Pair Of Operators Research Articles

Identity-based authenticated multi-keyword searchable encryption scheme for cloud-assisted telemedicine information system

In cloud-assisted telemedicine information system (CA-TMIS), patients upload data containing their health metrics to the cloud. Doctors can access the patient’s data through the cloud, thereby alleviating the geographical restrictions in the traditional medical system. To ensure the privacy of the patient, the patient will encrypt the data before uploading the data. How doctors can search through numerous encrypted files to locate specific patients’ relevant data is a topic worthy of research. Searchable encryption technology can fulfill the function of ciphertext retrieval. Some existing searchable encryption schemes use single-keyword for searching, resulting in insufficient search accuracy and increased search costs for doctors. Multi-keyword searchable encryption schemes can address this issue. Therefore, in this paper, we propose an identity-based authenticated multi-keyword searchable encryption scheme, which leverages multiple keywords for combined searching, enhancing search accuracy. The scheme is proven to be resistant to keyword guessing attacks in the standard model. Compared to four other existing schemes, our scheme does not utilize pairing operations and offers higher efficiency advantages. Consequently, our scheme is more suitable for CA-TMIS.

Reduction of the Laplace sequence and sine-Gordon type equations

Abstract In this work, we continue the development of methods for constructing Lax pairs and recursion operators for nonlinear integrable hyperbolic equations of soliton type, previously proposed in the work of Habibullin et al. (2016 {\it J. Phys. A: Math. Theor.} {\bf 57} 015203). This approach is based on the use of the well-known theory of Laplace transforms. The article completes the proof that for any known integrable equation of sine-Gordon type, the sequence of Laplace transforms associated with its linearization admits a third-order finite-field reduction. It is shown that the found reductions are closely related to the Lax pair and recursion operators for both characteristic directions of the given hyperbolic equation. Previously unknown Lax pairs and recursion operators were constructed.

RATIONAL SHIFTS OF THE BASIC RACK’S PROFILE FOR WHEELS OF A CYLINDRICAL SPUR GEAR PAIR TO DECREASE TEETH WEAR

Purpose. It is to create a method for determination of such shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair, that during gear pair operation time the wear rate of a surface layer on the most wearing sections of the teeth’ involute surfaces will be minimal. Research methods are based on integrated application of the involute gear pair theory and tribological laws. The golden section method is used to minimize the function. Results. We have obtained a dimensionless quantity, which is a function of shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair. Values of this function are proportional to the greatest wear rate in the neighborhood of characteristic points on teeth’ involute profiles of these wheels. The method is created for determination of rational shift coefficients of the basic rack’s profile, which minimize the obtained dimensionless function, and which maximize the service life of the spur gear pair until the greatest worn-layer thickness on the teeth’ active surfaces reaches limiting permissible value. Scientific novelty. It is proved, that increasing of the worn-layer thickness during spur gear pair operation time will be occurring most rapidly in the neighborhood of certain characteristic points on teeth’ involute profiles of the wheels. Calculation model is elaborated for determination of the worn-layer thicknesses in the neighborhood of extreme active points on teeth’ profiles of the cylindrical spur gear pair and in the neighborhood of the lowest and the highest bounding points of single-pair contact. This model takes into account the influence of specific slides and numbers of wheels’ teeth as well as hardness values of teeth’ surface layer on the wear rates at characteristic points of teeth’ profiles. In addition, the model takes into account sharing of total force of the wheels interaction between two teeth pairs in double-pair contact and also a change of force transmitted by single pair of teeth when it comes into or go out of engagement. Practical value. Application of the created method for determination of shift coefficients of the basic rack’s profile is expedient in design of cylindrical spur gear pairs for machines and equipment, which operate in conditions when ingress of abrasive particles in the teeth engagement region is possible. An example of application of this method in design calculation of the cylindrical spur gear pair is given.

An optimized dynamic attribute-based searchable encryption scheme.

