Computational Diffie-Hellman Assumption Research Articles

A strengthened eCK secure identity based authenticated key agreement protocol based on the standard CDH assumption

An Authenticated Key Agreement (AKA) protocol enables two communicating parties to compute a session key with equal partnership, such that each entity is assured of the authenticity of its peer. Identity-based AKA (ID-AKA) protocols facilitate implicit authentication of the participating entities, without certificate verification. However, most of the existing ID-AKA schemes are proven secure based on the strong Gap Diffie-Hellman (GDH) assumption. Currently, there are no known implementation methods to realize the GDH assumption without using bilinear pairings. Further, none of the existing ID-AKA protocols have provable security against practical attacks due to intermediate result leakages. To this end, we propose a purely pairing-free ID-AKA protocol based on the Computational Diffie-Hellman assumption. The protocol offers provable security under the strengthened eCK (seCK) model that captures attacks resulting from intermediate result leakages. Comparative analysis with other ID-AKA protocols suggests that the proposed protocol satisfies stronger security requirements, without the gap assumption.

Revocable Blockchain-Aided Attribute-Based Encryption With Escrow-Free in Cloud Storage

The massive amount of data generated by the Internet of Things (IoT) and the need to store that data presents a huge challenge for storage. However, meeting this challenge has also driven the development of storage technologies, especially those related to cloud storage. Although attribute-based encryption (ABE) schemes are commonly used to achieve data confidentiality and fine-grained access control in cloud storage, there is still an inherent problem with ABE schemes, namely the key escrow problem. In this paper, we propose a revocable blockchain-aided ABE with escrow-free (BC-ABE-EF) system that resolves the key escrow problem by replacing the traditional key authority with a consortium blockchain. The keys are generated between the blockchain and the data user through a secure key issuing protocol, and the blockchain cannot obtain the user's full key alone. Furthermore, utilize the decryption cloud server to schedule pre-decryption operations in cloud and introduce a group manager to update the group keys of unrecovered users and generate re-encryption keys. The security analysis shows that our scheme is secure under the Decisional Computation Diffie Hellman (DCDH) assumption. The effectiveness of the scheme is demonstrated by simulating the BC-ABE-EF scheme and comparing it based on performance analysis.

Provable Multiple-Copy Integrity Auditing Scheme for Cloud-Based IoT

Cloud-based Internet of Things systems facilitate cloud storage and provide cloud users with convenient data outsourcing service, although there are a number of associated risks to the users (e.g., an untrusted cloud server or their employee/vendor may delete rarely accessed data). In order to ensure that the cloud server stores the data correctly, users need to verify the integrity of remote data periodically. Most of the existing public auditing protocols only considered storing single copy on the cloud; in this case, the loss of users is irreparable when the data are damaged. Subsequently, some multicopy auditing schemes have been proposed where users can store multiple replicas on the cloud. However, it can be challenging to check the integrity of all the copies without incurring significant computation overheads for the auditor/user. Hence, this article proposes a provable multicopy integrity auditing scheme (PMCIA), which reduces the verification cost of the auditor to several lightweight hash operations. Using the medical settings (e.g., where electronic health records containing sensitive information of patients need to be preprocessed before outsourcing storage) as a use case, we explain how our proposed scheme can be deployed. Specifically, to minimize computation overhead for users (e.g., patients), we introduce a hospital information center to help patients generate multiple copies and corresponding tags. We then prove the security under the computational Diffie–Hellman assumption as well as evaluate the performance of our PMCIA scheme. Finally, we explain how PMCIA can be extended to support batch auditing to improve auditing efficiency for multiple auditing tasks.

