Statically Aggregate Verifiable Random Functions and Application to E-Lottery

Randomness is a critical issue in peer-to-peer networks because random numbers allow us to fairly select the candidates, resolve the lotteries, select block producers, etc. The difficulty is that each participant wants to verify that the random number was randomly generated, this led to the invention of verifiable random functions (VRF). The VRF is a pseudo-random function that provides a solution to blockchain-based random number generation. This paper focuses on the implementation of an elliptic curve-based VRF introduced by NIST called ECVRF-secp256r1 in Solidity. The algorithm verifies the randomness on-chain, tests the gas consumption at each stage, and compares it to the ECVRF-secp256k1.

In this paper, we focus on the constructions of adaptively secure identity-based encryption (IBE) from lattices and verifiable random function (VRF) with large input spaces. Existing constructions of these primitives suffer from low efficiency, whereas their counterparts with weaker guarantees (IBEs with selective security and VRFs with small input spaces) are reasonably efficient. We try to fill these gaps by developing new partitioning techniques that can be performed with compact parameters and proposing new schemes based on the idea.

We present a secure and private blockchain-based Verifiable Random Function (VRF) scheme addressing some limitations of classical VRF constructions. Given the imminent quantum computing adversarial scenario, conventional cryptographic methods face vulnerabilities. To enhance our VRF’s secure randomness, we adopt post-quantum RingLWE encryption for synthesizing pseudo-random sequences. Considering computational costs and resultant on-chain gas costs, we suggest a bifurcated architecture for VRF design, optimizing interactions between on-chain and off-chain. Our approach employs a secure ring signature supported by NIZK proof and a delegated key generation method, inspired by the Chaum-Pedersen equality proof and the Fiat-Shamir Heuristic. Our VRF scheme integrates multi-party computation (MPC) with blockchain-based decentralized identifiers (DID), ensuring both security and randomness. We elucidate the security and privacy aspects of our VRF scheme, analyzing temporal and spatial complexities. We also approximate the entropy of the VRF scheme and detail its implementation in a Solidity contract. Also, we delineate a method for validating the VRF’s proof, matching for the contexts requiring both randomness and verification. Conclusively, using the NIST SP800-22 of the statistical randomness test suite, our results exhibit a 98.86% pass rate over 11 test cases, with an average 𝑝-value of 0.5459 from 176 total tests.

In this paper, we introduce the notion of secret key encryption with non-interactive opening (SKENO). With SKENO, one can make a non-interactive proof π to show that the decryption result of a ciphertext C under a shared secret key K is indeed plaintext M without revealing K itself. SKENO is the secret key analogue of public key encryption with non-interactive opening (PKENO). We give a generic construction of SKENO from verifiable random function (VRF) with certain stronger uniqueness, for example, the Hohenberger–Waters VRF and the Berbain–Gilbert I V-dependent stream cipher construction. Although the strong primitive VRF is used, by taking advantage of the features of the stream cipher, we can still achieve good performance without sacrificing much of the efficiency. Though our VRF-based SKENO construction does not require random oracles, we show that SKENO can be constructed from weak VRF (which is strictly weaker primitive than VRF) in the random oracle model.

We give a simple and efficient construction of a verifiable random function (VRF) on bilinear groups. Our construction is direct. In contrast to prior VRF constructions [14,15], it avoids using an inefficient Goldreich-Levin transformation, thereby saving several factors in security. Our proofs of security are based on a decisional bilinear Diffie-Hellman inversion assumption, which seems reasonable given current state of knowledge. For small message spaces, our VRF’s proofs and keys have constant size. By utilizing a collision-resistant hash function, our VRF can also be used with arbitrary message spaces. We show that our scheme can be instantiated with an elliptic group of very reasonable size. Furthermore, it can be made distributed and proactive.

In this work, we introduce the first practical post-quantum verifiable random function (VRF) that relies on well-known (module) lattice problems, namely Module-SIS and Module-LWE. Our construction, named LB-VRF, results in a VRF value of only 84 bytes and a proof of around only 5 KB (in comparison to several MBs in earlier works), and runs in about 3 ms for evaluation and about 1 ms for verification.In order to design a practical scheme, we need to restrict the number of VRF outputs per key pair, which makes our construction few-time. Despite this restriction, we show how our few-time LB-VRF can be used in practice and, in particular, we estimate the performance of Algorand using LB-VRF. We find that, due to the significant increase in the communication size in comparison to classical constructions, which is inherent in all existing lattice-based schemes, the throughput in LB-VRF-based consensus protocol is reduced, but remains practical. In particular, in a medium-sized network with 100 nodes, our platform records a 1.14\(\times \) to 3.4\(\times \) reduction in throughput, depending on the accompanying signature used. In the case of a large network with 500 nodes, we can still maintain at least 24 transactions per second. This is still much better than Bitcoin, which processes only about 5 transactions per second.KeywordsPost-quantumVerifiable random functionBlockchainLatticeAlgorand

