Batch Verification Research Articles

ECDSA-based certificateless conditional privacy-preserving authentication scheme in Vehicular Ad Hoc Network

A Certificateless Public Key Cryptography (CL-PKC) aims to avoid the drawback of both traditional public key cryptography which requires a Public Key Infrastructure (PKI), and Identity-Based Public Key Cryptography (ID-PKC) which suffers from the inherent key escrow problem. In Vehicular Ad Hoc Network (VANET), a Certificateless Conditional Privacy Preserving Authentication (CCPPA) fulfills all known VANET security requirements in order to resolve challenges related to security and privacy. However, the existing certificateless schemes only achieve a trust level 2 according to the hierarchy defined by Girault. In case the partial private key is leaked, a malicious node can replace the public key since the public key is not bound to an identity. As a result, the trusted authority can only identify malicious nodes by using their pseudo identities. Al-Riyami and Paterson introduced a binding technique that allows to lift the trust level of a normal certificateless scheme to a trust level 3 by using a binding technique. This paper proposes new CCPPA schemes that use Al-Riyami and Paterson's technique, can achieve a stronger security and achieve a trust level 3. In case the partial private key is leaked, only the legitimate node can use the corresponding public key which has been certified by the trusted authority. As a result, the proposed CCPPA schemes address the vulnerability related to the public key replacement attack which is present in several CCPPA schemes. Our schemes also offer a tracing technique which consists of allowing the trusted authority to identify a malicious node using both its pseudo identity and public key. The proposed schemes use ECC cryptography and avoid Map-to-Hash function and bilinear pairing. Also, we called our schemes ECDSA-CCPPA and ECDSA*-CCPPA since they allow to respectively implement Elliptic Curve Digital Signature Algorithm (ECDSA) and the modified ECDSA* during authentication process in VANET. A security analysis is performed and proves that the ECDSA-CCPPA and ECDSA*-CCPPA schemes are secure in the random oracle. Actually, the ECDSA*-CCPPA scheme has an advantage over ECDSA-CCPPA in that it allows to perform a batch verification of signatures, where RSUs can support vehicles by collecting vehicle's signatures and verifying their messages in congested areas in order to reduce verification time. Additionally, a performance analysis is carried out to compare ECDSA*-CCPPA with several existing schemes. The simulation results show that ECDSA*-CCPPA outperforms the studied schemes with regard to the signature and verification process of one message. Moreover, it has the less overhead when compared to the studied certificateless schemes.

Blockchain-Based Self-Auditing Scheme with Batch Verification for Decentralized Storage

Data owners outsource their data to remote storage providers without keeping local replicas to save their precious storage resources. However, the ownership and management of data are separated after outsourcing. How to ensure the integrity and recoverability of outsourced data becomes a significant problem. Provable Data Possession (PDP) and Proofs of Retrievability (POR) are two cryptographic protocols that enable users to verify the integrity of outsourced data. Nevertheless, the state-of-the-art PDP and POR schemes either need users to perform the complicated audit tasks by themselves or delegate these tasks to a Third-Party Auditor (TPA). Moreover, these schemes are constructed on a centralized storage framework which vulnerably suffers single-point-of-failure. In this paper, we propose a blockchain-based decentralized self-auditing scheme with batch verification. Firstly, data owners outsource their data to decentralized storage nodes, which can achieve self-auditing based on blockchain without TPA. Secondly, our scheme uses Pedersen-based polynomial commitment to significantly reduce the number of authenticators. Furthermore, we propose a batch verification algorithm, which can verify multiple proofs from different storage nodes to improve the verification efficiency. Finally, we analyze the security of our scheme and implement a gas-efficient system prototype using the smart contracts of the Ethereum Reposten test network. The results demonstrate that the scheme is practical.