Efficient heterogeneous signcryption scheme based on Edge Computing for Industrial Internet of Things

In recent years, the Industrial Internet of Things (IIoT) has played an indispensable role in the age of intelligence. The data of IIoT is extremely private and valuable. Therefore, privacy protection and secure communication in the IIoT have been the focus of attention. Since terminal devices in the IIoT collect massive amounts of sensitive data in real time, traditional cloud computing architectures cannot satisfy the requirements of the IIoT. Edge computing is an emerging computing paradigm to solve the problems of delay and bandwidth in traditional cloud computing architectures. In edge computing architecture, one-to-many communication is a secure and highly efficient communication method. Due to the complex heterogeneity of the IIoT, it faces various potential threats. In order to solve the dilemma mentioned above, we propose an efficient heterogeneous signcryption scheme based on edge computing for IIoT to achieve multi-message and multi-receiver communication between edge servers and data users, where the edge server belongs to identity-based cryptography while data users belong to certificateless cryptography. In the random oracle model, our proposed scheme is proved to satisfy confidentiality and unforgeability based on the discrete logarithm assumption and the computational Diffie–Hellman assumption. Experimental results indicate that our proposal achieves better performance than existing schemes. Hence, our scheme has more advantages for IIoT.

Homomorphic cryptosystem-based secure data processing model for edge-assisted IoT healthcare systems

The substantial acceptance of Internet-of-Things (IoT) in digital healthcare systems necessitates secure data processing before storing it on a cloud server. Since resource-limited IoT devices engender complexity in secure processing, edge computing technology is adopted. Edge-assisted IoT locates edge nodes in proximity to user devices enabling computation offloading and seamless interaction between IoT applications and cloud servers. Integration of these entities results in severe security and privacy issues due to large amount of sensitive information transmitted over vulnerable communication channels. As such, information protection and data integrity in edge-assisted IoT have become critical factors for improvement. Several data processing models have been proposed regarding the above-stated concerns. However, under a powerful adversarial scenario, traditional solutions lack in preserving robust security and privacy. This motivates us to address critical challenges of communication security and privacy-preserving computation offloading in edge-assisted IoT systems. In this article, we design a homomorphic cryptosystem-based secure data processing model (HC-SDPM), enabling secure data collection and aggregation offloading on edge nodes for our hypothesized edge-assisted IoT healthcare system. Paillier homomorphic encryption and certificateless linear homomorphic ID-based signatures are utilized to achieve end-to-end confidentiality and data integrity during transmission and aggregation. Moreover, HC-SDPM involves a semi-trusted authority to enable key-escrow resilience. The security analysis of HC-SDPM assures signatures unforgeability in the random oracle model under computational Diffie–Hellman assumptions. Compared with similar modeled schemes, HC-SDPM demonstrates a relative advantage in computational overhead, communication overhead, and storage complexity.

Lightweight and Secure IoT-Based Payment Protocols from an Identity-Based Signature Scheme

After the great success of mobile wallets, the Internet of Things (IoT) leaves the door wide open for consumers to use their connected devices to access their bank accounts and perform routine banking activities from anywhere, anytime, and with any device. However, consumers need to feel safe when interacting with IoT-based payment systems, and their personal information should be protected as much as possible. Unlike what is usually found in the literature, in this paper, we introduce two lightweight and secure IoT-based payment protocols based on an identity-based signature scheme. We adopt a server-aided verification technique to construct the first scheme. This technique allows to outsource the heavy computation overhead on the sensor node to a cloud server while maintaining the user’s privacy. The second scheme is built upon a pairing-free ECC-based security protocol to avoid the heavy computational complexity of bilinear pairing operations. The security reduction results of both schemes are held in the Random Oracle Model (ROM) under the discrete logarithm and computational Diffie–Hellman assumptions. Finally, we experimentally compare the proposed schemes against each other and against the original scheme on the most commonly used IoT devices: a smartphone, a smartwatch, and the embedded device Raspberry Pi. Compared with existing schemes, our proposed schemes achieve significant efficiency in terms of communication, computational and storage overheads.

Hidden Issuer Anonymous Credential

Identity Management Systems (IMS) allow users to prove characteristics about themselves to multiple service providers. IMS evolved from impractical, site-by-site authentication, to versatile, privacyenhancing Self Sovereign Identity (SSI) Frameworks. SSI frameworks often use Anonymous Credential schemes to provide user privacy, and more precisely unlinkability between uses of these credentials. However, these schemes imply the disclosure of the identity of the Issuer of a given credential to any service provider. This can lead to information leaks. We deal with this problem by introducing a new Anonymous Credential scheme that allows a user to hide the Issuer of a credential, while being able to convince the service providers that they can trust the credential, in the absence of a trusted setup. We prove this new scheme secure under the Computational Diffie Hellman assumption, and Decisional Diffie Hellman assumption, in the Random Oracle Model. We show that this scheme is efficient enough to be used with laptops, and to be integrated into SSI frameworks or any other IMS.

