattice problems in a nested fashion, the dimensionality and overall complexity of the lattice structure is increased. This linked lattice framework obscures internal structure and mitigates cryptanalysis by applying a novel ’noisy roots’ technique. By relaxing the need for specifically correct nth ω roots in a given field, we apply offset values to create a framework of consisting of a set of uniquely transforming but arithmetically compatible NTTs. We provide specific parameters for conjectured NIST level V security. Communication costs are extremely low at 288-bytes per public key and 144-bytes per cipher-text or digital signature. Example protocols for key agreement, secure data exchange, additive accumulation, and digital signatures are provided. Peer review is in preliminary stages at time of dissemination. Claims within have not undergone rigorous validation and likely contain inaccuracies, errors, flaws or incomplete analysis. Contents may see significant modification through later iterations.

Trusted setup is commonly used for non-interactive proof and argument systems. However, there is no guarantee that the setup parameters in these systems are generated in a trustworthy manner. Building upon previous works, we conduct a systematic study of non-interactive zero-knowledge arguments in the common reference string model where the authority running the trusted setup might be corrupted. We explore both zero-knowledge and soundness properties in this setting. 

- We consider a new notion of NIZK called subversion advice-ZK NIZK that strengthens the notion of zero-knowledge with malicious authority security considered by Ananth, Asharov, Dahari and Goyal (EUROCRYPT'21), and present a construction of a subversion advice-ZK NIZK from the sub-exponential hardness of learning with errors.

- We introduce a new notion that strengthens the traditional definition of soundness, called accountable soundness, and present generic compilers that lift any NIZK for interesting languages in NP to additionally achieve accountable soundness.

- Finally, we combine our results for both subversion advice-ZK and accountable soundness to achieve a subversion advice-ZK NIZK that also satisfies accountable soundness. This results in the first NIZK construction that satisfies meaningful notions of both soundness and zero-knowledge even for maliciously chosen CRS.

Sharding enhances blockchain scalability by dividing the network into shards, each managing specific unspent transaction outputs or accounts. As an introduced new transaction type, cross-shard transactions pose a critical challenge to the security and efficiency of sharding blockchains. Current solutions, however, either prioritize security with assumptions and substantial investments, or focus on reducing overhead and overlooking security considerations.

In this paper, we present Kronos, a generic and efficient sharding blockchain consensus ensuring robust security. At the core of Kronos, we introduce a ''buffer'' mechanism for atomic cross-shard transaction processing. Shard members collectively maintain a buffer to manage cross-shard inputs, ensuring that a transaction is committed only if all inputs are available, and no fund is transferred for invalid requests. While ensuring security including atomicity, Kronos processes transactions with optimal intra-shard communication overhead. A valid cross-shard transaction, involving $x$ input shards and $y$ output shards, is processed with a minimal intra-shard communication overhead factor of $x+y$. Additionally, we propose a reduction for transaction invalidity proof generation to simple and fast multicasting, leading to atomic rejection without executing full-fledged Byzantine fault tolerance (BFT) protocol in optimistic scenarios. Moreover, Kronos adopts a newly designed ''batch'' mechanism, reducing inter-shard message complexity for cross-shard transactions from $\mathcal{O}(\lambda)$ to $\mathcal{O}((m \text{log} m/b)\lambda)$ without sacrificing responsiveness (where $m$ denotes number of shards, $b$ denotes the batch size of intra-shard consensus, and $\lambda$ is security parameter).

Kronos operates without dependence on any time or client honesty assumption, serving as a plug-in sharding blockchain consensus supporting applications in diverse network environments including asynchronous ones. We implement Kronos using two prominent BFT protocols: asynchronous Speeding Dumbo (NDSS'22) and partial synchronous HotStuff (PODC'19). Extensive experiments (over up to $1000$ AWS EC2 nodes across 4 AWS regions) demonstrate Kronos achieving a substantial throughput of $68.6$ktx/sec with $1.7$sec latency. Compared with state-of-the-art solutions, Kronos outperforms in all cases, achieving up to a $42 \times$ improvement in throughput and a $50\%$ reduction in latency when cross-shard transactions dominate the workload.

