Verifiable Random Function Research Articles

Capybara and Tsubaki: Verifiable Random Functions from Group Actions and Isogenies

In this work, we introduce two post-quantum Verifiable Random Function (VRF) constructions based on abelian group actions and isogeny group actions with a twist. The former relies on the standard group action Decisional Diffie-Hellman (GA-DDH) assumption. VRFs serve as cryptographic tools allowing users to generate pseudorandom outputs along with publicly verifiable proofs. Moreover, the residual pseudorandomness of VRFs ensures the pseudorandomness of unrevealed inputs, even when multiple outputs and proofs are disclosed. Our work aims at addressing the growing demand for post-quantum VRFs, as existing constructions based on elliptic curve cryptography (ECC) or classical DDH-type assumptions are vulnerable to quantum threats. In our contributions, our two VRF constructions, rooted in number-theoretic pseudorandom functions, are both simple and secure over the random oracle model. We introduce a new proof system for the factorization of group actions and set elements, serving as the proofs for our VRFs. The first proposal is based on the standard GA-DDH problem, and for its security proof, we introduce the (group action) master Decisional Diffie-Hellman problem over group actions, proving its equivalence to the standard GA-DDH problem. In the second construction, we leverage quadratic twists to enhance efficiency, reducing the key size and the proof sizes, expanding input size. The scheme is based on the square GA-DDH problem. Moreover, we employ advanced techniques from the isogeny literature to optimize the proof size to 39KB and 34KB using CSIDH-512 without compromising VRF notions. The schemes feature fast evaluations but exhibit slower proof generation. To the best of our knowledge, these constructions represent the first two provably secure VRFs based on isogenies.

Performance analysis and evaluation of postquantum secure blockchained federated learning

As the field of quantum computing progresses, traditional cryptographic algorithms such as RSA and ECDSA are becoming increasingly vulnerable to quantum-based attacks, underscoring the need for robust post-quantum security in critical systems like Federated Learning (FL) and Blockchain. In light of this, we propose a novel hybrid approach for blockchain-based FL (BFL) that integrates a stateless signature scheme, such as Dilithium or Falcon, with a stateful hash-based scheme like XMSS. This combination leverages the complementary strengths of both schemes to provide enhanced security. To further optimize performance, we introduce a linear formula-based device role selection method that takes into account key factors such as computational power and stake accumulation. This selection process is reinforced by a verifiable random function (VRF), which strengthens the blockchain consensus mechanism. Our extensive experimental results demonstrate that this hybrid approach significantly enhances both the security and efficiency of BFL systems, establishing a robust framework for the integration of post-quantum cryptography as we transition into the quantum computing era.

A Data Sharing Model for Blockchain Trusted Sensor Leveraging Mimic Hash Mechanism

Blockchain, as a distributed trust database, has been widely applied in the field of trustworthy sharing of Internet of Things (IoT) sensor data. A single hash mechanism has achieved, to some extent, the trustworthy on-chain storage of blockchain sensor data, that is, the consistency of data on and off the chain. However, it still faces potential security risks such as collision attacks, short password attacks, and rainbow table attacks. To address this issue, this paper proposes a resiliently secure blockchain sensor data trustworthy sharing model based on a mimic hash mechanism. Specifically, in response to the security risks that may arise from the single hash mechanism, this study innovatively introduces a mimic hash mechanism and proposes two methods for constructing mimic hashes based on Verifiable Random Function (VRF) and Cyber Mimic Defense (CMD) in dedicated Wireless Sensor Networks (WSNs) and open public networks, respectively. Theoretical analysis and experimental results demonstrate that this model effectively solves the problem of trustworthy on-chain storage of sensor data in edge computing environments, enhancing the trustworthiness and security of the data on the chain.