Cloud computing liberates enterprises and organizations from expensive data centers and complex IT infrastructures by offering the on-demand availability of vast storage and computing power over the internet. Among the many service models in practice, the public cloud for its operation cost saving, flexibility, and better customer support popularity in individuals and organizations. Nonetheless, this shift in the trusted domain from the concerned users to the third-party service providers pops up many privacy and security concerns. These concerns hindrance the wide adaptation for many of its potential applications. Furthermore, classical encryption techniques render the encrypted data useless for many of its valuable operations. The combined concept of attribute-based encryption (ABE) and searchable encryption (SE), commonly known as attribute-based keyword searching (ABKS), emerges as a promising technology for these concerns. However, most of the contemporary ABE-based keyword searching schemes incorporate costly pairing and computationally heavy secret sharing mechanisms for its realization. Our proposed scheme avoids the expensive bilinear pairing operation during the searching operation and costly Lagrange interpolation for secret reconstruction. Besides, our proposed scheme enables the updation of access control policy without entirely re-encrypting the ciphertext. The security of our scheme in the selective-set model is proved under the Decisional Bilinear Diffie-Hellmen (DBDH) assumption and collision-free. Finally, the experimental results and performance evaluation demonstrate its communication and overall efficiency.

TrustCNAV: Certificateless aggregate authentication of civil navigation messages in GNSS

The Global Navigation Satellite System (GNSS) is capable of accurate positioning because it can provide high-precision data. These data are transmitted to the receiver in the form of navigation messages, called civil navigation messages (CNAV). As it is transmitted in an open, transparent environment without data integrity protection mechanisms and secure data transmission measures, the CNAV is suspected to spoofing attacks. In 2023, the OPSGROUP has received approximately 50 reports of GPS spoofing activity. A spoofed plane's navigation system will show it as being in a different place - a security risk if a jet is guided to fly into a hostile country's airspace. To prevent the forging of GNSS positioning data by spoofing attacks targeting CNAV, we propose a certificateless aggregation authentication for CNAV by using the elliptic curve discrete logarithm problem and the combination of the GNAV structural characteristics, called TrustCNAV. Security proof and performance analysis indicate that this authentication scheme can resist spoofing attacks and ensure data security of CNAV, also it avoids pairing operations with high computational complexity, thus meeting security requirements without causing too much time and communication consumption.

Research on lubrication mechanism of plunger pair considering viscosity temperature and pressure effect

Aiming at the key problems such as serious friction and wear and large leakage of aviation piston pumps operating under high-speed and high-pressure harsh conditions, the lubrication characteristics of aviation plunger pumps are studied in this paper. In order to improve the lubrication performance of the plunger pump, as well as its working efficiency and service life, the equations of pressure, the thickness, and the leakage of the plunger pair oil film under the combined actions of viscosity temperature and pressure under pressure flow, shear flow, and cylinder elastic deformation are established. The finite difference method is used to analyze the lubrication characteristics and the leakage of the plunger pair under these four different conditions: considering, respectively, the effect of viscosity temperature and pressure, only considering the effect of viscosity temperature or viscosity pressure, without considering the effect of viscosity temperature and viscosity pressure. As a result, coupled by the effects of viscosity temperature and viscosity pressure, when the temperature increases from 20 to 60 °C, the oil film pressure increases, and the thickness decreases faster. When the temperature increases from 60 to 120 °C, the oil film pressure increases and the thickness decreases slower When the contact length of the plunger pair increases from 17 to 37 mm, the leakage ratio decreases more rapidly, and when it is greater than 37 mm, it decreases more slowly. The following conclusions were obtained: the viscosity of lubricating fluid is greatly affected by temperature and pressure. The viscosity decreases and increases hyperbolically with the increase in temperature and pressure, the maximum oil film pressure when considering the effect of viscosity temperature and pressure was significantly greater than that without considering the viscosity temperature and pressure, and the minimum oil film thickness was much smaller than that without considering the viscosity temperature and pressure. The leakage curve when considering the viscosity temperature and pressure effect was obviously different from when only considering a single factor or not considering the viscosity temperature and pressure effect. The magnitude of leakage in the four cases is: considering the viscosity temperature effect, considering the viscosity temperature and pressure effect, not considering the viscosity temperature and pressure effect, and considering the viscosity pressure effect. This study can provide a reference for the accurate theoretical design and safe and stable operation of the plunger pair in the plunger pump.

