Hellman Problem Research Articles

An Efficient Pairing-Free Ciphertext-Policy Attribute-Based Encryption Scheme for Internet of Things

The Internet of Things (IoT) is a heterogeneous network composed of numerous dynamically connected devices. While it brings convenience, the IoT also faces serious challenges in data security. Ciphertext-policy attribute-based encryption (CP-ABE) is a promising cryptography method that supports fine-grained access control, offering a solution to the IoT’s security issues. However, existing CP-ABE schemes are inefficient and unsuitable for IoT devices with limited computing resources. To address this problem, this paper proposes an efficient pairing-free CP-ABE scheme for the IoT. The scheme is based on lightweight elliptic curve scalar multiplication and supports multi-authority and verifiable outsourced decryption. The proposed scheme satisfies indistinguishability against chosen-plaintext attacks (CPA) under the elliptic curve decisional Diffie–Hellman (ECDDH) problem. Performance analysis shows that our proposed scheme is more efficient and better suited to the IoT environment compared to existing schemes.

A heterogeneous ring signcryption scheme with privacy protection and conditional tracing for smart grid

Smart grid develops rapidly, but there are still security risks such as user privacy leakage, power data tampering and audit data inconsistency. The existing schemes to ensure data security mainly use traceable ring signcryption, which is applied in distributed application scenarios such as smart grid. Traceable ring signcryption can ensure the anonymity, integrity, unforgeability and confidentiality of data, and can trace the real identity of anonymous users. However, the traceability of these schemes is arbitrary, any actor can trace the identity of anonymous users, and they do not resolve disputes caused by tampered or inconsistent data. To remedy these deficiencies, we combine ring signcryption with consortium blockchain technology for the first time to achieve privacy protection and conditional tracing, which can effectively avoid anonymous user identity being revealed at will. Consortium blockchain is a semi-distributed P2P network that can solve data disputes and is suitable for organizations that require certain access control mechanisms such as smart grid. In this paper, we propose a heterogeneous ring signcryption scheme with privacy protection and conditional tracing (CTHRSC) which between certificateless cryptographic system (CLC) and public key infrastructure (PKI). Besides, we prove that our scheme is secure under the discrete logarithm problem (DLP) and decisional Diffie–Hellman problem (DDHP) in random oracle model (ROM). Compared with other signature or signcryption schemes, our advantages are satisfying conditional tracing and known temporary session key security (KTSKS), requiring less computation cost and communication overhead.

Self-Bilinear Map from One Way Encoding System and i𝒪

A bilinear map whose domain and target sets are identical is called a self-bilinear map. Original self-bilinear maps are defined over cyclic groups. Since the map itself reveals information about the underlying cyclic group, the Decisional Diffie–Hellman Problem (DDH) and the computational Diffie–Hellman (CDH) problem may be solved easily in some specific groups. This brings a lot of limitations to constructing secure self-bilinear schemes. As a compromise, a self-bilinear map with auxiliary information was proposed in CRYPTO’2014. In this paper, we construct this weak variant of a self-bilinear map from generic sets and indistinguishable obfuscation. These sets should own several properties. A new notion, One Way Encoding System (OWES), is proposed to summarize these properties. The new Encoding Division Problem (EDP) is defined to complete the security proof. The OWES can be built by making use of one level of graded encoding systems (GES). To construct a concrete self-bilinear map scheme, Garg, Gentry, and Halvei(GGH13) GES is adopted in our work. Even though the security of GGH13 was recently broken by Hu et al., their algorithm does not threaten our applications. At the end of this paper, some further considerations for the EDP for concrete construction are given to improve the confidence that EDP is indeed hard.

PF-IBDA: Provably secure and pairing-free identity-based deniable authentication protocol for MANET environments

Mobile Adhoc Network (MANET) is used in various real-time applications, such as e-voting, army tactical communication, health-care applications, disaster rescue, online message exchange, etc. However, source authentication and deniability are essential properties in such applications. Typically, these properties can be achieved using a deniable authentication (DA) protocol. With the help of a DA protocol, a mobile receiver node can directly verify the source, another mobile node, of a message without consulting a trusted third party (TTP). Recently, many identity-based deniable authentication (IBDA) protocols have been proposed. Most of these protocols are insecure and computationally expensive since they use costly operations, such as bilinear pairing and map-to-point hash function. We proposed a pairing-free identity-based deniable authentication (PF-IBDA) protocol for MANET environments. We proved that the PF-IBDA protocol could provide indistinguishability against adaptive chosen ciphertext attack (IND-CCA2) in the random oracle model (ROM) based on the hardness assumption of the elliptic curve computational Diffie–Hellman (ECCDH) problem. We have computed the execution time of PF-IBDA protocol in different security levels: 80-bit, 112-bit, 128-bit, 192-bit, and 256-bit on a mobile device using the JPBC library and compared it with the state-of-the-art IBDA protocols. We found that the proposed PF-IBDA protocol is more efficient than the existing IBDA protocols.