Comments on efficient batch verification test for digital signatures based on elliptic curves

Abstract Batch verification for digital signature scheme is a method to verify multiple signatures simultaneously. The complex exponent test (CE test for short) proposed by Cheon and Lee is one of the most efficient batch verification tests for several digital signature schemes on certain types of elliptic curves (including Koblitz curves). The security of the CE test relies essentially on the cardinality of a subset of a residue ring of the endomorphism ring of an elliptic curve over an ideal. They have evaluated the cardinality of the above subset, and have illustrated the effectiveness of the CE test by using the evaluation. The aim of this paper is to point out that their evaluation contains a flaw. The flaw is generally related to two roots of a quadratic equation which is used in their argument. We mend the flaw of their evaluation. Our correct evaluation shows that the CE test can achieve the same security as the underlying signature scheme on Koblitz curves. As a result, the CE test is a secure batch verification when the underlying signature scheme uses Koblitz curves.

Compact Multiple Attribute-Based Signatures With Key Aggregation and Its Application

In blockchain-enabled applications, it is difficult to preserve privacy completely because of the openness of each signer’s public key. In this article, an efficient multiattribute-based signature scheme with key aggregation (M-ABS-KA) is presented that supports a flexible threshold predicate. This construction aggregates the public keys and provides a compact signature that is verified as a group, which realizes faster batch verification than confirming them individually. Furthermore, both the multisignature scale and the public key length are independent of the number of signers and attributes in this scheme. To the best of our knowledge, this M-ABS-KA scheme is the first multi-ABS protocol with an aggregated public key and fast batch verification. Based on the hardness of the computational Diffie–Hellman problem, it is formally proven that the proposal achieves unforgeability in the random oracle model and enjoys signer privacy. Additionally, the performance is evaluated in theoretical and experimental analyses with other related ABS schemes, and the results show that it is feasible and efficient in storage, bandwidth, and computational cost. Finally, as an illustrative application, we design a framework of the blockchain-enabled electronic health records assessment system based on this presented M-ABS-KA scheme.

Joint timeliness and security provisioning for enhancement of dependability in Internet of Vehicle system

The Internet of Things has emerged as a wonder-solution to numerous problems in our everyday lives, such as smart homes and intelligent transportation. As an extension of the IoTs, the Internet of Vehicles (IoVs) also requires increasingly high security and timeliness. This article proposes a vehicle-assisted batch verification (VABV) system for IoV, in which some vehicles called auxiliary authentication terminal (AAT) are selected to assist the roadside unit for Basic Safety Message (BSM) verification. As a measure to enhance the timeliness performance for system dependability, comprehensive AAT selection strategies are designed. To overcome the security weaknesses of VABV system, a Sybil detection scheme based on Extreme Learning Machine is developed. For the evaluation of VABV system, the quantified Age of Information (AoI) is used as an integrated timeliness and security indicator. The proposed AoI indicator synthesizes the effects of BSM verification, re-verification for failure of some AATs, Sybil attack, and Sybil detection scheme. As illustrated by the simulation results, by employing AoI as a performance evaluation indicator, we can better and more intuitively design an AAT optimal selection strategy based on changes in AoI. Simultaneously, the performance of the proposed Sybil detection scheme can be evaluated more intuitively and effectively under different IoV scenarios based on AoI.

On the Design of Blockchain-Based ECDSA With Fault-Tolerant Batch Verification Protocol for Blockchain-Enabled IoMT.

The blockchain-enabled internet of medical things (IoMT) is an emerging paradigm that could provide strong trust establishment and ensure the traceability of data sharing in the IoMT networks. One of the fundamental building blocks for Blockchain is Elliptic Curve Digital Signature Algorithm (ECDSA). Nevertheless, when processing a large number of transactions, the verification of multiple signatures will incur cumbersome overhead to the nodes in Blockchain. Although batch verification is able to provide a promising approach that verifies multiple signatures simultaneously and efficiently, the upper bound of batch size is limited to small-scale and the efficiency will drop rapidly as the batch size grows in the state-of-the-art ECDSA batch schemes. Meanwhile, most of the existing researches only focus on improving the efficiency of batch verification algorithms in various cryptosystem while ignoring the identification of invalid signatures, which could cause severe performance degradation when the batch verification fails. Motivated by these observations, this paper proposes an efficient and large-scale batch verification scheme with group testing technology based on ECDSA. The application of the presented protocols in Bitcoin and Hyperledger Fabric has been analyzed as supportive and effective. When the batch verification returns a false result, we utilize group testing technology to improve the efficiency of identifying invalid signatures. Comprehensive simulation results demonstrate that our protocol outperforms the related ECDSA batch verification schemes.