Verifiable Random Function Schemes Based on SM2 Digital Signature Algorithm and its Applications for Committee Elections

Verifiable Random Function Schemes Based on SM2 Digital Signature Algorithm and its Applications for Committee Elections

Quantum-Secure Hybrid Blockchain System for DID-Based Verifiable Random Function with NTRU Linkable Ring Signature

In this study, we present a secure smart contract-based Verifiable Random Function (VRF) model, addressing the shortcomings of existing systems. As quantum computing emerges, conventional public key cryptography faces potential vulnerabilities. To enhance our VRF’s robustness, we employ post-quantum Ring-LWE encryption for generating pseudorandom sequences and a NTRU lattice-based linkable ring signature scheme. Given the computational intensity of this approach and associated on-chain gas costs, we propose a hybrid architecture of VRF system where both on-chain and off-chain can communicate in a scalable and secure way. Our decentralized VRF employs multi-party computation (MPC) with blockchain-based decentralized identifiers (DID), ensuring the collective efforts of enhanced randomness and security. We show the security and privacy advantages of our proposed VRF model with the approximated estimation of overall temporal and spatial complexities. We also evaluate our VRF MPC model’s entropy and outline its Solidity smart contract integration. This research also provides a method to produce and verify the VRF output’s proof, optimal for scenarios necessitating randomness and validation. Lastly, using NIST SP800-22 test suite for randomness, we demonstrate the commendable result with a 97.73% overall pass rate on 11 standard tests and 0.5459 of average 𝑝-value for the total 176 tests.

Light-PerIChain: Using lightweight scalable blockchain based on node performance and improved consensus algorithm in IoT systems

With the development of the industry and the increase of smart devices in recent years, the Internet of Things has expanded as one of the solutions to meet human needs in smart societies. However, this emerging technology suffers from security vulnerabilities. In recent years, blockchain has attracted much attention due to its decentralization. However, blockchain is computationally expensive, with limited scalability and high overhead costs. Also, designing a secure and robust blockchain for use in the Internet of Things is challenging. In this article, we provide solutions to improve the sharding method to achieve a lightweight and scalable blockchain and enhance the efficiency of the Internet of Things. To assign nodes to shards in the first round, we use the Verifiable Random Function (VRF), and after a few rounds, nodes are assigned to shards according to their point and performance in the network. We use the IBFT consensus algorithm to process the transaction in shards. Unlike other consensus algorithms based on Byzantine fault tolerance, this algorithm requires 2f+1 replicas instead of 3f+1 for fault tolerance. Also, in this method, the team leader’s shard is considered, so nodes with the highest performance assign to this shard. If the malicious behavior of the team leader is detected, one of the nodes in the team leader’s shard is replaced by it. For cross-transaction processing, we present an improved two-phase commit method that solves many problems with existing two-phase commit methods. Finally, we analyze our design for efficiency and security. Our qualitative arguments show that this design is resistant to several security attacks and that the scalability and throughput of IoT are increased compared to previous designs.

An Efficient E-Voting System for Business Intelligence Innovation Based on Blockchain

AbstractBusiness intelligence (BI) is driven by data and provides valuable business insights and decision support through data analysis, mining, and visualization. The application of blockchain technology in electronic voting can make the voting process more fair and transparent. This is because the decentralized nature of blockchain technology ensures that voting data is not lost due to a single central server failure and also mitigates the risk of data tampering. However, electronic voting still faces security issues that are not easily resistant to quantum attacks. To address these challenges, we propose post-quantum cryptography and verifiable random functions for secure and efficient business intelligence electronic voting. Firstly, we propose a post-quantum verifiable random function algorithm that can resist quantum computer attacks. Secondly, we introduce a consensus algorithm based on random functions to achieve fast and efficient consensus. Thirdly, we propose a blockchain architecture based on the consensus algorithm to achieve secure and efficient blockchain applications. By integrating post-quantum verifiable random functions, consensus algorithms, and blockchain technology, we present an efficient business intelligence electronic voting system. Implementation and comparison with relevant designs demonstrate that this system provides efficient and secure electronic voting services for business intelligence users. Furthermore, the efficient consensus algorithm can be utilized to improve other blockchain applications or decentralized applications.