In this paper, we propose a novel bi-primality test to determine whether $N=pq$ is the product of two primes on any RSA modulus in which we relaxed the restriction, $p\equiv q \equiv 3 \mbox{ (mod } 4)$, that was assumed in most of current bi-primality tests. Our bi-primality test is generalized from Lucas primality test to the bi-prime case. Our test always accepts when $p$ and $q$ are both prime, and otherwise accepts with probability at most $1/2$. In addition, we also prove that the Boneh-Franklin's bi-primality test accepts composite with probability at most $1/4$ instead of $1/2$, if we add an additional condition $\gcd(N, p+q-1)=1$. Moreover, we design a multiparty protocol against of static semi-honest adversaries in the hybrid model and provide a security proof. We then implement the proposed protocol and run in a single thread on a laptop which turned out with average 224 seconds execution time, given that $N$ is around $2048$-bit.

Anonymous message delivery, as in privacy-preserving blockchain and private messaging applications, needs to protect recipient metadata: eavesdroppers should not be able to link messages to their recipients. This raises the question: how can untrusted servers assist in delivering the pertinent messages to each recipient, without learning which messages are addressed to whom?

Recent work constructed Oblivious Message Retrieval (OMR) protocols that outsource the message detection and retrieval in a privacy-preserving way, using homomorphic encryption. This exhibits significant costs in computation per message scanned (${\sim}109$ms), as well as in the size of the associated messages (${\sim}1$kB overhead) and public keys (${\sim}132$kB).

This work constructs more efficient OMR schemes, by replacing the LWE-based clue encryption of prior works with a Ring-LWE variant, and utilizing the resulting flexibility to improve several components of the scheme. We thus devise, analyze, and benchmark two protocols:

The first protocol focuses on improving the detector runtime, using a new retrieval circuit that can be homomorphically evaluated more efficiently. Concretely, this construction takes only ${\sim}7.3$ms per message scanned, about $15$x faster than the prior work.

The second protocol focuses on reducing the communication costs, by designing a different homomorphic decryption circuit. While the circuit is less homomorphic-encryption-friendly (than our first construction), it allows the parameter of the Ring-LWE encryption to be set such that both the public key and the message size are greatly reduced. Concretely, the public key size is about $235$x smaller than the prior work, and the message size is roughly $1.6$x smaller. The runtime of this second construction is ${\sim}40.0$ms per message, still more than $2.5$x faster than prior works.

Fully Homomorphic Encryption (FHE) is a powerful tool for performing privacy-preserving analytics over encrypted data. A promising method for FHE over real and complex numbers is approximate homomorphic encryption, instantiated with the Cheon-Kim-Kim-Song (CKKS) scheme. The CKKS scheme enables efficient evaluation for many privacy-preserving machine learning applications. Despite its high efficiency, there is currently a lot of confusion on how to securely instantiate CKKS for a given application, especially after secret-key recovery attacks were proposed by Li and Micciancio (EUROCRYPT'21) for the $IND-CPA^{D}$ setting, i.e., where decryption results are shared with other parties. On the one hand, the generic definition of $IND-CPA^{D}$ is application-agnostic and often requires impractically large parameters. On the other hand, practical CKKS implementations target specific applications and use tighter parameters. A good illustration are the recent secret-key recovery attacks against a CKKS implementation in the OpenFHE library by Guo et al. (USENIX Security'24). We show that these attacks misuse the library by employing different (incompatible) circuits during parameter estimation and run-time computation, yet they do not violate the generic (application-agnostic) $IND-CPA^{D}$ definition.

To address this confusion, we introduce the notion of application-aware homomorphic encryption and devise related security definitions, which correspond more closely to how homomorphic encryption schemes are implemented and used in practice. We then formulate the guidelines for implementing the application-aware homomorphic encryption model to achieve $IND-CPA^{D}$ security for practical applications of CKKS. We also show that our application-aware model can be used for secure, efficient instantiation of exact homomorphic encryption schemes.

We focus on the problem of constructing fully homomorphic encryption (FHE) schemes that achieve some meaningful notion of adaptive chosen-ciphertext security beyond CCA1. Towards this, we propose a new notion, called security against verified chosen-ciphertext attack (vCCA). The idea behind it is to ascertain integrity of the ciphertext by imposing a strong control on the evaluation algorithm. Essentially, we require that a ciphertext obtained by the use of homomorphic evaluation must be "linked" to the original input ciphertexts. We formalize the vCCA notion in two equivalent formulations; the first is in the indistinguishability paradigm, the second follows the non-malleability simulation-based approach, and is a generalization of the targeted malleability introduced by Boneh et al. in 2012.