The Outcome after Endovascular and Open Repair of Abdominal Aortic Aneurysms-A Binational Study Conducted between 1998 and 2017.

Objective: We aimed to analyse patient outcomes following open (OAR) or endovascular repair (EVAR) of an abdominal aortic aneurysm (AAA) in Finland and Sweden from 1998 to 2017. Both intact and ruptured AAAs (rAAAs) were included in the analysis. Methods: Patient-level data from national registries in Finland and Sweden were analysed, pairing operations for intact and ruptured AAA repair with mortality data (date of death). All-cause mortality was the primary endpoint. Anonymized patient data from both countries were pooled, comprising a total of 32,324 operations. Ruptured and intact AAAs were considered separately. In total, EVAR was performed on 9619 intact AAAs and 1470 rAAAs, while OAR was performed on 13,241 intact AAAs and 7994 rAAAs. The patient's age, sex and the date of operation were obtained as demographic information. Cox regression and Kaplan-Meier analyses were used to evaluate long-term (10-year) survival after the treatment of AAA or rAAA with either modality. Kaplan-Meier analysis was performed in three different age groups (<65 years, 65-79 years and ≥80 years). Results: Considering all age groups together, the 1-, 3- and 10-year Kaplan-Meier survival rates after EVAR were 93.4%, 80.5% and 35.3%, respectively, for intact AAA repair and 67.2%, 55.9% and 22.2%, respectively, for rAAA repair. For OAR of intact AAAs, the 1-, 3- and 10-year Kaplan-Meier survival rates were 92.1%, 84.8% and 48.7%, respectively. The respective rates for OAR of rAAAs were 55.4%, 49.3% and 24.6%. In a Cox regression analysis, a more recent year of operation was associated with improved survival, and older age affected survival negatively for both intact and ruptured AAA repair. If patients survived the first 90 days after the operation, the survival after intact AAA repair was 13.5 years for those <65 years (general population: 18.0 years), and 7.3 years for those ≥80 years (general population: 7.9 years). After rAAA repair, the mean survival was 13.1 years for patients <65 years and 5.5 years for patients ≥80 years, respectively. Conclusions: The long-term survival of patients undergoing intact AAA treatment at the age of 80 or older is close to that of the general population, provided they survive the operation. Conversely, for patients younger than 65, the long-term survival is markedly worse. The long-term survival of AAA patients has improved over time. Open surgery is still a safe and effective option for young patients undergoing intact AAA repair. Our results support the ESVS guidelines recommendation of EVAR being the first-line treatment for patients with rAAA.

Anonymous data sharing scheme for resource-constrained internet of things environments

With the rapid development of Internet of Things (IoT) technology in industrial, agricultural, medical and other fields, IoT terminal devices face security and privacy challenges when sharing data. Among them, ensuring data confidentiality, achieving dual-side privacy protection, and performing reliable data integrity verification are basic requirements. Especially in resource-constrained environments, limitations in the storage, computing, and communication capabilities of devices increase the difficulty of implementing these security safeguards. To address this problem, this paper proposes a resource-constrained anonymous data-sharing scheme (ADS-RC) for the IoT. In ADS-RC, we use elliptic curve operations to replace computation-intensive bilinear pairing operations, thereby reducing the computational and communication burden on end devices. We combine an anonymous verifiable algorithm and an attribute encryption algorithm to ensure double anonymity and data confidentiality during the data-sharing process. To deal with potential dishonest behavior, this solution supports the revocation of malicious user permissions. In addition, we designed a batch data integrity verification algorithm and stored verification evidence on the blockchain to ensure the security and traceability of data during transmission and storage. Through experimental verification, the ADS-RC scheme achieves reasonable efficiency in correctness, security and efficiency, providing a new solution for data sharing in resource-constrained IoT environments.

