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Due to the current standard of Security Credential Management System (SCMS) for Vehicle-to-Everything (V2X) communications using asymmetric cryptography, specifically Elliptic-Curve Cryptography (ECC), which may be vulnerable to quantum computing attacks. Therefore, the V2X SCMS is threatened by quantum computing attacks. However, although the National Institute of Standards and Technology (NIST) has already selected Post-Quantum Cryptography (PQC) algorithms as the standard, the current PQC algorithms may have issues such as longer public key lengths, longer signature lengths, or lower signature generation and verification efficiency, which may not fully meet the requirements of V2X communication applications. In view of the challenges in V2X communication, such as packet length, signature generation and verification efficiency, security level, and vehicle privacy, this study proposes a hybrid certificate scheme of PQC and ECC. By leveraging the strengths of both PQC and ECC, this scheme aims to overcome the challenges in V2X communication. PQC is used to establish a security level resistant to quantum computing attacks, while ECC is utilized to establish anonymous certificates and reduce packet length to meet the requirements of V2X communication. In the practical experiments, the study implemented the SCMS end entity based on the Chunghwa Telecom SCMS and the Clientron On-Board Unit (OBU) to conduct field tests in Danhai New Town in New Taipei City. The performance of various existing hybrid certificate schemes combining PQC (e.g., Dilithium, Falcon, and SPHINCS+) and ECC is compared, and a practical solution is provided for V2X industries., Comment: The manuscript is written in Chinese language

In recent years, U.S. Department of Transportation has adopts Institute of Electrical and Electronics Engineers (IEEE) 1609 series to build the security credential management system (SCMS) for being the standard of connected cars in U.S. Furthermore, a butterfly key expansion (BKE) method in SCMS has been designed to provide pseudonym certificates for improving the privacy of connected cars. However, the BKE method is designed based on elliptic curve cryptography (ECC) in the standard of IEEE 1609.2.1, but more execution time is required for key expansion. Therefore, this study proposes an original efficient key expansion method, and the mathematical principles have been proposed to prove the encryption/decryption feasibility, car privacy, and method efficiency. In a practical environment, the proposed method improves the efficiency of key expansion method in IEEE 1609.2.1-2022 with the same security strength thousands of times., Comment: The manuscript was submitted to arXiv on 27 November 2023, but it was rejected on 2 December 2023. The appeal was submitted on 18 September 2024, and it was accepted on 9 January 2025. The manuscript is written in Chinese language

With the advancement of quantum computing technologies, recent years have seen increasing efforts to identify cryptographic methods resistant to quantum attacks and to establish post-quantum cryptography (PQC) approaches. Among these, hash-based digital signature algorithms (DSAs) are a notable category of PQC. Hash functions are not only utilized in digital signatures but are also widely applied in pseudorandom number generators (PRNGs). Building on the foundation of hash-based DSAs, this study proposes a modified approach that introduces a DSA based on PRNGs, suitable for one-time signature (OTS) applications. The study explores the security of the proposed PRNG-based OTS algorithm and validates its feasibility through experiments comparing various parameter configurations. These experiments examine key length, signature length, key generation time, signature generation time, and signature verification time under different parameter settings., Comment: in Chinese language

As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption methods, such as RSA, ElGamal, and Paillier, to quantum computing attacks, this study proposes a lattice-based post-quantum homomorphic encryption scheme. The approach leverages lattice cryptography to build resilience against quantum threats while enabling practical homomorphic encryption applications. This research provides mathematical proofs and computational examples, alongside a security analysis of the lattice-based post-quantum homomorphic encryption scheme. The findings are intended to serve as a reference for developers of homomorphic encryption applications, such as federated learning systems., Comment: in Chinese language

This study examines the performance and structural differences between the two primary standards for Security Credential Management Systems (SCMS) in Vehicular-to-Everything (V2X) communication: the North American IEEE standards and the European ETSI standards. It focuses on comparing their respective Public Key Infrastructure (PKI) architectures, certificate application workflows, and the formats of request/response messages used during certificate applications. The research includes a theoretical analysis of message length and security features inherent in each standard. Additionally, practical implementations of both systems are conducted to evaluate their efficiency in certificate management processes. Based on the findings, the study provides recommendations to guide future development of SCMS., Comment: in Chinese language