Obtaining simulation extractable NIZKs in the updatable CRS model generically

Non-interactive zero-knowledge proofs as well as succinct non-interactive argument of knowledge (SNARK) are playing a central role in both theory and application of cryptography. Simulation extractable for SNARKs is considered a necessary security requirement by most applications which prevents the protocol from malleable attacks. However, a trusted party is required to generate the common reference string (CRS) for SNARKs which can be quite problematic in real applications. Recently, the subvertible and updatable CRS model has been proposed to relax the trust in the CRS generation procedure.In this paper, we propose two generic compilers that can achieve simulation extractable in the updatable CRS model. By using an efficient updatable verifiable random function defined in this paper which may be of independent interest, we show that our compiler can lift the updatable knowledge soundness of the underlying SNARKs to achieve updatable simulation extractability. We extend our results by proposing another compiler that can lift a NIZK that has an even weaker security notion called updatable soundness to achieve updatable simulation extractability. We instantiate our compilers and compare them to other related works. This shows that our efficient compilers can be used in various applications.

NativeVRF: A Simplified Decentralized Random Number Generator on EVM Blockchains

Smart contracts refer to small programs that run in a decentralized blockchain infrastructure. The blockchain system is trustless, and the determination of common variables is done by consensus between peers. Developing applications that require generating random variables becomes significantly challenging – for instance, lotteries, games, and random assignments. Many random number generators (RNGs) for smart contracts have been developed for the decentralized environment. The methods can be classified into three categories: on-chain RNG, Verifiable Random Function (VRF), and the Commit–reveal scheme. Although the existing methods offer different strengths and weaknesses, none achieves the three important requirements for an ideal RNG solution: security, applicability, and cost efficiency. This paper proposes a novel RNG approach called Native VRF, which offers application development simplicity and cost efficiency while maintaining strong RNG security properties. Experimental results show that Native VRF has the same security properties as the widely used RNG methods, i.e., Randao and Chainlink VRF. On top of that, our work offers a much simpler setup process and lower hardware resources and developer expertise requirements. Most importantly, the proposed Native VRF is compatible with all Ethereum virtual machine (EVM) blockchains, contributing to the overall growth of the blockchain ecosystem.

Dynamic Transaction Confirmation Sharding Protocol for Alliance Chain

Alliance chain has gained widespread popularity in industrial and commercial fields due to its multi-centralization and node manageability. Current implementations of the alliance chain suffer from scalability obstacles, such as communication congestion and throughput drop, when the number of nodes increases. In this paper, a novel dynamic transaction confirmation sharding protocol is proposed, which improves transaction processing efficiency by partitioning nodes and assigning different transactions to different shards. It utilizes dynamic transaction confirmation consensus as a sharding intra-consensus mechanism to minimize message size and package transactions into microblocks, which modifies communication content during transaction propagation among shards and reduces network congestion and shard reconfigure cost. The protocol leverages a review system and reputation model to identify and punish malicious nodes and also incorporates a verifiable random function for node configuration, which ensures a sufficient number of honest nodes within the shard and prevents repeated consensus processes. Simulation results show that the proposed protocol outperforms mainstream used permissioned chain sharding protocols Attested HyperLedger and Sharper, achieving a throughput improvement of at least 20%. This protocol is suitable for scenarios requiring high throughput and reliability in industrial and commercial fields such as finance, logistics, and supply chain management. Even if the number of alliance chain nodes increases to the usual maximum, or there are some faulty nodes, the protocol can still maintain stable performance.

Simulatable verifiable random function from the LWE assumption

A verifiable random function (VRF) is a pseudorandom function F that can be publicly verified. A simulatable VRF (sVRF) is an important variant of a VRF, which additionally provides simulatability. Informally, the simulatability of a VRF depicts the ability to simulate a valid proof π that y=F(sk,x) for any input x and any output value y. A (simulatable) VRF can be used in the E-Cash, E-Lottery, blockchain and constructing the multi-theorem non-interactive zero-knowledge (NIZK) proof. However, up to now, the existing constructions of an sVRF either rely on non-standard assumptions (e.g., the Q-type ones), or are built in the random oracle model, or resort to time-consuming techniques like the Cook-Levin reduction.In this paper, we design the first sVRF from the LWE assumption in the standard model (free of a random oracle) without using a Cook-Levin reduction. In our construction of an sVRF, we take as building blocks a pseudorandom function, a trapdoor fully homomorphic commitment (FHC) scheme, and a NIZK proof system for a language specified by FHC. Our trapdoor FHC is the key technical tool, which helps the simplification of the underlying NIZK language, thus making possible an instantiation of a NIZK proof from LWE without a Cook-Levin reduction. Together with an LWE-based PRF, we obtain an sVRF scheme from LWE.