AP-HBSG: Authentication protocol for heterogeneous blockchain-based smart grid environment

The smart grid (SG) is one of the largest Internet of Things (IoT) applications. Therefore, it encompasses a variety of smart objects, including smart appliances, smart meters, and sensors, among others. All of these devices are scattered throughout the SG to serve a variety of objectives. As a result, the SG network architecture is exposed to various security threats. Furthermore, numerous authentication and key agreement techniques have been developed throughout the years to protect the communication between entities. However, several of them are homogeneous protocols, which means that only entities running similar cryptographic schemes can communicate. In addition, the SG communication system is centralized and susceptible to a single point of failure and management. Moreover, the existing protocols involve extensive cryptographic elements that cannot be processed by a smart meter’s (SM) computing power. To address the aforementioned issues, an AP-HBSG: authentication protocol for heterogeneous blockchain-based smart grid environment is designed. The designed protocol operates in a decentralized environment, thus eliminating a single point of failure and management. Furthermore, a blind signature is applied to the blockchain network to add authentication security among blockchain nodes. In addition, AP-HBSG is lightweight and it fits the SM computing capability. Moreover, AP-HBSG can protect the communication of parties interacting in a heterogeneous environment. On the other hand, the security of the presented protocol is analyzed in the random oracle model (ROM) and proved under the elliptic curve discrete logarithm (ECDL) problem and the computational Diffie–Hellman (CDH) problem. The protocol’s performance analysis shows that, compared to the most recent protocols, ours has lower communication and computation costs. The computation cost (ms) is 122,68, 216.86, 391.34, and 92.01 for WHZS, KKN, WLCTA, and ours, respectively. On the other hand, the communication cost (bytes) is 344, 184, 568, and 182 for WHZS, KKN, WLCTA, and ours, respectively.

Multi-party anonymous authentication scheme in heterogeneous network slicing

Network slicing is a logical network function that supports communication service requirements for specific usage scenarios or business models. It has become an essential factor in solving future network architecture. In recent years, heterogeneous network slicing between multiple autonomous domains has emerged, with significant limitations compared to single-domain networks. Data sharing in heterogeneous network slices challenge the confidentiality of sensitive data significantly. Preventing sensitive data from leaking and protecting core data have become urgent problems to be solved. Therefore, we propose a multi-party (multi-sender to multi-receiver) anonymous authentication scheme on certificateless cryptography(CLC) and identity-based cryptosystem(IBC) institutional domain Internet of Vehicles(IoV) to smart healthcare. Our scheme realizes heterogeneous communication between multiple senders and multiple receivers, and uses different system parameters for heterogeneous cryptographic systems. In this work, the limitation of one-to-many or many-to-one communication in existing heterogeneous networks is broken through. The proposed work utilizes the pseudo-identity generated by the trusted authority to communicate in IoV slices, ensuring the anonymity of the sender; The authorization Center TA can uniquely determine the true identity of the vehicle through pseudo-random values for traceability. What is more, the Lagrange interpolation formula is employed to prevent the leakage of the identities of smart healthcare slices, ensuring the anonymity of the receiver. Under the random oracle model, the proposed scheme has proved to satisfy unforgeability, confidentiality, and anonymity under the computational Diffie–Hellman problem. Experimental results indicate that our proposal achieves better performance than existing schemes.

Blockchain-assisted certificateless signcryption for vehicle-to-vehicle communication in VANETs

In vehicular ad-hoc networks (VANETs), real-time messages are used to guarantee transportation efficiency and passenger safety through the exchange among vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I). Therefore, the timely acceptance of safety messages is critical to establishing efficient and reliable communication in VANETs, which hinges on an efficient privacy-preserving authentication mechanism. However, these mechanisms face either security or performance problems. Although some state-of-the-art signcryption schemes meet the needs of security requirements of authentication, performance is not efficient in computational overhead for an increase of the bilinear pairing operations in batch unsigncryption verification. Therefore, we have designed an efficient and provably secure blockchain-assisted certificateless signcryption (BACLS) that provides a feasible security communication in theoretical analysis and experiments. The BACLS scheme ensures security against type-I and type-II attackers in regard to existential unforgeability against adaptively chosen message attacks (EUF-CMA) under the hardness assumption of the gap bilinear Diffie–Hellman problem and indistinguishability against adaptive chosen ciphertext attack (IND-CCA2) under the hardness assumption of the elliptic curve discrete logarithm problem in the random oracle model (ROM). The experiments demonstrate that the BACLS scheme significantly reduces unsigncryption computational costs and power consumption in contrast to state-of-the-art schemes, and promotes the development of a decentralized authentication system in VANETs.