With the maturation of quantum computing technology, research has gradually shifted towards exploring its applications. Alongside the rise of artificial intelligence, various machine learning methods have been developed into quantum circuits and algorithms. Among them, Quantum Neural Networks (QNNs) can map inputs to quantum circuits through Feature Maps (FMs) and adjust parameter values via variational models, making them applicable in regression and classification tasks. However, designing a FM that is suitable for a given application problem is a significant challenge. In light of this, this study proposes an Enhanced Quantum Neural Network (EQNN), which includes an Enhanced Feature Map (EFM) designed in this research. This EFM effectively maps input variables to a value range more suitable for quantum computing, serving as the input to the variational model to improve accuracy. In the experimental environment, this study uses mobile data usage prediction as a case study, recommending appropriate rate plans based on users' mobile data usage. The proposed EQNN is compared with current mainstream QNNs, and experimental results show that the EQNN achieves higher accuracy with fewer quantum logic gates and converges to the optimal solution faster under different optimization algorithms., Comment: in Chinese language

This document focuses on developing a key expansion method based on the internet X.509 public key infrastructure and elliptic curve cryptography, which is applied in the context of anonymous voting. The method enables end entities to maintain anonymity from other end entities, the registration authority, and the certificate authority, while still allowing the validity of end entity certificates to be verified, thereby facilitating anonymous voting services., Comment: This document has been made available as a draft on the IETF website (https://datatracker.ietf.org/doc/draft-chen-x509-anonymous-voting/)

As quantum computing technology matures, it poses a threat to the security of mainstream asymmetric cryptographic methods. In response, the National Institute of Standards and Technology released the final version of post-quantum cryptographic (PQC) algorithm standards in August 2024. These post-quantum cryptographic algorithms are primarily based on lattice-based and hash-based cryptography. Therefore, this study proposes the Post-Quantum Cryptography Winternitz-Chen (PQCWC) anonymous scheme, aimed at exploring the design of anonymous schemes based on PQC for future applications in privacy protection. The anonymous scheme designed in this study is mainly built on the Winternitz signature scheme, which can prevent the original public key from being exposed in the certificate. Furthermore, the PQCWC anonymous scheme integrates the butterfly key expansion mechanism, proposing the first hash-based butterfly key expansion mechanism in the world, achieving anonymity for both the registration authority and the certificate authority, thereby fully protecting privacy. In the experimental environment, this study compares various hash algorithms, including Secure Hash Algorithm-1 (SHA-1), the SHA-2 series, the SHA-3 series, and the BLAKE series. The results demonstrate that the proposed anonymous scheme can achieve anonymity without increasing key length, signature length, key generation time, signature generation time, or signature verification time., Comment: in Chinese language

The blockchain system has emerged as one of the focal points of research in recent years, particularly in applications and services such as cryptocurrencies and smart contracts. In this context, the hash value serves as a crucial element in linking blocks within the blockchain, ensuring the integrity of block contents. Therefore, hash algorithms represent a vital security technology for ensuring the integrity and security of blockchain systems. This study primarily focuses on analyzing the security and execution efficiency of mainstream hash algorithms in the Proof of Work (PoW) calculations within blockchain systems. It proposes an evaluation factor and conducts comparative experiments to evaluate each hash algorithm. The experimental results indicate that there are no significant differences in the security aspects among SHA-2, SHA-3, and BLAKE2. However, SHA-2 and BLAKE2 demonstrate shorter computation times, indicating higher efficiency in execution.

In recent years, with the advancement of quantum computing, mainstream asymmetric cryptographic methods in the current Public Key Infrastructure (PKI) systems are gradually being threatened. Therefore, this study explores X.509 security certificates based on Post-Quantum Cryptography (PQC) and discusses implemented solutions. This study compares mainstream asymmetric cryptographic methods (including RSA and Elliptic Curve Digital Signature Algorithm (ECDSA)) with standard PQC methods (including Falcon, Dilithium, SPHINCS+), comparing the efficiency of certificate generation, signature generation, and signature verification. Finally, recommendations for a solution based on PQC for X.509 security certificates are proposed., Comment: The manuscript was submitted to arXiv on 6 May 2024, but it was rejected on 11 July 2024. The appeal was submitted on 11 July 2024, and it was accepted on 2 August 2024. The manuscript is written in Chinese language