Decentralized storage powered by blockchain is becoming a new trend that allows data owners to outsource their data to remote storage resources offered by various storage providers. Unfortunately, unqualified storage providers easily encounter unpredictable downtime due to security threats, such as malicious attacks or system failures, which is unacceptable in many real-time or data-driven applications. As a result, continuous data integrity should be guaranteed in decentralized storage, which ensures that data is intact and available for the entire storage period. However, this requires frequent checking for long time periods and incurs heavy burdens of both communication and computation, especially in a big data scenario. In this paper, we propose an efficient continuous big data integrity checking approach for decentralized storage. We design a data-time sampling strategy that randomly checks the integrity of multiple files at each time slot with high checking probability. Furthermore, to tackle the fairness problem derived from the sampling strategy, we propose a fair approach by designing an arbitration algorithm with the verifiable random function. Security analysis shows the security of our approach under the random oracle model. Evaluation and experiments demonstrate that our approach is more efficient in the big data scenario compared with the state-of-the-arts.

Practical Byzantine Fault Tolerance (PBFT) is a deterministic consensus algorithm, which is widely used in blockchain due to the advantage of no forks. However, PBFT still has some problems, such as not being suitable for dynamic networks, requiring large communication overhead, and not being able to identify Byzantine nodes. Therefore, we propose Extensible-PBFT (EPBFT) consensus algorithm, it can take different steps to reach consensus according to the network environment of the system. Firstly, we add the election of consensus nodes based on verifiable random function (VRF), which makes EPBFT suitable for dynamic networks. Then, we modify the consistency protocol so that EPBFT can reach consensus with less communication in a stable network, and it can also identify Byzantine nodes and reduce confirmation latency. Finally, we simplify the checkpoint protocol and the view-change protocol, reducing the time and communication overhead they require.

Diverse technologies, such as machine learning and big data, have been driving the prosperity of the Internet of Things (IoT) and the ubiquitous proliferation of IoT devices. Consequently, it is natural that IoT becomes the driving force to meet the increasing demand for frictionless transactions. To secure transactions in IoT, blockchain is widely deployed since it can remove the necessity of a trusted central authority. However, the mainstream blockchain-based IoT payment platforms, dominated by Proof-of-Work (PoW) and Proof-of-Stake (PoS) consensus algorithms, face several major security and scalability challenges that result in system failures and financial loss. Among the three leading attacks in this scenario, double-spend attacks and long-range attacks threaten the tokens of blockchain users, while eclipse attacks target Denial of Service. To defeat these attacks, a novel bidirectional-linked blockchain (BLB) using chameleon hash functions is proposed, where bidirectional pointers are constructed between blocks. Furthermore, a new committee members auction (CMA) consensus algorithm is designed to improve the security and attack resistance of BLB while guaranteeing high scalability. In CMA, distributed blockchain nodes elect committee members through a verifiable random function. The smart contract uses Shamir's secret-sharing scheme to distribute the trapdoor keys to committee members. To better investigate BLB's resistance against double-spend attacks, an improved Nakamoto's attack analysis is presented. In addition, a modified entropy metric is devised to measure eclipse attack resistance across different consensus algorithms. Extensive evaluation results show the superior resistance against attacks and demonstrate high scalability of BLB compared with current leading paradigms based on PoS and PoW.

Federated Learning, as a multi-party machine learning paradigm, has garnered significant attention, but model updates may still leak sensitive information. Secure aggregation protocols are considered an effective solution for privacy protection in Federated Learning. However, in large-scale federated learning systems, designing efficient and practical secure aggregation remains a critical challenge. Moreover, while secure aggregation effectively conceals model updates, it unintentionally complicates the detection and mitigation of poisoning attacks, thereby exposing the system to vulnerabilities from both data and model poisoning. To address these challenges, we propose ClusterGuard, a secure clustered aggregation scheme. ClusterGuard leverages Verifiable Random Function (VRF) to ensure fair and transparent client clustering. Within each cluster, it employs a lightweight key-homomorphic masking mechanism combined with verifiable secret sharing to enable secure and efficient aggregation. Fur thermore, we design a dual filtering mechanism based on cosine similarity and norm to effectively detect and resist poisoning attacks. We provide two variants of ClusterGuard for both client-server and decentralized environments with blockchains, respectively. Extensive experiments on standard datasets demonstrate that ClusterGuard achieves over 2× efficiency improvement compared to advanced secure aggregation methods. Even with 20% of clients being malicious, the trained model maintains accuracy comparable to the original model, outperforming state-of-the art robustness solutions. ClusterGuard provides a more efficient, secure, and robust solution for practical federated learning.