A new Private Mutual Authentication scheme with group discovery

If users from the same group would like to securely distinguish each other and negotiate a session key, the Private Mutual Authentication (PMA) protocol is a good choice. During the interaction, no group information will be leaked to non-members, so as to protect the users’ private affiliations. In practical applications, users generally belong to multiple groups and would like to discover other members who are also authorized by more common groups. To solve such group discovery problem efficiently, we propose a new private mutual authentication scheme denoted by PMA-GD in this paper. The key idea of PMA-GD is derived from Authorized Private Set Intersection (APSI) based on Identity-Based Encryption(IBE), which achieves linear complexity in essence. In PMA-GD, two participants distinguish each other secretly only if the authentication policy is satisfied, which requires that the intersection of groups in common is non-empty or reaches a threshold value. Our proposal is designed on the basis of Bilinear Diffie–Hellman (BDH) problem, so it is provably secure in the Random Oracle Model(ROM). Compared with previous work, the performance analysis demonstrates that PMA-GD is still competitive and applicable for scenarios with limited resources.

SED-SGC: A scalable, efficient, and distributed secure group communication scheme based on superlattice PUF

A critical challenge in group communication is to guarantee the authenticity, integrity, and confidentiality of sensitive data, especially in scenarios with potential and prospective massive device access, such as the Internet of Everything (IoE). This paper explores a scalable, efficient, distributed secure group communication (SED-SGC) scheme that employs superlattice Physical Unclonable Function (PUF), tree structure, and the Decision Diffie–Hellman Problem. In SED-SGC, superlattice PUF facilitates lightweight, high-security mutual authentication and key generation. The Decision Diffie–Hellman Problem and tree structure construct group key agreement and dynamic member management protocol with logarithmic complexity, achieving forward and backward secrecy. Also, we demonstrate that SED-SGC can effectively guarantee security against multiple attack methods such as collusion attacks, man-in-the-middle attacks (MITM), and impersonation attacks.

Revocable identity‐based matchmaking encryption in the standard model

AbstractIdentity‐based Matchmaking Encryption (IB‐ME) is an extension notion of matchmaking encryption (CRYPTO 2019), where a sender and a receiver can specify an access policy for the other party. In IB‐ME, data encryption is performed by not only a receiver identity but also a sender's encryption key. Nevertheless, previous IB‐ME schemes have not considered the problem of efficient revocation. Hence, the authors introduce a new notion of revocable IB‐ME (RIB‐ME) and formalise the syntax and security model of RIB‐ME. In particular, the authors give an effective and simple construction of RIB‐ME in the standard model, whose security is reduced to the hardness of decisional bilinear Diffie—Hellman problem and computational Diffie—Hellman problem. In addition, the authors show two extensions of our RIB‐ME scheme to consider chosen‐ciphertext security and forward privacy.

Design of three-factor secure and efficient authentication and key-sharing protocol for IoT devices

The remarkable advance of the Internet of Things (IoT) has smoothed the way to the interconnection of various mobile devices in secure access and communication. In order to guarantee user privacy and anonymity in public networks, a large number of mutual authentication and key-sharing protocols between different IoT devices and multi-servers have been proposed. Due to resource-constrained and inefficient IoT devices, most previous protocols can confront assorted malicious attacks, such as eavesdropping, counterfeiting, chip cloning, device forgery, and other attacks. These attacks may be exposed the user’s private key or other sensitive data. To solve these problems, physical unclonable function (PUF) is a lightweight security primitive that utilizes random process deviations that cannot be controlled during chip manufacturing to generate device-unique digital signatures. In this paper, we combined the key-sharing scheme based on PUF on the hardware side, which solves relevant security problems such as device cloning and key tampering. Furthermore, we propose a three-factor secure and efficient authentication and key-sharing protocol, leveraging the inherent security properties of passwords, biometrics, and PUFs. We demonstrate the security of our proposed protocol based on computational Bilinear Diffie–Hellman Problem (BDH) and k-CAA hard problems and the Proverif tool. Compared with existing relevant protocols, our protocol meets various security properties and defends against varied security threats. The low computational cost, communication overhead, and device storage indicate that our protocol is applicable to resource-constrained IoT devices.