In recent years, the countries of the world have drafted the specifications of connected cars; for instance, the Security Credential Management System (SCMS) has been proposed by United States Department of Transportation (USDOT), and the Cooperative Intelligent Transportation System (C-ITS) Credential Management System (CCMS) has been proposed by European Union (EU). Therefore, several companies have developed the technology and productions of connected cars based on specifications, and connected car patent portfolios have been proactively performed. Therefore, this study uses Patent Search System (PSS) to find and analyze the contents of patents for obtaining the innovation reports of connected cars according to patents. This study considers the single-factor and two-factors to analyze the relationships of annuals, major technology leaders, major market leaders, and major technology and applications for exploring the patent portfolios of technology leaders and market leaders in connected cars., Comment: in Chinese language

With the maturation of quantum computing technology, many cryptographic methods are gradually facing threats from quantum computing. Although the Grover algorithm can accelerate search speeds, current research indicates that the Advanced Encryption Standard (AES) method can still enhance security by increasing the length of the secret key. However, the AES method involves multiple modes in implementation, and not all modes are secure. Therefore, this study proposes a normalized Gini impurity (NGI) to verify the security of each mode, using encrypted images as a case study for empirical analysis. Furthermore, this study primarily compares the Electronic Codebook (ECB) mode, Cipher Block Chaining (CBC) mode, Counter (CTR) mode, Counter with CBC-Message Authentication Code (MAC) (CCM) mode, and Galois Counter Mode (GCM)., Comment: in Chinese language

In recent years, quantum computers and Shor quantum algorithm have posed a threat to current mainstream asymmetric cryptography methods (e.g. RSA and Elliptic Curve Cryptography (ECC)). Therefore, it is necessary to construct a Post-Quantum Cryptography (PQC) method to resist quantum computing attacks. Therefore, this study proposes a PQC-based neural network that maps a code-based PQC method to a neural network structure and enhances the security of ciphertexts with non-linear activation functions, random perturbation of ciphertexts, and uniform distribution of ciphertexts. In practical experiments, this study uses cellular network signals as a case study to demonstrate that encryption and decryption can be performed by the proposed PQC-based neural network with the uniform distribution of ciphertexts. In the future, the proposed PQC-based neural network could be applied to various applications., Comment: 2023 International Conference on Smart Systems for applications in Electrical Sciences (ICSSES) 7-8 July 2023. The manuscript was written in Chinese and submitted on 10 March 2023, but it was rejected on 22 April 2023. The appeal was accepted on 24 February 2024

With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic encryption algorithms have been proposed based on prime factorization problems, the algorithms may be cracked by quantum computing attacks. Therefore, this study proposes a post-quantum cryptography (PQC)-based homomorphic encryption method which includes the homomorphic encryption function based on a code-based cryptography method for avoiding quantum computing attacks. Subsection 3.2 proposes mathematical models to prove the feasibility of the proposed method, and Subsection 3.3 gives calculation examples to present the detailed steps of the proposed method. In experimental environments, the mainstream cryptography methods (i.e. RSA cryptography and elliptic curve cryptography (ECC)) have been compared, and the results show that the encryption time and decryption time of the proposed method are shorter than other cryptography methods. Furthermore, the proposed method is designed based on a non-negative matrix factorization problem (i.e. a NP problem) for resisting quantum computing attacks.

The current blockchain system for cryptocurrency exchanges primarily employs elliptic curve cryptography (ECC) for generating key pairs in wallets, and elliptic curve digital signature algorithms (ECDSA) for generating signatures in transactions. Consequently, with the maturation of quantum computing technology, the current blockchain system faces the risk of quantum computing attacks. Quantum computers may potentially counterfeit signatures produced by ECDSA. Therefore, this study analyzes the vulnerabilities of the current blockchain system to quantum computing attacks and proposes a post-quantum cryptography (PQC)-based blockchain system to enhance security by addressing and improving each identified weakness. Furthermore, this study proposes PQC-based wallets and PQC-based transactions, utilizing PQC digital signature algorithms to generate PQC-based signatures for the inputs in PQC-based transactions, thereby preventing signatures from being counterfeited by quantum computing. Experimental results demonstrate that the efficiency of the Dilithium algorithm, a PQC digital signature algorithm, in producing wallets, generating signatures, and verifying signatures surpasses that of ECDSA in the current blockchain system. Furthermore, the Dilithium algorithm also exhibits a higher security level., Comment: in Chinese language