Signed (Group) Diffie–Hellman Key Exchange with Tight Security

We propose the first tight security proof for the ordinary two-message signed Diffie–Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie–Hellman assumption and the multiuser security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a new notion called verifiable key exchange. In contrast to a known tight three-message variant of the signed Diffie–Hellman protocol (Gjøsteen and Jager, in: Shacham, Boldyreva (eds) CRYPTO 2018, Part II. LNCS, Springer, Heidelberg, 2018), we do not require any modification to the original protocol, and our tightness result is proven in the “Single-Bit-Guess” model which we know can be tightly composed with symmetric cryptographic primitives to establish a secure channel. Finally, we extend our approach to the group setting and construct the first tightly secure group authenticated key exchange protocol.

An Anonymous Authentication Protocol With Delegation and Revocation for Content Delivery Networks

By redirecting a user’s request to the nearest cache server, content delivery networks (CDNs) enable users to obtain services in time and reduce the burden of the origin server. Nevertheless, the origin server suffers from the private key leakage problem when delegating the authentication capability to untrusted CDN nodes. To handle this challenge, this article proposes an anonymous authentication protocol with delegation and revocation for CDNs depending on the proxy resignature (PRS) cryptography. Specifically, we first present an efficient revocable PRS (R-PRS) scheme, which is proved to be secure under the extended Computational Diffie-Hellman assumption. Then, based on R-PRS scheme, the proposed protocol enables the origin server to delegate and revoke the authentication capability to the CDN nodes without leaking its private key. Furthermore, our protocol not only provides anonymity, mutual authentication, and session key establishment, but also achieves forward security. Eventually, theoretical analysis and implementation demonstrate that the proposed protocol has an excellent performance in efficiency and practicality.

SHT-based public auditing protocol with error tolerance in FDL-empowered IoVs

With the intelligentization of the Internet of Vehicles (IoVs), Artificial Intelligence (AI) technology is becoming more and more essential, especially deep learning. Federated Deep Learning (FDL) is a novel distributed machine learning technology and is able to address the challenges like data security, privacy risks, and huge communication overheads from big raw data sets. However, FDL can only guarantee data security and privacy among multiple clients during data training. If the data sets stored locally in clients are corrupted, including being tampered with and lost, the training results of the FDL in intelligent IoVs must be negatively affected. In this paper, we are the first to design a secure data auditing protocol to guarantee the integrity and availability of data sets in FDL-empowered IoVs. Specifically, the cuckoo filter and Reed-Solomon codes are utilized to guarantee error tolerance, including efficient corrupted data locating and recovery. In addition, a novel data structure, Skip Hash Table (SHT) is designed to optimize data dynamics. Finally, we illustrate the security of the scheme with the Computational Diffie-Hellman (CDH) assumption on bilinear groups. Sufficient theoretical analyses and performance evaluations demonstrate the security and efficiency of our scheme for data sets in FDL-empowered IoVs.

Provably Secure Linearly Homomorphic Aggregate Signature Scheme for Electronic Healthcare System

In recent years, deploying Internet of Things (IoT) in electronic healthcare systems (EHS) has made great progress in healthcare detection. It is extremely important to reduce the cost of communication and ensure the authenticity and integrity of data. A linearly homomorphic signature scheme can solve the above problems. However, when the scale of EHS is too large, the transmission, storage and verification of signatures need a high cost. An aggregate signature can combine many signatures generated by many different users into a short one. Therefore, only one aggregate signature needs to be processed during verification, transmission and storage. Combining the advantages of aggregate signature and linearly homomorphic signature, this paper proposes an aggregate signature scheme based on a linearly homomorphic signature for EHS, which has both linear homomorphism and aggregation, and realizes double data compression. Moreover, our scheme can resist a potential real attack, named a coalition attack. The security of this scheme is rigorously demonstrated based on the computational Diffie–Hellman assumption in the random oracle model.