We strengthen the credibility of our definitions by exploring relations to existing security notions for homomorphic encryption schemes, namely CCA1, RCCA, FuncCPA, CCVA, and HCCA. We prove that vCCA security is the strongest notion known so far, that can be achieved by an FHE scheme; in particular, vCCA is strictly stronger than CCA1.

Finally, we provide a general transformation, that takes any CPA-secure FHE scheme and makes it vCCA-secure. Our transformation first turns an FHE scheme into a CCA2-secure scheme where a part of the ciphertext retains the homomorphic properties and then extends it with a succinct non-interactive argument of knowledge (SNARK) to verifiably control the evaluation algorithm. In fact, we obtain four general variation of this transformation. We handle both the asymmetric and the symmetric key FHE schemes, and for each we give two variations differing in whether the ciphertext integrity can be verified publicly or requires the secret key. We use well-known techniques to achieve CCA security in the first step of our transformation. In the asymmetric case, we use the double encryption paradigm, and in the symmetric case, we use Encrypt-then-MAC techniques. Furthermore, our transformation also gives the first CCA-secure FHE scheme based on bootstrapping techniques.

This paper introduces an algorithm to efficiently break the Decisional Diffie-Hellman (DDH) assumption in totally non-maximal imaginary quadratic orders, specifically when $\Delta_1 = 3$, and $f$ is non-prime with knowledge of a single factor. Inspired by Shanks and Dedekind's work on 3-Sylow groups, we generalize their observations to undermine DDH security.

We propose a modification to the fork choice rule of proof-of-work blockchains. Instead of choosing the heaviest chain, we choose the chain with the most intrinsic work. The intrinsic work of a block is roughly the number of zeroes at the front of its hash. This modification allows us to safely decrease the confirmations required, yielding a $28.5\%$ improvement in confirmation delay or, dually, safely increase the block production rate, yielding a $16.3\%$ improvement in throughput, as compared to the vanilla Bitcoin proof-of-work fork choice rule. Our modification is at the level of the proof-of-work inequality, and thus can be composed with any other methods to improve latency or throughput that have been proposed in the literature. We report the experimental findings by measuring them on a production-grade implementation of our system, whose testnet is already deployed in the wild. Lastly, we formally prove the security of our new protocol in the Bitcoin Backbone model.

Masking is one of the most popular countermeasures to side- channel attacks, because it can offer provable security. However, depend- ing on the adversary’s model, useful security guarantees can be hard to provide. At first, masking has been shown secure against t-threshold probing adversaries by Ishai et al. at Crypto’03. It has then been shown secure in the more generic random probing model by Duc et al. at Euro- crypt’14. Prouff and Rivain have introduced the noisy leakage model to capture more realistic leakage at Eurocrypt’13. Reduction from noisy leakage to random probing has been introduced by Duc et al. at Euro- crypt’14, and security guarantees were improved for both models by Prest et al. at Crypto’19, Duc et al. in Eurocrypt’15/J. Cryptol’19, and Masure and Standaert at Crypto’23. Unfortunately, as it turns out, we found that previous proofs in either random probing or noisy leakage models are flawed, and such flaws do not appear easy to fix. In this work, we show that the Doeblin coefficient allows one to over- come these flaws. In fact, it yields optimal reductions from noisy leakage to random probing, thereby providing a correct and usable metric to properly ground security proofs. This shows the inherent inevitable cost of a reduction from the noisy leakages to the random probing model. We show that it can also be used to derive direct formal security proofs using the subsequence decomposition of Prouff and Rivain.

Generating and integrating shared randomness into a blockchain can expand applications and strengthen security. We aim to have validators generating blockchain randomness autonomously, and fresh shared randomness is generated for each block. We focus on proof-of-stake blockchains, where each validator has a different amount of stake (aka weight). Such chains introduce a weighted threshold setting where subset authorization relies on the cumulative weight of validators rather than the subset size.

We introduce three cryptographic protocols to enable generating shared randomness in a weighted setting: A publicly verifiable secret sharing scheme (PVSS) which is weighted and aggregatable, a weighted distributed key generation protocol (DKG), and a weighted verifiable unpredictable function (VUF). Importantly, in the VUF protocol, which is the protocol that is run most frequently, the computation and communication costs of participants are independent of their weight. This feature is crucial for scalability.