In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate scheme has found application in security credential management systems (SCMS) and secure vehicle-to-everything (V2X) communication to issue pseudonymous certificates. However, the vulnerability of elliptic-curve cryptography (ECC) to polynomial-time attacks posed by quantum computing raises concerns. In order to enhance resistance against quantum computing threats, various post-quantum cryptography methods have been adopted as standard (e.g. Dilithium) or candidate standard methods (e.g. McEliece cryptography), but state of the art has proven to be challenging to implement implicit certificates using lattice-based cryptography methods. Therefore, this study proposes a post-quantum cryptography McEliece-Chen (PQCMC) based on an efficient random invertible matrix generation method to issue pseudonymous certificates with less computation time. The study provides mathematical models to validate the key expansion process for implicit certificates. Furthermore, comprehensive security evaluations and discussions are conducted to demonstrate that distinct implicit certificates can be linked to the same end entity. In experiments, a comparison is conducted between the certificate length and computation time to evaluate the performance of the proposed PQCMC. This study demonstrates the viability of the implicit certificate scheme based on PQC as a means of countering quantum computing threats.

In IEEE 1609.2 and IEEE 1609.2.1 standards for Vehicle-to-everything (V2X) secure communication, various security algorithms based on Elliptic Curve Cryptography (ECC) have been adopted and designed. To enhance the efficiency of the Security Credential Management System (SCMS), this study evaluates the computational time for key generation, key expansion, signature generation, and signature verification under different security strengths. This study discusses relevant techniques based on Elliptic Curve Qu-Vanstone (ECQV) implicit certificates, analyzes the length of uncompressed elliptic curve points, compressed elliptic curve points, explicit certificates, and implicit certificates. Furthermore, this study proposes mathematical models to demonstrate the probability of ECQV cracking and provides suggestions for mitigating ECQV cracking risks., Comment: in Chinese language

In Vehicle-to-Everything (V2X) communications, providing accurate information and safeguarding the privacy of end entities is one of the crucial information security issues. Therefore, several international standardization organizations have begun to develop V2X communication security standards in recent years. For instance, the IEEE 1609.2.1 standard designs a Security Credential Management System (SCMS) that specifies certificate application and issuance processes, as well as certificate revocation processes. Furthermore, the IEEE 1609.2 standard defines certificate formats and Secure Protocol Data Units (SPDUs) for secure data transmission based on these standards. As a result, end entity manufacturers and SCMS providers worldwide have started building V2X security systems in accordance with these standards and conducting interoperability testing. Although international standards mainly employ Elliptic-Curve Cryptography (ECC) for signature/verification and encryption/decryption functions, performance analysis remains a crucial issue for the practical deployment of these systems. Therefore, this study implements end entities and a SCMS conforming to IEEE 1609.2 and IEEE 1609.2.1 standards. It measures the computation and transmission times for each security communication action within the system from the perspective of end entities and identifies potential system bottlenecks. In the experimental results, this study analyzes the most performance-intensive actions and provides relevant suggestions for enhancing system efficiency for SCMS developers to reference., Comment: in Chinese language

This study mainly modifies the butterfly key expansion (BKE) mechanism and applies it to the healthcare system. The system mainly includes a Root Certificate Authority (RCA), an Enrollment Certificate Authority (ECA), a Pseudonym Certificate Authority (PCA), a Registration Authority (RA), and End Entities (EEs)(i.e. user devices). Certificates can be issued by the RCA to the ECA, PCA, and RA to make them legal entities in the system. The ECA then issues device certificates (similar to identification cards for devices) to the EEs (e.g. blood pressure monitors). When patients use EEs to measure physiological information, the RA verifies that the EE is legal based on the issued multiple pseudonym certificates by the PCA. The EE then uses the pseudonym certificates to send physiological information to the RA, ensuring data integrity and non-repudiation, while also preventing identity information from being stolen. To verify the pseudonymous certificate-based healthcare system proposed in this study, the security of the system was verified using the security strengths defined by the National Institute of Standards and Technology (NIST) in the United States. Furthermore, as the BKE mechanism is primarily based on Elliptic Curve Cryptography (ECC), this study also verified the efficiency under different security strengths. Furthermore, under 256 of security strength, the mean computation time of key expansion is between 24186.584 microseconds and 57894.552 microseconds, so more than 18 public keys could be generated in one second., Comment: in Chinese language