LBVP: A Lightweight Batch Verification Protocol for Fog-Based Vehicular Networks Using Self-Certified Public Key Cryptography

To achieve efficient vehicular network communication and service, researchers proposed fog-based vehicular networks (FVNs). One of the prerequisites for developing large-scale FVNs is ensuring the security and privacy of the entire network environment. However, the existing schemes proposed for FVNs exist considerable calculation and communication costs and/or security vulnerabilities. Therefore, to promote efficient FVN authentication, we propose a lightweight security protocol using self-certified public key cryptography. In the protocol, the trusted authority does not need to participate in the authentication process between the vehicle and the fog node online. And the vehicle can dynamically update its login password and pseudonym, without performing complicated interactive steps with the trusted authority. In addition, our protocol supports batch verification, which significantly improves the system authentication efficiency. A detailed security analysis reveals that our protocol can meet the security requirements of vehicular networks while resisting the common types of attack. Calculation and communication overhead comparisons further prove that our protocol exhibits better performance than related schemes.

EPMDA-FED: Efficient and Privacy-Preserving Multidimensional Data Aggregation Scheme With Fast Error Detection in Smart Grid

Smart grids bring advantages of reliabilty and high efficiency by real-time communication technologies in contrast to the traditional grids. However, smart grids also raise concerns about privacy and security for the individual fine-grained information collection. In order to guarantee privacy and securtiy in the grids, we propose an efficient and privacy-preserving multidimensional data aggregation scheme without a third trusted party and supporting fast error detection, named EPMDA-FED, in the paper. Firstly, we adopt Chinese Remainder Theorem to pack multidimensional data and encrypt the processed data using the keys generated by the negotiation among users and the control center. Secondly, our scheme is efficient for encryption without high-cost additive homomorphic public key encryption scheme, such as Paillier cryptosystem and supporting batch verification with fast error detection. Our proposed error detection algorithm is quite efficient with sublinear computation complexity. Besides, through security analysis, EPMDA-FED is semantically secure against collusion attack and the consistency of negotiated key, authenticity and data integrity of the users’ reports are guaranteed. Finally, performance evaluation shows EPMDA-FED is more efficient than existing competing approaches in terms of computation and communication overhead.

Efficient deniable authentication and its application in location-based services

Deniable authentication (DA) assures message authentication between sets of participants. The actual participants can be certain about the messages’ authenticity but cannot prove it to any third party after the event. In applications such as location-based service (LBS) systems, DA is inevitably relevant to assure the coercion-free state of its usage and to protect user privacy. To protect user privacy in LBS systems, we present two heterogeneous deniable authentication (HDA) schemes called HDA-I and HDA-II scheme. The HDA-I scheme permits communication sessions from certificateless cryptography (CLC) to identity-based cryptography (IBC) setting, whiles the HDA-II scheme runs in a vice versa mode. Our schemes admit security proof in random oracle model (ROM) under computational Diffie–Hellman (CDH) and bilinear Diffie–Hellman (BDH) assumptions. Furthermore, both HDA-I and HDA-II provide batch verification, that can accelerate the verification of authenticators. Lastly, via comprehensive performance evaluation, our schemes show up efficient against other recent related schemes.

A fuzzy-based trust evaluation framework for efficient privacy preservation and secure authentication in VANET

ABSTRACT The Vehicular Adhoc Network (VANET) is a newly added smart technique in vehicles to ensure safety and reduce time consumption. Even though it saves time and guarantees safe travel, security and privacy are the most difficult issues in the VANET. Moreover, this is due to the fact that the methods exploit public key infrastructure, group signature, etc., Meanwhile, the hackers can acquire the sensitive data’s which are usually kept in the tamper-proof devices by using side-channel attacks. The VANET also possesses several security-related issues. To circumvent this we propose an efficient privacy-preserving and fuzzy-based trust evaluation scheme. This method ensures the security and authenticity of the VANET. To ensure security our proposed method utilizes a modified Elliptical Curve cryptographic (ECC) method which also reduces the computational complexities created by the conventional ECC. In our proposed method the TPD parameters are renewed more often to eliminate the attacks and permits batch verification methods to reduce the time. The experimental analysis is conducted in Matlab simulator in terms of computational cost, communication cost, evaluation of trustworthiness, privacy protection. The experimental analysis shows that proposed method provides 94% of trustworthiness and time consumption and communication overheads are reduced to greater extent.