We implemented our schemes on top of Aptos blockchain, which is a proof-of-stake blockchain deployed in production. Our micro-benchmarks demonstrate that the signing and verification time, as well as the signature size, are independent of the total weight of the parties, whereas the signing time and signature size of the baseline (BLS with virtualization) increase significantly. For instance, our VUF reduces the signature size by factors of 7X and 34X for total weights of 821 and 4053, respectively. We also demonstrate the practicability of our design via an end-to-end evaluation.

Over the past decade, cryptocurrencies have garnered attention from academia and industry alike, fostering a diverse blockchain ecosystem and novel applications. The inception of bridges improved interoperability, enabling asset transfers across different blockchains to capitalize on their unique features. Despite their surge in popularity and the emergence of Decentralized Finance (DeFi), trustless bridge protocols remain inefficient, either relaying too much information (e.g., light-client-based bridges) or demanding expensive computation (e.g., zk-based bridges). These inefficiencies arise because existing bridges securely prove a transaction's on-chain inclusion on another blockchain. Yet this is unnecessary as off-chain solutions, like payment and state channels, permit safe transactions without on-chain publication. However, existing bridges do not support the verification of off-chain payments.

This paper fills this gap by introducing the concept of Pay2Chain bridges that leverage the advantages of off-chain solutions like payment channels to overcome current bridges' limitations. Our proposed Pay2Chain bridge, named Alba, facilitates the efficient, secure, and trustless execution of conditional payments or smart contracts on a target blockchain based on off-chain events. Alba, besides its technical advantages, enriches the source blockchain's ecosystem by facilitating DeFi applications, multi-asset payment channels, and optimistic stateful off-chain computation.

We formalize the security of Alba against Byzantine adversaries in the UC framework and complement it with a game theoretic analysis. We further introduce formal scalability metrics to demonstrate Alba’s efficiency. Our empirical evaluation confirms Alba efficiency in terms of communication complexity and on-chain costs, with its optimistic case incurring only twice the cost of a standard Ethereum transaction of token ownership transfer.

In this note, we show that some of the parameters of the Quotient-Ring transform proposed for VOX are vulnerable. More precisely, they were chosen to defeat an attack in the field extension $\mathbb F_{q^l}$ obtained by quotienting $\mathbb F_q[X]$ by an irreducible polynomial of degree $l$. We observe that we may use a smaller extension $\mathbb F_{q^{l'}}$ for any $l'|l$, in which case the attacks apply again. We also introduce a simple algebraic attack without the use of the MinRank problem to attack the scheme. These attacks concern a subset of the parameter sets proposed for VOX: I, Ic, III, IIIa, V, Vb. We estimate the cost of our attack on these parameter sets and find costs of at most $2^{67}$ gates, and significantly lower in most cases. In practice, our attack requires $0.3s, 1.35s, 0.56s$ for parameter sets I,III,V for the initial VOX parameters, and $56.7s, 6.11s$ for parameter sets IIIa, Vb proposed after the rectangular MinRank attack.

As CPU performance is unable to keep up with the dramatic growth of the past few decades, CPU architects are looking into domain-specific architectures to accelerate certain tasks. A recent trend is the introduction of matrix-multiplication accelerators to CPUs by manufacturers such as IBM, Intel and ARM, some of which have not launched commercially yet. Apple's systems-on-chip (SoCs) for its mobile phones, tablets and personal computers include a proprietary, undocumented CPU-coupled matrix multiplication coprocessor called AMX. In this paper, we leverage AMX to accelerate the post-quantum lattice-based cryptosystems Saber and FrodoKEM, and benchmark their performance on Apple M1 and M3 SoCs. We propose a variant of the Toeplitz Matrix-Vector Product algorithm for polynomial multiplication, which sets new speed records for Saber using AMX (up to 13% for the main KEM operations, and 151% for matrix-vector multiplication of polynomials). For FrodoKEM, we set new speed records with our AMX implementation (up to 21% for the main KEM operations, and 124% for matrix multiplication, with even greater improvements for $4 \times$-batching). Such speedups are relative to our optimized NEON implementation, also presented here, which improves upon the state-of-the-art implementation for ARMv8 CPUs.