Secure PBFT Consensus-Based Lightweight Blockchain for Healthcare Application

Recent advancement in IoT technology has boosted the healthcare domain with enormous usage of IoT devices to provide elevated services to patients with chronic disorders on a real-time basis by the incorporation of IoT sensors on patients’ bodies. However, providing services ensuring security and maintaining the privacy of patients is a challenging task. Blockchain technology promises security in a distributed environment but popular consensus algorithms such as Proof of Work (PoW) and Proof of Stake (PoS) require huge computational resources and energy by making the IoT environment inefficient. This paper introduces a secure Practical Byzantine Fault Tolerance (PBFT) consensus-based lightweight blockchain algorithm for healthcare applications. To strengthen the PBFT consensus, highly trusted nodes were allowed to participate in the consensus algorithm using the Eigen Trust model and Verifiable Random Function (VRF) to select a random primary node from a group of trusted consensus nodes. The proposed algorithm is tested in a simulated environment and evaluated against the traditional PBFT consensus algorithm considering throughput, latency, and fault tolerance.

A Parallel Consensus Mechanism Using PBFT Based on DAG-Lattice Structure in the Internet of Vehicles

The blockchain technology in the Internet of Vehicles (IoV) can be applied to solve security problems. Due to the high dynamics and resource constraints of the IoV, the traditional single-chain blockchain system is not suitable for the practical scenarios. In our previous work, we proposed a lightweight blockchain architecture based on the directed acyclic graph lattice (DAG-lattice) structure for the IoV. However, the current consensus algorithms are not suitable for the previous architecture mentioned above. Therefore, this article proposes a parallel consensus mechanism based on the DAG-lattice structure in the IoV using practical Byzantine fault tolerance (PBFT) as consensus algorithm. This mechanism solves the problem of low efficiency of PBFT caused by too many consensus nodes and the mobility of nodes by adopting the method of network sharding, and meanwhile to ensure that transactions can be reached on consensus parallelly. To avoid the selection of primary nodes from being predicted in advance, this article proposes a primary node selection method based on verifiable random function (VRF). Moreover, a method is proposed of selecting transactions based on weighted round robin (WRR) scheduling to motivate nodes for the purpose of maintaining a high reputation score. Finally, the performance of the proposed scheme is verified by experiments whose results show that the proposed consensus mechanism shows better performance than other comparable schemes in terms of the time added to the blockchain, transaction per second (TPS), consensus success rate, and the time of obtaining transaction. And the proposed mechanism is less dependent on roadside unit (RSU).

The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications

AbstractSequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators were proposed for cryptographic use in 1988. Major interest has been shown towards pseudorandom functions (PRF) recently, based on the Legendre and power residue symbols, due to their efficiency in the multi-party setting. The security of these PRFs is not known to be reducible to standard cryptographic assumptions. In this work, we show that key-recovery attacks against the Legendre PRF are equivalent to solving a specific family of multivariate quadratic (MQ) equation system over a finite prime field. This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance. We show that the currently known techniques and attacks fall short in solving these sparse quadratic equation systems. Furthermore, we build novel cryptographic applications of the Legendre PRF, e.g., verifiable random function and (verifiable) oblivious (programmable) PRFs.

A Scalable Byzantine Fault Tolerance Algorithm Based on a Tree Topology Network

The consortium chain is the main form of application of blockchain technology in the actual industry, and its consensus mechanism mostly adopts the practical Byzantine fault tolerance (PBFT) algorithm. The traditional PBFT algorithm is only suitable for small-scale local area networks, but in large-scale wide-area network environments, its scalability bottleneck has a serious impact on the performance of the system. Therefore, in this paper, a scalable Byzantine fault tolerance algorithm based on a tree topology network is proposed (STBFT), which can take different steps to reach consensus according to the abnormal situation of the system. First, the STBFT algorithm divides the consensus nodes into different layers and groups based on the tree topology network structure, which transforms from global consensus to local consensus and drastically reduces communication consumption. Then, the division method of the group is based on a verifiable random function (VRF), with the purpose of preventing targeted attacks and colluding Byzantine nodes from affecting the normal consensus of the system. Finally, a feedback mechanism is proposed for the first time to reduce the influence of Byzantine failure on hierarchical network systems. The simulation results show that the proposed algorithm reduces the communication complexity and improves the fault tolerance of the system, and the scalability of the tree topology network structure can be better applied in large-scale scenarios such as IoT and health care.