A certificateless authentication scheme with fuzzy batch verification for federated UAV network

Recently, the explosive development of unmanned aerial vehicles (UAVs) promotes its wide application in various services such as package delivery, traffic monitoring. However, due to the high-speed movement, current UAVs usually adopts the unsecure channel without the complicated authentication mechanism to ensure real-time communication. In this paper, we introduce a certificateless authentication scheme with fuzzy batch verification (CLFBV) to achieve once-for-all verification of parallel messages and ensure the real-time secure communication of UAVs. CLBFV defines the error tolerance property for authenticated communication, which allows a tolerance threshold for the messages that are unable to pass authentication. In addition, our proposed scheme is proved to be secure and existentially unforgeable under the chosen message attack and fuzzy identity attack in the random oracle model. The efficiency analysis shows that CLBFV is more efficient and feasible than other existing batch verification schemes.

A Lightweight BT-Based Authentication Scheme for Illegal Signatures Identification in VANETs

Research related to vehicular ad hoc networks (VANETs) has received some significant attention in recent years. Despite all the advantages, the security and privacy in VANETs still become the main challenge that is widely open to discussion. The authentication scheme plays a substantial role to guarantee the security and privacy of information circulation and verification efficiency in VANETs. In this high-density environment, a scalability issue would emerge when the number of message-signature pairs received by a roadside unit (RSU) or vehicles becomes large. This issue happens because those entities cannot sequentially verify each received signature according to the required time limit. Some researchers believe that the symmetric cryptography-based authentication scheme provides a lightweight verification operation, which leads to low computation and communication costs. Combined with the batch verification process, this approach can be very beneficial. However, to the best of our knowledge, not many of those related schemes provide a realistic scenario regarding some illegal signatures’ appearance. Could the system identify the forged messages? Is it still efficient enough to do such an operation? In this paper, we propose a lightweight binary tree-based (BT-based) authentication scheme with a batch verification mechanism, that could efficiently identify a modest amount of illegal signatures in the sum of messages. To even improve the operation, we combine our BT-based batch verification scheme with our vehicle reputation scoring system. Given any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> received messages with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> ≥ 1 illegal ones, the computation cost to verify all these messages only requires approximately (2[⌈lg <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ⌉ - lg(⌈ b/2 ⌉2)] + 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⌈lg(⌈ b/2 ⌉2)⌉+1</sup> - 1) pairing operations, as the best-case scenario. By this approach, we can guarantee the best-case scenario (the most desirable condition) in our BT-based identification appear as much as possible. Hence, the computation cost can be kept low.

An improved efficient authentication scheme for vehicular ad hoc networks with batch verification using bilinear pairings

Research related to the authentication schemes in vehicular ad hoc networks (VANETs) still becomes a hot issue to discuss. In 2019, Cui and Tu proposed an efficient authentication scheme for vehicular ad hoc networks (VANETs) with batch verification using bilinear pairings. Their scheme was designed to improve the utilisation of the double-secret key in the identity-based batch signature (IBS) scheme published by Jianhong et al. and Bayat et al. Unfortunately, we found that Cui and Tu's identity-based conditional privacy-preserving authentication (IBCPPA) scheme is also insecure against non-repudiation attack. By those defects, a malicious user can broadcast some wrong messages to mislead the roadside unit (RSU) and deny its behaviour when a trusted authority (TA) traces it. In this article, we address the issue and give our improvement to withstand the above security threat.