With the maturity of web services, containers, and cloud computing technologies, large services in traditional systems (e.g. the computation services of machine learning and artificial intelligence) are gradually being broken down into many microservices to increase service reusability and flexibility. Therefore, this study proposes an efficiency analysis framework based on queuing models to analyze the efficiency difference of breaking down traditional large services into n microservices. For generalization, this study considers different service time distributions (e.g. exponential distribution of service time and fixed service time) and explores the system efficiency in the worst-case and best-case scenarios through queuing models (i.e. M/M/1 queuing model and M/D/1 queuing model). In each experiment, it was shown that the total time required for the original large service was higher than that required for breaking it down into multiple microservices, so breaking it down into multiple microservices can improve system efficiency. It can also be observed that in the best-case scenario, the improvement effect becomes more significant with an increase in arrival rate. However, in the worst-case scenario, only slight improvement was achieved. This study found that breaking down into multiple microservices can effectively improve system efficiency and proved that when the computation time of the large service is evenly distributed among multiple microservices, the best improvement effect can be achieved. Therefore, this study's findings can serve as a reference guide for future development of microservice architecture., Comment: in Chinese language

In recent years, although some homomorphic encryption algorithms have been proposed to provide additive homomorphic encryption and multiplicative homomorphic encryption. However, similarity measures are required for searches and queries under homomorphic encrypted ciphertexts. Therefore, this study considers the cosine similarity, angular similarity, Tanimoto similarity, and soft cosine similarity and combines homomorphic encryption algorithms for similarity calculation. This study proposes mathematical models to prove the proposed homomorphic encryption-based similarity calculation methods and gives practical cases to explain the proposed methods. In experiments, the performance of the proposed homomorphic encryption-based similarity calculation methods has been evaluated under different security strengths., Comment: in Chinese language

If the information system is intruded or attacked by hackers, leaked personal data or serious economic loss may occur; the threats may be serious security problems. For security services, information security certification is built based on Public Key Infrastructure (PKI) to be an important tool for the services of bank transactions, natural person certificate, blockchain, and Hyper Text Transfer Protocol Secure (HTTPS). Therefore, this study uses Taiwan Patent Search System (TPSS) to find and analyze the contents of patents for obtaining the innovation reports of information security certification in Taiwan according to patents. This study considers the single-factor and two-factors to analyze the relationships of annuals, technology leaders, market leaders, and major applications for exploring the patent portfolios of technology leaders and market leaders in information security certification., Comment: in Chinese language

For avoiding the exposure of plaintexts in cloud environments, some homomorphic hashing algorithms have been proposed to generate the hash value of each plaintext, and cloud environments only store the hash values and calculate the hash values for future needs. However, longer hash value generation time and longer hash value summary time may be required by these homomorphic hashing algorithms with higher security strengths. Therefore, this study proposes a homomorphic hashing based on elliptic curve cryptography (ECC) to provide a homomorphic hashing function in accordance with the characteristics of ECC. Furthermore, mathematical models and practical cases have been given to prove the proposed method. In experiments, the results show that the proposed method have higher efficiency with different security strengths., Comment: in Chinese language

In recent years, several swarm intelligence optimization algorithms have been proposed to be applied for solving a variety of optimization problems. However, the values of several hyperparameters should be determined. For instance, although Particle Swarm Optimization (PSO) has been applied for several applications with higher optimization performance, the weights of inertial velocity, the particle's best known position and the swarm's best known position should be determined. Therefore, this study proposes an analytic framework to analyze the optimized average-fitness-function-value (AFFV) based on mathematical models for a variety of fitness functions. Furthermore, the optimized hyperparameter values could be determined with a lower AFFV for minimum cases. Experimental results show that the hyperparameter values from the proposed method can obtain higher efficiency convergences and lower AFFVs., Comment: in Chinese language

In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam) have been applied to the parameter optimization of several deep learning models with higher accuracies or lower errors. These optimization algorithms may need to set the values of several hyperparameters which include a learning rate, momentum coefficients, etc. Furthermore, the convergence speed and solution accuracy may be influenced by the values of hyperparameters. Therefore, this study proposes an analytical framework to use mathematical models for analyzing the mean error of each objective function based on various gradient descent algorithms. Moreover, the suitable value of each hyperparameter could be determined by minimizing the mean error. The principles of hyperparameter value setting have been generalized based on analysis results for model optimization. The experimental results show that higher efficiency convergences and lower errors can be obtained by the proposed method., Comment: in Chinese language