We introduce Helium, a novel framework that supports scalable secure multiparty computation for lightweight participants and tolerates churn. Helium relies on multiparty homomorphic encryption (MHE) as its core building block. While MHE schemes have been well studied in theory, prior works fall short of addressing critical considerations paramount for adoption such as supporting resource-constrained participants and ensuring liveness and security under network churn. In this work, we systematize the requirements of MHE-based MPC protocols from a practical lens, and we propose a novel execution mechanism, that addresses those considerations. We implement this execution in Helium, which makes it the first implemented solution that effectively supports sub-linear-cost MPC among lightweight participants and under churn. This represents a significant leap in applied MPC, as most previously proposed frameworks require the participants to have high bandwidth and to be consistently online. We show that a Helium network of $30$ parties connected with a $100$Mbits/s link and experiencing a system-wide churn rate of $40$ failures per minute can compute the product of a fixed secret $512\times512$ matrix (e.g., a collectively trained model) with an input secret vector (e.g., a feature vector) $8.3$ times per second. This is $\sim1500$ times faster than a state-of-the art MPC implementation without churn.

The submission of the Triangular Unbalanced Oil and Vinegar (TUOV) digital signature scheme to the NIST competition in 2023 claims that if the Multivariate Quadratic (MQ) problem (with suitable parameters) is hard, then the TUOV problem must also be hard. We show why the proof fails and why the claimed theorem cannot be true in general.

Function secret sharing (FSS) for a class $\cal{F}$ allows to split a secret function $f \in \cal{F}$ into (succinct) secret shares $f_0,f_1$, such that for all $x\in \{0,1\}^n$ it holds $f_0(x)-f_1(x)=f(x)$. FSS has numerous applications, including private database queries, nearest neighbour search, private heavy hitters and secure computation in the preprocessing model, where the supported class $\cal{F}$ translates to richness in the application. Unfortunately, concretely efficient FSS constructions are only known for very limited function classes.

In this work we introduce the notion of pseudorandom generators with encoded-output homomorphism (EOH-PRGs), and give direct FSS constructions for bit-fixing predicates, branching programs and more based on this primitive. Further, we give constructions of FSS for deterministic finite automatas (DFAs) from a KDM secure variant of EOH-PRGs.

- New abstractions. Following the work of Alamati et al.(EUROCRYPT '19), who classify minicrypt primitives with algebraic structure and their applications, we capture the essence of our FSS constructions in the notion of EOH-PRG, paving the road towards future efficiency improvements via new instantiations of this primitive. The abstraction of EOH-PRG and its instantiations may be of independent interest, as it is an approximate substitution of an ideal homomorphic PRG. - Better efficiency. We show that EOH-PRGs can be instantiated from LWE and a small-exponent variant of the DCR assumption. A theoretical analysis of our instantiations suggest efficiency improvements over the state of the art both in terms of key size and evaluation time: We show that our FSS instantiations lead to smaller key sizes, improving over previous constructions by a factor of $3.5$ and more. While for bit-fixing predicates our FSS constructions show comparable or mildly improved run time (depending on the instantiation), we achieve considerable improvements for branching programs by avoiding the expensive generic transformation via universal circuits, shaving off a factor of $w$ and more in the number of abstract operations, where $w$ corresponds to an upper bound on the width of the underlying class of branching programs. - New constructions. We show that our instantiations of EOH-PRGs additionally support a form of KDM-security, without requiring an additional circular-security assumption. Based on this, we give the first FSS construction for DFAs which supports the evaluation of inputs of a-priori unbounded length without relying on FHE. - Applications. We outline applications of our FSS constructions including pattern matching with wild cards, image matching, nearest neighbor search and regular expression matching.

Abelian group actions appear in several areas of cryptography, especially isogeny-based post-quantum cryptography. A natural problem is to relate the analogues of the computational Diffie-Hellman (CDH) and discrete logarithm (DLog) problems for abelian group actions. Galbraith, Panny, Smith and Vercauteren (Mathematical Cryptology '21) gave a quantum reduction of DLog to CDH, assuming a CDH oracle with perfect correctness. Montgomery and Zhandry (Asiacrypt '22, best paper award) showed how to convert an unreliable CDH oracle into one that is correct with overwhelming probability. However, while a theoretical breakthrough, their reduction is quite inefficient: if the CDH oracle is correct with probability $\epsilon$ then their algorithm to amplify the success requires on the order of $1/\epsilon^{21}$ calls to the CDH oracle.

We revisit this line of work and give a much simpler and tighter algorithm. Our method only takes on the order of $1/\epsilon^{4}$ CDH oracle calls and is conceptually simpler than the Montgomery-Zhandry reduction. Our algorithm is also fully black-box, whereas the Montgomery-Zhandry algorithm is slightly non-black-box. Our main tool is a thresholding technique that replaces the comparison of distributions in Montgomery-Zhandry with testing equality of thresholded sets.