An improved efficient authentication scheme for vehicular ad hoc networks with batch verification using bilinear pairings

An improved efficient authentication scheme for vehicular ad hoc networks with batch verification using bilinear pairings

Bulletproofs+: Shorter Proofs for a Privacy-Enhanced Distributed Ledger

This paper presents a new short zero-knowledge argument for the range proof and arithmetic circuits without a trusted setup. In particular, it can achieve the shortest proof size of the proof system categories without a trusted setup. More specifically, when proving that a committed value is a positive integer less than 64 bits, except for negligible error in the 128-bit security parameter, the proof size is 576 bytes long, which is 85.7% the size of the previous shortest proof due to Bünz <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (Bulletproofs, IEEE Security and Privacy 2018). Similarly, circuit satisfiability can be proven with less communication overhead. Nevertheless, computational overheads in both proof generation and verification are comparable with those of Bulletproofs. Bulletproofs is established as one of the important privacy-enhancing technologies for a distributed ledger due to its trustless feature and short proof size. In particular, it has been implemented and optimized in various programming languages for practical usage by independent entities since it was proposed. The essence of Bulletproofs is based on the logarithmic inner product argument with no zero-knowledge. This paper revisits Bulletproofs from the viewpoint of the first sublinear zero-knowledge argument for linear algebra due to Groth (CRYPTO 2009) and then propose Bulletproofs+, an improved variety of Bulletproofs. The main component is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zero-knowledge weighted inner product argument (zk-WIP)</i> which enables to reduce both the range proof and the arithmetic circuit proof. It already has zero-knowledge properties, there is no additional information when reducing zk-WIP, and it incurs a minimal transmission cost during the reduction process. Note that zk-WIP has all characteristics of the inner product argument, such as an aggregating range proof and batch verification; thus, Bulletproofs+ is superior to Bulletproofs in all aspects.

Anonymous and Efficient Authentication Scheme for Privacy-Preserving Distributed Learning

Distributed learning is proposed as a promising technique to reduce heavy data transmissions in centralized machine learning. By allowing the participants training the model locally, raw data is unnecessarily uploaded to the centralized cloud server, reducing the risks of privacy leakage as well. However, the existing studies have shown that an adversary is able to derive the raw data by analyzing the obtained machine learning models. To tackle this challenge, the state-of-the-art solutions mainly depend on differential privacy and encryption techniques (e.g., homomorphic encryption). Whereas, differential privacy degrades data utility and leads to inaccurate learning, while encryption based approaches are not effective to all machine learning algorithms due to the limited operations and excessive computation cost. In this work, we propose a novel scheme to resolve the privacy issues from the anonymous authentication approach. Different from the two types of existing solutions, this approach is generalized to all machine learning algorithms without reducing data utility, while guaranteeing privacy preservation. In addition, it can be integrated with detection schemes against data poisoning attacks and free-rider attacks, being more practical for distributed learning. To this end, we first design a pairing-based certificateless signature scheme. Based on the signature scheme, we further propose an anonymous and efficient authentication protocol which supports dynamic batch verification. The proposed protocol guarantees the desired security properties while being computationally efficient. Formal security proof and analysis have been provided to demonstrate the achieved security properties, including confidentiality, anonymity, mutual authentication, unlinkability, unforgeability, forward security, backward security, and non-repudiation. In addition, the performance analysis reveals that our proposed protocol significantly reduces the time consumption in batch verification, achieving high computational efficiency.

Efficient Hierarchical Signature Scheme with Batch Verification Function Suitable for ADS-B System

The federal aviation administration (FAA) has ruled that starting January 1, 2020, all aircraft flying over the United States must be equipped with an automatic dependent surveillance-broadcast (ADS-B) system to broadcast aircraft location information. The plaintext communication between the ADS-B system and the ground transmission tower is extremely vulnerable to interception and tampering by criminals. In addition, because of the increasing volume of airport air traffic, the airport tower is unable to quickly and efficiently verify large numbers of aircraft from all over the world. To address these issues, a three-level hierarchical signature scheme with batch verification function suitable for ADS-B system is proposed. Based on computational Diffie-Hellman (CDH) assumption, we prove that the proposed scheme is secure against existing unforgeability. Futhermore, we show the advantages of our scheme in computational cost through experiments.