A Privacy-Preserving Friend Matching Scheme Based on Attribute Encryption in Mobile Social Networks

In mobile social networks, users can easily communicate with others through smart devices. Therefore, the protection of user privacy in social networks is becoming a significant subject. To solve this problem, this paper proposes a fine-grained data access control scheme that uses attributes to match friends. In our scheme, the friend-making parties generate friend preference and self-description lists, respectively, realizing attribute hiding by converting friendship preference into ciphertext access control policies and self-description into attribute keys. The social platform matches user profiles to quickly eliminate unmatched users and avoids invalid decryption. In order to reduce the computational burden and communication cost of mobile devices, we adopt an algorithm mechanism for outsourcing decryption. When the user meets the matching conditions, the algorithm outsources the bilinear pair operation with large computation to the friend server. After that, the user finally decrypts the ciphertext. Security analysis shows that our scheme is safe and effective. In addition, performance evaluation shows that the proposed scheme is efficient and practical.

ASSESSMENT OF THE PERFORMANCE OF FRICTION PAIRS OF AN AXIAL PISTON PUMP BASED ON A REFINED DYNAMIC MODEL

The article presents a method for testing the performance of the main friction pair of an axial piston pump. To describe the force interaction of the parts of a tribological pair, a precise dynamic model has been compiled, which provides a number of classical criteria for the operation of a friction pair under given conditions. The dynamic model used a calculated theoretical indicator diagram, the process of switching working fluids, the type of loaded pump and the force interaction of friction pair parts. Comparative results of calculating the performance of the main friction pairs developed using classical methods and a composite dynamic model are presented.

Hierarchical Identity-Based Authenticated Encryption with Keyword Search over encrypted cloud data

With the rapid development of cloud computing technology, cloud storage services are becoming more and more mature. However, the storage of sensitive data on remote servers poses privacy risks and is presently a source of concern. Searchable Encryption (SE) is an effective method for protecting sensitive data while preserving server-side searchability. Hierarchical Public key Encryption with Keyword Search (HPEKS), a new variant of SE, allows users with higher access permission to search over encrypted data sent to lower-level users. To the best of our knowledge, there exist only four HPEKS schemes in the literature. Two of them are in traditional public-key setting, and the remaining ones are identity-based public key cryptosystems. Unfortunately, all of the four existing HPEKS schemes are vulnerable against inside Keyword Guessing Attacks (KGAs). Moreover, all of the existing HPEKS schemes are based on the computationally expensive bilinear pairing operation which dramatically increases the computational costs. To overcome these issues, in this paper, we introduce the notion of Hierarchical Identity-Based Authenticated Encryption with Keyword Search (HIBAEKS). We formulate a security model for HIBAEKS and propose an efficient pairing-free HIBAEKS scheme. We then prove that the proposed HIBAEKS scheme is secure under the defined security model and is resistant against KGAs. Finally, we compare our proposed scheme with related constructions regarding security requirements, computational and communication costs to indicate the overall superiority of our proposed scheme.

Improved RSA dynamic cryptographic accumulator-based anonymous batch authentication scheme for Internet of Vehicles

The Internet of Vehicles (IoV) provides various services to vehicles through information sharing to ensure road safety and improve traffic efficiency. However, malicious attackers can challenge the privacy and security systems of the IoV by conducting security attacks. Currently, many schemes use bilinear pairing or elliptic curves to construct authentication systems, ensuring anonymity of vehicle identities and message security. However, these schemes suffer drawbacks such as low computational efficiency and high communication overhead in highly dynamic IoV. Therefore, we propose a new efficient certificateless message authentication scheme. The proposed scheme constructs a lightweight security authentication protocol by improving the RSA dynamic accumulator and combining it with non-interactive discrete logarithm zero-knowledge proofs. In addition, our scheme eliminates the need for bilinear pairing operations, thereby reducing computational overhead. Simultaneously, it enables real-time tracking and revocation of malicious vehicle identities. Security analysis shows that our scheme can be reduced to a secure S-RSA assumption under the random oracle model, meeting various security requirements of the IoV. Performance analysis shows that our scheme diminishes not only the computational overhead but also the communication overhead.