Practical Private Aggregation in Federated Learning Against Inference Attack

Federated learning (FL) enables multiple worker devices share local models trained on their private data to collaboratively train a machine learning model. However, local models are proved to imply the information about the private data and, thus, introduce much vulnerabilities to inference attacks where the adversary reconstructs or infers the sensitive information about the private data (e.g., labels, memberships, etc.) from the local models. To address this issue, existing works proposed homomorphic encryption, secure multiparty computation (SMC), and differential privacy methods. Nevertheless, the homomorphic encryption and SMC-based approaches are not applicable to large-scale FL scenarios as they incur substantial additional communication and computation costs and require secure channels to delivery keys. Moreover, differential privacy brings a substantial tradeoff between privacy budget and model performance. In this article, we propose a novel FL framework, which can protect the data privacy of worker devices against the inference attacks with minimal accuracy cost and low computation and communication cost, and does not rely on the secure pairwise communication channels. The main idea is to generate the lightweight keys based on computational Diffie–Hellman (CDH) problem to encrypt the local models, and the FL server can only get the sum of the local models of all worker devices without knowing the exact local model of any specific worker device. The extensive experimental results on three real-world data sets validate that the proposed FL framework can protect the data privacy of worker devices, and only incurs a small constant of computation and communication cost and a drop in test accuracy of no more than 1%.

Improved and Provably Secure ECC-Based Two-Factor Remote Authentication Scheme with Session Key Agreement

The remote authentication scheme is a cryptographic protocol incorporated by user–server applications to prevent unauthorized access and security attacks. Recently, a two-factor authentication scheme using hard problems in elliptic curve cryptography (ECC)—the elliptic curve discrete logarithm problem (ECDLP), elliptic curve computational Diffie–Hellman problem (ECCDHP), and elliptic curve factorization problem (ECFP)—was developed, but was unable to address several infeasibility issues while incurring high communication costs. Moreover, previous schemes were shown to be vulnerable to privileged insider attacks. Therefore, this research proposes an improved ECC-based authentication scheme with a session key agreement to rectify the infeasible computations and provide a mechanism for the password change/update phase. The formal security analysis proves that the scheme is provably secure under the random oracle model (ROM) and achieves mutual authentication using BAN logic. Based on the performance analysis, the proposed scheme resists the privileged insider attack and attains all of the security goals while keeping the computational costs lower than other schemes based on the three hard problems. Therefore, the findings suggest the potential applicability of the three hard problems in designing identification and authentication schemes in distributed computer networks.

An anonymity-preserving mobile user authentication protocol for global roaming services

In this article, we put forward an anonymity-preserving mobile user authentication protocol for global roaming services. It deals with Mutual Authentication and Key Agreement (MAKA) between Mobile User (MU) and Foreign Agent (FA). It replaces the traditional Elliptic Curve Computational Diffie–Hellman Problem (ECCDHP) by Elliptic Curve Factorization Problem (ECFP) to reduce the computational overhead of the authentication system while keeping the system security unaltered. It can preserve user anonymity and conditional privacy using session-wise unique anonymous identities of MU, where each anonymous identity hides the real identity in such a way so that only Home Agent (HA) can recompute it. Besides, our protocol also concentrates on the anonymity and conditional privacy of FA. It also provides a simplified revocation strategy which minimizes the revocation and re-registration costs of the authentication system. We validate the security features through informal and formal security analysis. Finally, we present a performance comparison, and discuss the efficiency of the proposed protocol.

On the decisional Diffie–Hellman problem for class group actions on oriented elliptic curves

We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order {mathcal {O}} in an unknown ideal class [{mathfrak {a}}] in {{,textrm{cl},}}({mathcal {O}}) that connects two given {mathcal {O}}-oriented elliptic curves (E, iota ) and (E', iota ') = [{mathfrak {a}}](E, iota ). When specialized to ordinary elliptic curves over finite fields, our method is conceptually simpler and often somewhat faster than a recent approach due to Castryck, Sotáková and Vercauteren, who rely on the Tate pairing instead. The main implication of our work is that it breaks the decisional Diffie–Hellman problem for practically all oriented elliptic curves that are acted upon by an even-order class group. It can also be used to better handle the worst cases in Wesolowski’s recent reduction from the vectorization problem for oriented elliptic curves to the endomorphism ring problem, leading to a method that always works in sub-exponential time.

