Multiparty Generation of an RSA Modulus

We present a new multiparty protocol for the distributed generation of biprime RSA moduli, with security against any subset of maliciously colluding parties assuming oblivious transfer and the hardness of factoring. Our protocol is highly modular, and its uppermost layer can be viewed as a template that generalizes the structure of prior works and leads to a simpler security proof. We introduce a combined sampling-and-sieving technique that eliminates both the inherent leakage in the approach of Frederiksen et al. (Crypto\u2718), and the dependence upon additively homomorphic encryption in the approach of Hazay et al. (JCrypt\u2719). We combine this technique with an efficient, privacy-free check to detect malicious behavior retroactively when a sampled candidate is not a biprime, and thereby overcome covert rejection-sampling attacks and achieve both asymptotic and concrete efficiency improvements over the previous state of the art

PURED: A unified framework for resource-hard functions

Algorithm hardness can be described by 5 categories: hardness in computation, in sequential computation, in memory, in energy consumption (or bandwidth), in code size. Similarly, hardness can be a concern for solving or for verifying, depending on the context, and can depend on a secret trapdoor or be universally hard. Two main lines of research investigated such problems: cryptographic puzzles, that gained popularity thanks to blockchain consensus systems (where solving must be moderately hard, and verification either public or private), and white box cryptography (where solving must be hard without knowledge of the secret key). In this work, we improve upon the classification framework proposed by Biryukov and Perrin in Asiacypt 2017 and offer a united hardness framework, PURED, that can be used for measuring all these kinds of hardness, both in solving and verifying. We also propose three new constructions that fill gaps previously uncovered by the literature (namely, trapdoor proof of CMC, trapdoor proof of code, and a hard challenge in sequential time trapdoored in verification), and analyse their hardness in the PURED framework

PURED: A unified framework for resource-hard functions

Algorithm hardness can be described by 5 categories: hardness in computation, in sequential computation, in memory, in energy consumption (or bandwidth), in code size. Similarly, hardness can be a concern for solving or for verifying, depending on the context, and can depend on a secret trapdoor or be universally hard. Two main lines of research investigated such problems: cryptographic puzzles, that gained popularity thanks to blockchain consensus systems (where solving must be moderately hard, and verification either public or private), and white box cryptography (where solving must be hard without knowledge of the secret key). In this work, we improve upon the classification framework proposed by Biryukov and Perrin in Asiacypt 2017 and offer a united hardness framework, PURED, that can be used for measuring all these kinds of hardness, both in solving and verifying. We also propose three new constructions that fill gaps previously uncovered by the literature (namely, trapdoor proof of CMC, trapdoor proof of code, and a hard challenge in sequential time trapdoored in verification), and analyse their hardness in the PURED framework

SoK: Delay-based Cryptography

In this work, we provide a systematisation of knowledge of delay-based cryptography, in which we discuss and compare the existing primitives within cryptography that utilise a time-delay. We start by considering the role of time within cryptography, explaining broadly what a delay aimed to achieve at its inception and now, in the modern age. We then move on to describing the underlying assumptions used to achieve these goals, and analyse topics including trust, decentralisation and concrete methods to implement a delay. We then survey the existing primitives, discussing their security properties, instantiations and applications. We make explicit the relationships between these primitives, identifying a hierarchy and the theoretical gaps that exist. We end this systematisation of knowledge by highlighting relevant future research directions within the field of delay-based cryptography, from which this area would greatly benefit

The return of Eratosthenes: Secure Generation of RSA Moduli using Distributed Sieving

Secure multiparty generation of an RSA biprime is a challenging task, which increasingly receives attention, due to the numerous privacy-preserving applications that require it. In this work, we construct a new protocol for the RSA biprime generation task, secure against a malicious adversary, who can corrupt any subset of protocol participants. Our protocol is designed for generic MPC, making it both platform-independent and allowing for weaker security models to be assumed (e.g., honest majority), should the application scenario require it. By carefully ``postponing the check of possible inconsistencies in the shares provided by malicious adversaries, we achieve noteworthy efficiency improvements. Concretely, we are able to produce additive sharings of the prime candidates, from multiplicative sharings via a semi-honest multiplication, without degrading the overall (active) security of our protocol. This is the core of our sieving technique, increasing the probability of our protocol sampling a biprime. Similarly, we perform the first biprimality test, requiring several repetitions, without checking input share consistency, and perform the more costly consistency check only in case of success of the Jacobi symbol based biprimality test. Moreover, we propose a protocol to convert an additive sharing over a ring, into an additive sharing over the integers. Besides being a necessary sub-protocol for the RSA biprime generation, this conversion protocol is of independent interest. The cost analysis of our protocol demonstrated that our approach improves the current state-of-the-art (Chen et al. -- Crypto 2020), in terms of communication efficiency. Concretely, for the two-party case with malicious security, and primes of 2048 bits, our protocol improves communication by a factor of ~37