A Verifiable Credentials System with Privacy-Preserving Based on Blockchain

Decentralized identity authentication is generally based on blockchain, with the protection of user privacy as the core appeal. But traditional decentralized credential system requires users to show all the information of the entire credential to the verifier, resulting in unnecessary overexposure of personal information. From the perspective of user privacy, this paper proposed a verifiable credential scheme with selective disclosure based on BLS (Bohen- Lynn-Shacham) aggregate signature. Instead of signing the credentials, we sign the claims in the credentials. When the user needs to present the credential to verifier, the user can select a part of but not all claims to be presented. To reduce the number of signatures of claims after selective disclosure, BLS aggregate signature is achieved to aggregate signatures of claims into one signature. In addition, our scheme also supports the aggregation of credentials from different users. As a result, verifier only needs to verify one signature in the credential to achieve the purpose of batch verification of credentials. We analyze the security of our aggregate signature scheme, which can effectively resist aggregate signature forgery attack and credential theft attack. The simulation results show that our selective disclosure scheme based on BLS aggregate signature is acceptable in terms of verification efficiency, and can reduce the storage cost and communication overhead. As a result, our scheme is suitable for blockchain, which is strict on bandwidth and storage overhead.

Light-Weight Secure Aggregated Data Sharing in IoT-Enabled Wireless Sensor Networks

Internet of Things (IoT) is a network of physical objects or things that can communicate and share information. In IoT-enabled Wireless Medical Sensor Network (WMSN), the smart sensing devices share remote patient monitoring data towards central repositories. During medical data aggregation and transmission, security is mandatory to guard against intruders. The main problem in existing base schemes is that complex multiplication operations are used for batch key creation. These schemes are computationally expensive and require huge memory space at the aggregator node (AN). This paper presents a lightweight Secure Aggregation and Transmission Scheme (SATS) for secure and lightweight data computation and transmission. SATS provides a lightweight XOR operation for obtaining batch keys instead of the expensive multiplication operation. Furthermore, the AN Receiving Message Algorithm (ARMA) is presented at the AN to aggregate data generated by sensor nodes. The Receiving Message Extractor (RME) algorithm is presented to decrypt the message and perform batch verification at the Fog-Server. SATS protects against several security threats such as denial of service attacks, the man in the middle attack, and reply attacks. The proposed SATS is simulated by using simulation tool NS 2.35. The results show that SATS provides lightweight data transmission by reducing computation and communication costs.The computation cost of the SATS scheme is 14%, 23% and 59% at AN, and at Fog-Node 6.5%, 21.5% and 51%, and Communication cost 6%, 3%, and 4% at Sensor Node, and at AN 6%, 9%, and 12% better than PPDAS, IDAP, and ASAS respectively. The proposed SATS is compared with relevant schemes and the results show that it provides better storage capacity, computations cost, communications cost, and energy consumption.

An Efficient Privacy-Preserving Aggregation Scheme for Multidimensional Data in IoT

Internet of Things (IoT) enables terminal devices connecting with the Internet and provides various intelligent applications by analyzing devices data. As a typical IoT technique, edge computing provides a three-tier architecture to reduce communications and improve efficiency. Specifically, edge nodes are responsible for collecting and aggregating device data, and then send processed results to the cloud for subsequent analysis. However, the data aggregation function will compromise the privacy of device data. In this article, we proposed an efficient privacy-preserving multidimensional data aggregation scheme for IoT, called PMDA. The scheme uses the Chinese remainder theorem to design a homomorphic encryption method that encryptes a multiple-dimensional small integer vector into one ciphertext and keeps linear homomorphic properties per dimension. Combining with the signature mechanism and the batch verification method, the scheme guarantees nonrepudiation of device data and enhance verification efficiency at edge nodes. Through theoretical analysis, we demonstrate that the proposed scheme can achieve correctness, privacy, authentication, and integrity. After performance evaluation, we demonstrate that our scheme is superior to other schemes in terms of computation and communication costs. In particular, as the message dimension increases, our scheme computation costs almost a tenth of others at the 80-bits security level.