ECAAP‐SG: Efficient certificateless anonymous authentication protocol for SG

AbstractA smart meter (SM) is an essential device within a smart grid (SG). It collects electrical power data from the customer and reports it to the service provider at regular intervals. Unfortunately, these regular reports may disclose confidential customer information without their knowledge. Moreover, SM is a device with limited resources, which means it cannot manage heavy security protocols. To mitigate these problems, an efficient certificateless anonymous authentication protocol for SG (ECAAP‐SG) protocol was designed. It cannot allow an adversary to tap into the communication channel and access exchanged information. In addition, the designed scheme fits SM's resource capacity. Furthermore, the authentication security provided by ECAAP‐SG guarantees that legal entities are communicating. Moreover, ECAAP‐SG provides key agreement security that establishes the session key. The established session key will be used to secure future communication. Besides, a random oracle model is used for the security analysis of the proposed protocol, and we prove that it is secure under the discrete logarithm problem and the computational Diffie–Hellman problem.

Practical Three-Factor Authentication Protocol Based on Elliptic Curve Cryptography for Industrial Internet of Things.

Because the majority of information in the industrial Internet of things (IIoT) is transmitted over an open and insecure channel, it is indispensable to design practical and secure authentication and key agreement protocols. Considering the weak computational power of sensors, many scholars have designed lightweight authentication protocols that achieve limited security properties. Moreover, these existing protocols are mostly implemented in a single-gateway scenario, whereas the multigateway scenario is not considered. To deal with these problems, this paper presents a novel three-factor authentication and key agreement protocol based on elliptic curve cryptography for IIoT environments. Based on the elliptic curve Diffie–Hellman problem, we present a protocol achieving desirable forward and backward secrecy. The proposed protocol applies to single-gateway and is also extended to multigateway simultaneously. A formal security analysis is described to prove the security of the proposed scheme. Finally, the comparison results demonstrate that our protocol provides more security attributes at a relatively lower computational cost.

Privacy-Preserving Mutual Heterogeneous Signcryption Schemes Based on 5G Network Slicing

With the wide application of 5G network, much research has been carried out in recent years toward the 5G network slicing technology in order to save 5G network resources and satisfy the service requirements of different users. Different public key cryptosystems may be deployed in different 5G network slicings. Therefore, heterogeneous signcryption is required to achieve secure communications between different 5G network slices. The existing scheme is a one-to-one communication between 5G network slicings. To obtain one-to-many and many-to-one secure communications, two new privacy-preserving heterogeneous signcryption schemes have been proposed in this article based on 5G network slicings, which can accomplish mutual communications between the public key infrastructure (PKI) and the certificateless public-key cryptography. In this work, we present PKI <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\to $ </tex-math></inline-formula> CLC completely anonymous multireceiver signcryption (PMRCHS) and CLC <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\to $ </tex-math></inline-formula> PKI heterogeneous aggregate signcryption (CPHAS) schemes based on the 5G Internet of Things (IoT) slicing and the 5G Internet of Vehicle (IoV) slicing. Under the random oracle model (ROM), the proposed schemes have proved to satisfy confidentiality and unforgeability under the computational Diffie–Hellman problem and discrete logarithm problem (DLP). Furthermore, we make comparisons of the proposed work with the existing works in terms of computational cost, communication cost, anonymity, and communication direction. The results show that the proposed schemes are more secure and effective.

A New Certificateless Signcryption Scheme for Securing Internet of Vehicles in the 5G Era

The application of digital signature technology to the Internet of vehicles (IoV) is affected by its network and communication environment. In the 5G era, the influx of a large number of intelligent devices into the mobile Internet requires a low transmission delay and power consumption as well as high-security requirements. To the best of our knowledge, a well-designed solution in which signcryption technology is used has not been proposed in the IoV research area. Motivated by the fact, a certificateless signcryption scheme based on the elliptic curve digital signature algorithm, in which pseudonym and timestamp mechanism are also considered, has been designed in this paper. We prove that the scheme proposed by us can be reduced to solving the difficulty of the computational Diffie–Hellman problem with a standard model, showing that the scheme meets requirements on both security and efficiency, which provides a comparative analysis with the state-of-the-art schemes in terms of security analysis, computational cost, and communication cost, demonstrating that the scheme proposed by us is suitable to be deployed in the IoV environment, which is of the characteristics of high-speed vehicle movement.

Breaking the Decisional Diffie–Hellman Problem for Class Group Actions Using Genus Theory: Extended Version

Breaking the Decisional Diffie–Hellman Problem for Class Group Actions Using Genus Theory: Extended Version