Verifying the Elliptic Curve Verifiable Random Function Secp256r1 on Blockchain

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.

Workload-based randomization byzantine fault tolerance consensus protocol

This paper introduces a new Byzantine fault tolerance protocol called workload-based randomization Byzantine fault tolerance protocol (WRBFT). Improvements are made to the Practical Byzantine Fault Tolerance (PBFT), which has an important position in the Byzantine Fault consensus algorithm. Although PBFT has numerous advantages, its primary node selection mechanism is overly fixed, the communication overhead of the consensus process is also high, and nodes cannot join and exit dynamically. To solve these problems, the WRBFT proposed in this paper combines node consensus workload and verifiable random function (VRF) to randomly select the more reliable primary node that dominates the consensus. The selection of the nodes involved in the consensus is based on the node workload, and the optimization of the agreement protocol of the PBFT is also based on this. Simulation results show that the WRBFT has higher throughput, lower consensus latency, and higher algorithmic efficiency compared to the PBFT.

Blockchain Consensus Mechanism for Distributed Energy Transactions

In order to reduce the cost of grid dispatching and increase the transparency of energy transactions, the distributed energy transaction model based on blockchain is constructed. At the same time, in order to improve the high communication overhead and low throughput of the traditional PBFT algorithm in the consortium blockchain, an efficient Byzantine fault-tolerant consensus mechanism (DE-BFT) for the energy blockchain is designed. The algorithm improves from two aspect: node election and main chain consensus. In the stage of node election, the model uses a health score evaluation and a verifiable random function to improve the security and randomness of node selection. In the stage of main chain consensus, the efficient data consistency interaction protocol decreases the complexity of the communications between nodes, down to a constant term level from exponential one. The result shows that, compared with other consensus algorithm, the DE-BFT algorithm performs better in terms of consensus delay, communication overhead, throughput, and consensus node reliability.

Traceability model based on improved witness mechanism

Traceability system is one of the popular applications of graphic blockchains. However, there are centralisation problems and a long time for final consistency confirmation in the graphic blockchain. In addition, the blockchain system in the traceability application scenario has the problem of insufficient supervision. Therefore, a witness-based graphic blockchain consensus mechanism is proposed. In the consensus mechanism, a verifiable random function is used to screen the publishers of the unit; an SM2 threshold signature is used to sign the unit information to improve the non-repudiation of the traceability information uploaders to the unit information under the supervision of the witness. The improved consistency algorithm cancels the process of finding a stable main chain and makes relatively many nodes to participate in the consensus process. The experimental results show that the graphic blockchain using the improved witness mechanism can reduce the degree of centralisation, shorten the time for new units to reach consensus, and greatly ensure the security and scalability of the blockchain system.

Consensus algorithm based on verifiable randomness

Consensus algorithms are the core of blockchain technology, which can cause nodes to reach consistency or liveness when there are Byzantine nodes in the network. The generation of public randomness in decentralized networks has been significantly demanding and challenging in terms of the consensus mechanism. Previously, the multi-party random number generator (mRNG), which is a mechanism for creating a single value from the contributions of decentralized multiple parties, was mainly designed based on the verifiable random function. In this study, we first construct novel, efficient verifiable mRNG protocols from any one-way function. The protocols can achieve the properties of fairness, no trusted third party, public verifiability, and manipulation resistance. Subsequently, we propose a delegated PoS (DPoS)-based consensus algorithm that adopts the verifiable mRNG. The new algorithm can solve the problem of low fairness caused by the artificial election of master nodes using DPoS, while addressing the issue of manipulating the consensus process owing to the pseudo-random number generated by the traditional RNG, thereby improving the credibility of the consensus algorithm.