An Efficient Certificateless Ring Signcryption Scheme With Conditional Privacy-Preserving in VANETs

As an ever-increasing ingredient of intelligent transportation systems, vehicular ad hoc networks (VANETs) can be leveraged to improve road safety and driving convenience. However, the extreme mobility and volatility of VANETs can arouse serious concerns about vehicle identity privacy leakages as well as the authenticity and confidentiality of safety messages in vehicular communication. To cope with these issues, we propose a certificateless ring signcryption scheme with conditional privacy-preserving based on elliptic curve cryptography, which can provide secure vehicular communication with low transmission latency and communication overhead. Besides, by integrating a tracking mark into the safety message, we design a tracking algorithm that enables the trusted party to distinguish malicious vehicles from the ring member list. It realizes conditional privacy while avoiding the huge cost of vehicular storage resources. Through security analysis, this scheme is proven to be secure under the Elliptic curve discrete logarithm and Elliptic curve computational Diffie–Hellman assumptions in the random oracle model. Finally, we implement the performance evaluations in terms of the computational overhead, the communication bandwidth and the packet loss rate. By utilizing the MIRACL cryptography library and the Veins simulation framework, the results illustrate that the proposed scheme can support an efficient and highly reliable communication protocol for safety-related applications in VANETs environment.

Group public key encryption supporting equality test without bilinear pairings

In cloud computing scenarios, it is a common approach to encrypt the data before uploading in order to maintain the privacy. Public key encryption with equality test (PKEET) provides a generic solution to equality comparisons on encrypted data. Considering the practical requirements of PKEET in group user scenarios, Ling et al. presented a group public key encryption scheme with equality test (G-PKEET) by utilizing the computationally expensive bilinear pairing operations. In this paper, we propose an efficient and verifiable group public key encryption with equality test construction without bilinear pairings (GPKEET/BP). Our proposal is developed from a basic observation that two points determine a straight line, and is proven to be indistinguishable against the chosen-ciphertext attacks (IND-CCA) in the random oracle model under the computational Diffie-Hellman (CDH) assumption. Theoretical analysis shows that our construction only involves several modular exponentiations in the encryption, decryption and test algorithms. The theoretical results are well supported by experimental simulations, which show that the test algorithm of GPKEET/BP performs about 92% faster than that of Ling et al.’s scheme. So our GPKEET/BP scheme turns out to be better suited for group ciphertext equality test situations.

Identity-Based Privacy Preserving Remote Data Integrity Checking With a Designated Verifier

The remote data possession checking mechanism can effectively verify the integrity of outsourced data, which can usually be divided into public verification and private verification. The verifier of public verification can be any cloud user, while private verification can only be the data owner. However, in most practical situations, the data owner expects that only a specific verifier can perform integrity checking tasks and that verifier cannot gain any knowledge about the data. Yan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> proposed a remote data possession checking scheme with the designated verifier, which can guarantee that only the designated verifier can check data integrity, whereas others cannot do it. However, this scheme relies on public key infrastructure technology and does not consider data privacy protection issues. To overcome these shortcomings, we propose an identity-based remote data possession checking scheme that satisfies the data owner’s requirement to specify a unique verifier. Moreover, in this scheme, we use a random integer to blind data integrity proof to protect data privacy and use Merkle hash tree structure to achieve dynamic update of data. At the same time, our scheme can avoid the complex certificate management in public key infrastructure. We proved the safety of our scheme based on the discrete logarithm assumption and the computational Diffie-Hellman assumption. Theoretical analysis and experimental results show that our scheme is feasible and effective in practical applications.

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.

Data Integrity Audit Based on Data Blinding for Cloud and Fog Environment

Cloud-fog computing is a novel computing model that expands the functionality of cloud computing, which provides various services through fog nodes. The issue of traditional data integrity auditing are low data security, slow data processing speed and low communication efficiency. To solve these problems, this paper proposes a data integrity audit scheme based on data blinding. This scheme uses the edge devices in the transmission node to establish a fog computing layer between the cloud service provider and the data owner to reduce transmission delay. The subordinate distribution relationship and weight between fog nodes dynamically allocate the optimal path and transmit the data to reduce transmission delay. At the same time, a blind factor is added to the integrity audit in the evidence generation process to avoid data leakage. This paper gives a security model and security proof based on computational Diffie-Hellman (CDH) assumptions. The experimental results show that the fog computing layer and blind factor are introduced into the data integrity audit process, which can reduce the data communication delay effectively and improve the security of data audit.