A quantum-secure certificateless aggregate signature protocol for vehicular ad hoc networks

Vehicular ad hoc networks (VANETs) have revolutionized communication between vehicles and infrastructure, notably enhancing traffic management and passenger safety. However, VANETs are vulnerable to security threats, especially regarding data authenticity. Aggregate signature is a powerful technique that reduces computational and communication burdens by aggregating multiple signatures from different signers into a single signature. Traditional aggregate signature schemes, based on large prime number decomposition and the discrete logarithm problem, cannot effectively resist quantum attacks. This paper introduces a novel quantum secure certificateless aggregate signature (QSCLAS) scheme designed to enhance data security and privacy in VANETs. Our proposed scheme employs the number theory research unit (NTRU) algorithm. As a lattice-based cryptographic algorithm, NTRU is renowned for its security against quantum computer attacks, making it an essential component of our quantum-secure solution. By eliminating the need for expensive bilinear pairing operations, our proposed scheme achieves high efficiency and practicality in resource-limited VANETs environments. The security analysis demonstrates our scheme's resilience against both Type-I and Type-II adversaries in the random oracle model under the small integer solution (SIS) problem on the NTRU lattice. Furthermore, compared with existing approaches, the results illustrate that our proposed scheme offers significant advantages in signature generation and verification cost, as well as lower transmission overhead than other lattice-based schemes, thereby making it highly suitable for VANETs environments.

Blockchain-based efficient verifiable outsourced attribute-based encryption in cloud

Attribute-based encryption (ABE) has been widely applied in cloud services for access control. However, a large number of pairing operations required for decryption affect the wide use of ABE on lightweight devices. A general solution is to outsource the heavy computation to the cloud service provider (CSP), leaving the lighter computation to the data user. Nevertheless, it is impractical to assume that the CSP will provide free services. A recent ABE scheme with payable outsourced decryption ABEPOD (TIFS’20) provides a solution for the above payment issue. The CSP is generally untrusted, however, ABEPOD does not offer a verification mechanism for the data user to verify the correctness of the message. Moreover, the use of dual key pairs in ABEPOD incurs a significant computational overhead for data users during the key generation phase. We address the above issues by presenting a new blockchain-based verifiable outsourced attribute-based encryption system that enables data users to verify the correctness of plaintexts. We implement batch verification using homomorphic technical to optimize the verification process. We use the technique of dichotomous search to accurately locate problematic plaintexts. Additionally, we optimize three key-generation algorithms to transfer the computational cost from the data user to the key generation center. We offer the formal security models and the instantiation system with security analysis. As compared to ABEPOD, we further optimize the key-generation algorithms such that the computational overhead of transformation-key and verification-key generation for data users is reduced from O(Ω) to O(1) and reduced by half respectively, where Ω is the number of attributes.

Paired Kernels and Their Applications

This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^2$$\\end{document}. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence of a minimal Toeplitz kernel containing any projected paired kernel and, more generally, any nearly S∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S^*$$\\end{document}-invariant subspace of H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^2$$\\end{document}, is derived. The results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.

Units Coordination, Combinatorial Reasoning, and the Multiplication Principle: The Case of Ashley, an Advanced Stage 2 College Student

ABSTRACT The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research literature, however, has not captured, generally, how students establish these unit relationships. We provide a second order model of an advanced stage 2 college student, Ashley, who had no prior combinatorics instruction, as she engaged in solving combinatorics problems that we considered to involve the MP. Our findings suggest that Ashley began by interpreting combinatorics problems using her whole number iterative units coordination scheme. Through engagement with the teacher-researcher, Ashley constructed combinatorial composites using a pairing operation, units coordination, and units simplification. We also found that Ashley was able to create a three-level-of-unit structure in activity, and to use notation that she produced to re-instantiate the reasoning that produced this unit structure. Doing so provides novel insights into how advanced stage 2 students, especially those at the college level, can use notation to manage complex unit relationships.

