Practical Post-quantum Few-Time Verifiable Random Function with Applications to Algorand

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.

This paper focuses on the capacity of wireless ad hoc networks and analyzes the effect of key factors viz. network size, traffic patterns and detailed local radio interactions on the capacity of such networks. The capacity is evaluated with several different network layouts and traffic patterns through simulations. To demonstrate the impact of these factors, the capacity evaluation starts with a simple case of a chain of evenly spaced nodes in a network environment and progresses to a network with random traffic and randomly spaced nodes. Initially, capacity of static nodes is evaluated for various network layouts and traffic patterns. Since, in most scenarios, nodes do not travel significant distances during packet transmissions. As an enhancement, mobility of nodes is introduced into the network scenario and the performance is again evaluated. The simulations are carried out using OPNET modeler and the results obtained are presented in this report. The results are analyzed to understand the impact of these factors on the capacity and consequently suggest measures to increase the same. This work shows that the achievable capacity of ad hoc network depends on network size, traffic pattern and mobility. In a single cell topology, it is found that there is a 50% reduction in network throughput, if the node size increases from 2 to 10 nodes, whereas there is a 74% reduction in the throughput for chain topology for the same increase in node size. In a lattice topology with horizontal traffic, there is a 46 % reduction in network throughput when the lattice size increases from 4X4 to 5x5.The same percentage of reduction is observed when both horizontal and network traffic is introduced. In a random network topology with random traffic, there is an 80 % reduction in network throughput when the node size increases from 150 to 750 nodes. However, for the same scenario with the introduction of mobility to the nodes, a slight improvement is achieved with an overall 75% reduction in network throughput.

Cohen, Goldwasser, and Vaikuntanathan (TCC’15) introduced the concept of aggregate pseudo-random functions (PRFs), which allow efficiently computing the aggregate of PRF values over exponential-sized sets. In this paper, we explore the aggregation augmentation on verifiable random function (VRFs), introduced by Micali, Rabin and Vadhan (FOCS’99), as well as its application to e-lottery schemes. We introduce the notion of static aggregate verifiable random functions (Agg-VRFs), which perform aggregation for VRFs in a static setting. Our contributions can be summarized as follows: (1) we define static aggregate VRFs, which allow the efficient aggregation of VRF values and the corresponding proofs over super-polynomially large sets; (2) we present a static Agg-VRF construction over bit-fixing sets with respect to product aggregation based on the q-decisional Diffie–Hellman exponent assumption; (3) we test the performance of our static Agg-VRFs instantiation in comparison to a standard (non-aggregate) VRF in terms of costing time for the aggregation and verification processes, which shows that Agg-VRFs lower considerably the timing of verification of big sets; and (4) by employing Agg-VRFs, we propose an improved e-lottery scheme based on the framework of Chow et al.’s VRF-based e-lottery proposal (ICCSA’05). We evaluate the performance of Chow et al.’s e-lottery scheme and our improved scheme, and the latter shows a significant improvement in the efficiency of generating the winning number and the player verification.

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 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.

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.

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.

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.

OFDM (orthogonal frequency division multiplexing) is an excellent technology that will almost certainly play a large role in next generation wireless communication systems. However, in OFDM, no frequency diversity is exploited to improve BER performance. Today's OFDM systems attempt to overcome this limitation by application of channel coding and interleaving, which requires a reduction in throughput. In our earlier work, we showed how carrier interferometry (CI) codes may be used to spread OFDM symbols over all N subcarriers to exploit frequency diversity without loss in throughput. However, only BPSK was considered in the earlier work. In this paper, we extend the proposed CI/OFDM (carrier interferometry with OFDM) system by updating it for application with QAM modulation schemes. (For example, minimized mean square error combining (MMSEC) is derived for CI/OFDM with QAM modulation schemes.) Simulation results over multi-path fading channels show that 64QAM CI/OFDM significantly outperforms 64QAM OFDM at the cost of a small increase in complexity.

SummaryComplex networks have been used in many scientific disciplines like sociology, microbiology, and telecommunication to represent the interactions among them. Graphs are generally used for representing such complex networks. Mining significant frequent patterns from graph databases has been a challenging area of research. A number of sub graph mining algorithms have been proposed for finding frequent fragments in molecular databases. A very few algorithms have been proposed for mining frequent patterns from large communication networks. All these algorithms perform well on medium size networks and fail on very large graphs. The scalability of these algorithms has been an issue because of the enormous memory requirements and also due to the exponential number of frequent sub graphs possible. In this paper, we propose a compact way of representing graph databases and also use it in a maximal frequent sub graph mining algorithm. The algorithm is found to be efficient and scalable to very large graph databases.

Location of infrastructure in urban railway networks

Activation of the human supraptic and paraventricular nucleus neurons with aging and in Alzheimer's disease as judged from increasing size of the Golgi apparatus