Leakage-Resilient Certificate-Based Authenticated Key Exchange Protocol

Certificate-based public key cryptography (CB-PKC) removes the problem of certificate management in traditional public key systems and avoids the key escrow problem in identity-based public key systems. In the past, many authenticated key exchange (AKE) protocols based on CB-PKC systems, called CB-AKE, were proposed to be applied to secure communications between two remote participants. However, these existing CB-AKE protocols become insecure since attackers could compute and obtain the whole secret key from some partial leaked information of the secret key by side channel attacks. In this paper, our goal is to propose the <inline-formula><tex-math notation="LaTeX">$first$</tex-math></inline-formula> CB-AKE protocol with the property to resist side channel attacks, called leakage-resilient CB-AKE (LR-CB-AKE). The proposed LR-CB-AKE protocol is formally proven to be secure in the generic bilinear group (GBG) model under the discrete logarithm (DL) and computational Diffie-Hellman (CDH) assumptions.

Unidirectional Identity-Based Proxy Re-Signature with Key Insulation in EHR Sharing System

The introduction of the electronic medical record (EHR) sharing system has made a great contribution to the management and sharing of healthcare data. Considering referral treatment for patients, the original signature needs to be converted into a re-signature that can be verified by the new organization. Proxy re-signature (PRS) can be applied to this scenario so that authenticity and nonrepudiation can still be insured for data. Unfortunately, the existing PRS schemes cannot realize forward and backward security. Therefore, this paper proposes the first PRS scheme that can provide key-insulated property, which can guarantee both the forward and backward security of the key. Although the leakage of the private key occurs at a certain moment, the forward and backward key will not be attacked. Thus, the purpose of key insulation is implemented. What’s more, it can update different corresponding private keys in infinite time periods without changing the identity information of the user as the public key. Besides, the unforgeability of our scheme is proved based on the extended Computational Diffie-Hellman assumption in the random oracle model. Finally, the experimental simulation demonstrates that our scheme is feasible and in possession of promising properties.

Obfuscating encrypted threshold signature algorithm and its applications in cloud computing.

Current cloud computing causes serious restrictions to safeguarding users’ data privacy. Since users’ sensitive data is submitted in unencrypted forms to remote machines possessed and operated by untrusted service providers, users’ sensitive data may be leaked by service providers. Program obfuscation shows the unique advantages that it can provide for cloud computing. In this paper, we construct an encrypted threshold signature functionality, which can outsource the threshold signing rights of users to cloud server securely by applying obfuscation, while revealing no more sensitive information. The obfuscator is proven to satisfy the average case virtual black box property and existentially unforgeable under the decisional linear (DLIN) assumption and computational Diffie-Hellman (CDH) assumption in the standard model. Moreover, we implement our scheme using the Java pairing-based cryptography library on a laptop.

Identity-Based Verifiable Aggregator Oblivious Encryption and Its Applications in Smart Grids

Verifiable aggregator oblivious encryption is a useful notion that not only allows an untrusted aggregator to compute aggregated data without learning any other information but also requires the aggregator to generate a proof of the aggregated data so that anyone can verify the accuracy. Since the aggregator does not learn data that may reveal users' private information and also cannot forge the aggregated data, verifiable aggregator oblivious encryption is suitable for privacy-preserving smart metering. However, NIST has recommended not using public-key-based cryptography in the smart grid because public-key cryptography cannot provide sufficient scalability. Thus, we propose a notion of identity-based verifiable aggregator oblivious encryption and design concrete schemes in this paper. We prove the aggregator oblivious security and aggregator unforgeability of our schemes via the smooth projective hash function and computational Diffie-Hellman assumption. Furthermore, based on our identity-based verifiable aggregator oblivious encryption scheme, we propose an identity-based data aggregation protocol for the smart grid and provide a security analysis in the context of seven typical attacks on smart grids. The implementation of our protocol via the Intel Edison platform shows that it is sufficiently lightweight for resource-constrained smart meters.