Cryptanalysis and improvement of “group public key encryption scheme supporting equality test without bilinear pairings”

Public key encryption with equality test (PKEET) is a novel primitive which supports equality comparisons on two encrypted messages. Currently, most of the existing PKEET schemes are based on bilinear pairing and require heavy computational overheads. To address this issue, Shen et al. recently proposed an efficient group public key encryption supporting equality test without bilinear pairings scheme. Compared with other schemes, their scheme reduces the usage of expensive bilinear pairing operations and enjoys higher computation efficiency. They claimed that their scheme achieved one-wayness security in the random oracle model and resisted offline message recovery attack. In this letter, we analyze Shen et al.'s scheme through two concrete attacks and demonstrate that their scheme can not support the above two security requirements. An improved scheme is provided to overcome the security vulnerabilities in their scheme. Performance analysis shows that our improved scheme has certain advantages in both computation overhead and storage overhead.

Increasing the operational parameters of worm gears

An analysis of factors that reduce the operational parameters of worm gearboxes has been carried out. Equations for calculating the efficiency of a worm gear, contact pressure, and the residual service life are given. It is shown that the friction angle and friction coefficient depend on the material of the worm and wheel teeth, the roughness of the working surfaces of the worm pair matings, the quality of the lubrication, and the sliding speed. Significant contact pressures and friction losses in meshing lead to heat generation, a decrease in efficiency and service life of the worm gear. To produce a worm gear with a maximum radius of a conjugate globoid-cylindrical pair with an involute profile, it is proposed to use rotational turning of the globoid worm turns with a multi-blade forcedly rotating tool, and the wheel teeth with a hob cutter. A nickel antifriction solid lubricating coating containing carbon nanotubes has increased hardness and resistance to abrasion. A method for manufacturing a ZT-type worm gear is proposed, as well as methods that reduce contact stresses and the coefficient of friction during operation of a mating worm pair to increase the service life of worm gears.

The effect of gear-manufacturing quality on the mechanical and thermal responses of a polymer-gear pair

Abstract Gear-manufacturing quality affects the load sharing between the meshing gears as well as the load distribution along the width of the tooth. This study aims to investigate the effect of gear-manufacturing quality on the mechanical and thermal states of polymer-gear pairs and consequently on their lifetime. The deviations of the geometric quality parameters, i.e., the lead profile and pitch, were found to have a substantial effect on the stress (root and flank) state of the gear. The effect of the lead deviation was found to be most pronounced for the quality grades Q12 to Q10, where depending on the load, a 30–80% stress reduction was observed when improving the gear quality from Q12 to Q10. Improving the quality from Q10 to Q8 did not lead to a substantial improvement in the load distribution and the observed stress reduction was in range of 5–20%. Similar trends were found for the pitch deviation, where again the most pronounced stress reduction was seen when improving the quality grade from Q12 to Q10. The study reveals where the most effective changes, leading to an increased gear-life, can be achieved. Improving the gear quality grade from Q12 to Q11 proved to have a much more substantial effect than improving the gear quality from Q9 to Q8. Considering that improving the gear quality from Q12 to Q11 or even Q10 can be achieved by a proper tool design and corrective iterations with the right process parameters, while improving the quality from Q9 to Q8 is by far more challenging. A novel methodology is proposed to assess the effect of the gear’s quality on the generation of heat and the resulting operational temperature. The proposed methodology enables more accurate prediction of the gear pair’s operating temperature.

Cryptanalysis and Improvement of Several Identity-Based Authenticated and Pairing-Free Key Agreement Protocols for IoT Applications.

Internet of Things (IoT) applications have been increasingly developed. Authenticated key agreement (AKA) plays an essential role in secure communication in IoT applications. Without the PKI certificate and high time-complexity bilinear pairing operations, identity-based AKA (ID-AKA) protocols without pairings are more suitable for protecting the keys in IoT applications. In recent years, many pairing-free ID-AKA protocols have been proposed. Moreover, these protocols have some security flaws or relatively extensive computation and communication efficiency. Focusing on these problems, the security analyses of some recently proposed protocols have been provided first. We then proposed a family of eCK secure ID-AKA protocols without pairings to solve these security problems, which can be applied in IoT applications to guarantee communication security. Meanwhile, the security proofs of these proposed ID-AKA protocols are provided, which show they can hold provable eCK security. Some more efficient instantiations have been provided, which show the efficient performance of these proposed ID-AKA protocols. Moreover, comparisons with similar schemes have shown that these protocols have the least computation and communication efficiency at the same time.