Nowadays, the implemetation scheme of blockchain system generally has the defect of insufficient saclability, which can not meet the needs of large-scale applications, and imped its development. Sharding technology is regarded as the most likely solution to the current blockchain bottleneck, it divides the nodes of the blockchain network into each shard, which can maximize the transaction processing capacity of the system. In a sharding scheme, the blockchain is split into several blocks, networks with fewer nodes are created, so the reliability of the nodes in the network becomes critical. In this work, a blockchain sharding scheme based on Verifiable Random Functions(VRF) and node reputation is proposed. The nodes are randomly assigned to each shard by VRF, and the nodes are encouraged to work actively through the reputation score of the in-shard nodes. At the same time, the aggregation of malicious nodes is cotrolled to reduce the probability of fragmentation deterioration and influence of the whole blockchain.

NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). Security proofs and attacks for NMAC can typically be lifted to HMAC.NMAC was introduced by Bellare, Canetti and Krawczyk [Crypto’96], who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto’06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. Our first contribution is a simpler and uniform proof for this fact: If f is an ε-secure PRF (against q queries) and a δ-non-adaptively secure PRF (against q queries), then NMACf is an (ε + ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. We then show that this ε + ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(łε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto’99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight łq2/2c bound for this step, improving over the trivial bound of ł2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto’05]. KeywordsMessage authentication codespseudorandom functionsNMACHMACNI

Blockchain technology, renowned for its decentralized, immutable, and transparent features, offers a reliable framework for trust in distributed systems. The growing popularity of consortium blockchains, which include public, private, hybrid, and consortium chains, stems from their balance of privacy and collaboration. A significant challenge in these systems is the scalability of consensus mechanisms, particularly when employing the Practical Byzantine Fault Tolerance (PBFT) algorithm. This review focuses on enhancing PBFT's scalability, a critical factor in the effectiveness of consortium chains. Innovations such as Boneh–Lynn–Shacham (BLS) signatures and Verifiable Random Functions (VRF) are highlighted for their ability to reduce algorithmic complexity and increase transaction throughput. The discussion extends to real-world applications, particularly in platforms like Hyperledger Fabric, showcasing the practical benefits of these advancements. This paper provides a concise overview of the latest methodologies that enhance the performance scalability of PBFT-based consortium chains, serving as a valuable resource for researchers and practitioners aiming to optimize these systems for high-performance demands.

Proof of Stake (PoS) models are energy-efficient and require limited computational power. These features are critical in telemedicine environments, where resource-constrained devices must handle sensitive data securely. The growing need for auditable and privacy-preserving data storage in telemedicine underscores the importance of PoS models optimized for lightweight devices while complying with strict regulatory requirements, such as the Health Insurance Portability and Accountability Act (HIPAA).This study was guided by two research questions: (i) Which PoS models are lightweight and suitable for telemedicine? and (ii) What features make lightweight PoS models effective for privacy and efficiency in telemedicine? To address these questions, a systematic literature review (SLR) guided by the PICOC framework was conducted to investigate lightweight PoS models that can enhance privacy in telemedicine systems. Out of 2,394 papers studies screened, 55 were included in the analysis. The findings identified Algorand, Ouroboros Praos, Tendermint, Nxt, and Casper CBC as promising candidates. Key enabling features included lightweight voting mechanisms, such as Byzantine Agreement protocols and Verifiable Random Functions, as well as cryptographic techniques like symmetric encryption and multiparty computation. Performance metrics evaluated included latency, throughput, energy efficiency, and battery consumption, with Grey Relational Analysis ranking Algorand highest due to its low latency, high throughput, and minimal energy consumption.

As a new distributed computing paradigm, blockchain is rapidly evolving in areas such as digital finance and cryptocurrency. However, existing blockchain projects adopt different blockchain architectures and protocols, as a result it is difficult for different blockchain systems to flow value to each other or communicate information, and different blockchain systems become isolated islands. This has brought limitations to the usable range, function and scalability of blockchain technology. In order to solve this problem, and bulid trust between different blockchain networks, cross-chain technology has been proposed and received a lot of attention. In this paper we proposed a cross-chain mechanism based on verifiable random functions ( VRF ) and threshold cryptography, we name this scheme as Vger. In Vger, through VRF based cryptographic sortition to select management committee for escrow account and dynamic security setting mechanism, that optimize the security and efficiency about cross-chain transaction.