Mitigating MEV via Multiparty Delay Encryption

Ethereum is a decentralized and permissionless network offering several attractive features. However, block proposers in Ethereum can exploit the order of transactions to extract value. This phenomenon, known as maximal extractable value (MEV), not only disrupts the optimal functioning of different protocols but also undermines the stability of the underlying consensus mechanism. In this work, we present a new method to alleviate the MEV problem by separating transaction inclusion and execution, keeping transactions encrypted before execution. We formulate the notion of multiparty delay encryption (MDE) and construct a practical MDE scheme based on time-lock puzzles. Unlike other encryption-based methods, our method excels in scalability (in terms of transaction decryption), efficiency (minimizing communication and storage overhead), and security (with minimal trust assumptions). To demonstrate the effectiveness of our MDE scheme, we have implemented it on a local Ethereum testnet. We also prove that with the presence of just one honest attestation aggregator per slot, the MEV threat can be significantly mitigated in a practical way

Cryptanalysis of Algebraic Verifiable Delay Functions

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth++, Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation $x^e$ requires at least $\log_2 e$ sequential multiplications. In this work, we analyze the security of these algebraic VDF candidates. In particular, we show that the latency of exponentiation can be reduced using parallel computation, against the preliminary assumptions

RandChain: A Scalable and Fair Decentralised Randomness Beacon

We propose RANDCHAIN, a Decentralised Randomness Beacon (DRB) that is the first to achieve both scalability (i.e., a large number of participants can join) and fairness (i.e., each participant controls comparable power on deciding random outputs). Unlike existing DRBs where participants are collaborative, i.e., aggregating their local entropy into a single output, participants in RANDCHAIN are competitive, i.e., competing with each other to generate the next output. The competitive design reduces the communication complexity from at least O(n2) to O(n) without trusted party, breaking the scalability limit in existing DRBs. To build RANDCHAIN, we introduce Sequential Proof-of-Work (SeqPoW), a cryptographic puzzle that takes a random and unpredictable number of sequential steps to solve. We implement RANDCHAIN and evaluate its performance on up to 1024 nodes, demonstrating its superiority (1.3 seconds per output with a constant bandwidth of 200KB/s per node) compared to state-of-the-art DRBs RandHerd (S&P’18) and HydRand (S&P’20)

On the (Im)possibility of Distributed Samplers: Lower Bounds and Party-Dynamic Constructions

Distributed samplers, introduced by Abram, Scholl and Yakoubov (Eurocrypt ’22), are a one-round, multi-party protocol for securely sampling from any distribution. We give new lower and upper bounds for constructing distributed samplers in challenging scenarios. First, we consider the feasibility of distributed samplers with a malicious adversary in the standard model; the only previous construction in this setting relies on a random oracle. We show that for any UC-secure construction in the standard model, even with a CRS, the output of the sampling protocol must have low entropy. This essentially implies that this type of construction is useless in applications. Secondly, we study the question of building distributed samplers in the party-dynamic setting, where parties can join in an ad-hoc manner, and the total number of parties is unbounded. Here, we obtain positive results. First, we build a special type of unbounded universal sampler, which after a trusted setup, allows sampling from any distributed with unbounded size. Our construction is in the shared randomness model, where the parties have access to a shared random string, and uses indistinguishability obfuscation and somewhere statistically binding hashing. Next, using our unbounded universal sampler, we construct distributed universal samplers in the party-dynamic setting. Our first construction satisfies one-time selective security in the shared randomness model. Our second construction is reusable and secure against a malicious adversary in the random oracle model. Finally, we show how to use party-dynamic, distributed universal samplers to produce ideal, correlated randomness in the party-dynamic setting, in a single round of interaction