Some applications of the traces of Frobenius of elliptic curves in a certain family

In this paper we study genus-4 curves obtained as double covers of elliptic curves. Firstly we shall give explicit defining equations of such curves with explicit criterion for whether it is nonsingular, and show the irreducibility of the long polynomial determining whether the genus-4 curve is nonsingular or not, in any characteristic ≠ 2 , 3 . Secondly, as an application, we enumerate superspecial genus-4 double covers of elliptic curves in small characteristic.

Visual Cryptography (VC) is a method of encryption that allows images to be encrypted in such a manner that their decryption can be accomplished simply by viewing, which eliminates the need for complex algorithms. This method is crucial for protecting the sensitive visual data during transmission, which ensures its confidentiality. In light of this, the current research proposes a new method called Self-Improved Secretary Bird Optimization algorithm (SI-SBO)-based Visual Cryptography, which aims to enhance the security and efficiency of image encryption. Embedding and Extraction are the two main processes in this proposed method. The initial input for this method consists of three original and two secret images. The encryption employs a sharing image construction method based on Modified Principal Component Analysis (MPCA), followed by Kronecker product-based encryption using keys produced by the SI-SBO algorithm. A one-time password (OTP) is created using the HMAC-based One-time Password (HOTP) technique and integrated into a Modified Elliptic Curve Cryptography (MECC) algorithm, which is then securely sent to the client. For decryption, the process starts with MECC-based decryption, followed by Kronecker product-based decryption using the OTP for authentication. Finally, the MPCA-based encryption is decrypted, and the original secret images are reconstructed. The significance of this SI-SBO method lies in its capacity to improve security by integrating multiple encryption techniques and protective measures. To assess its effectiveness, the method has undergone several evaluations, which confirm its ability to securely transmit and reconstruct secret images in Visual Cryptography applications.

The [Formula: see text] symmetric Pascal matrix [Formula: see text] is a generalized discrete time and band-limiting operator for the binomial transform and its eigenvectors are generalized discrete prolate spheroidal wave functions which we call binomial prolates. Their generating functions are also generalized prolate spheroidal functions in the sense that they are simultaneously eigenfunctions of a third-order differential operator and an integral operator over the line [Formula: see text]. For even, positive integers N, we obtain an explicit formula for the generating function of an eigenvector of the symmetric Pascal matrix with eigenvalue 1. When [Formula: see text] for an odd prime p, we show that the generating function is equivalent modulo p to [Formula: see text], where [Formula: see text] is the number of points on the Legendre elliptic curve [Formula: see text] over the finite field [Formula: see text]. Furthermore when [Formula: see text], our generating function is the square of a period of [Formula: see text] modulo [Formula: see text] in the open p-adic unit disk.

Enhanced elliptic curve Diffie–Hellman key exchange for multimedia security using AHC with cubic Bézier and Arnold transform

As a critical infrastructure for new energy vehicles, the Electric Vehicle Charging System (EVCS) is gradually integrating into household daily usage scenarios, leveraging its environmental and economic advantages. For securely enabling the charging service from EVCS, the technology of authentication and key agreement (AKA) can ensure that only legal entities can access the charging data without charging accident resulted from the malicious attacker. To our knowledge, existing related state-of-the-art (SOTA) AKA schemes entails extensive parameter computation prior to verification, not only results in an inevitable susceptibility to Denial-of-Service (DoS) attacks but also prolong authentication procedure in the EVCS and lead to diminished charging efficiency. To illustrate this deficiency more concretely, existing schemes typically require the verifier to perform multiple expensive cryptographic operations (such as scalar multiplications) before determining a request's legitimacy. An attacker can exploit this by flooding the verifier with forged requests, forcing it to expend computational resources on each one. In contrast, our proposed E2C2AKA protocol, by embedding a pre-shared secret, enables the verifier to first perform a lightweight hash-based verification. Only after a packet is validated as legitimate does the protocol proceed to the more expensive ECC operations, thereby effectively neutralizing DoS threats. To address these issues, this study, based on elliptic curve cryptography (ECC), designs a robust E2C2AKA protocol. Security analysis and performance analysis demonstrate that compared to SOTA, the designed E2C2AKA holds more robustness in security and streamlines AKA procedure in efficiency and so can be a good candidate for securing charging service in EVCS.

The deep penetration of IoT terminals in water systems, healthcare, transportation, and other fields has exacerbated security threats such as cyber-physical attacks and traffic anomalies. However, traditional anomaly detection methods have limitations such as dependence on labeled data, weak generalization ability, high resource consumption, and prominent privacy risks. Although Vision Transformer (ViT) has the advantage of capturing global features, it is difficult to directly adapt to resource-constrained IoT terminals. In existing research, hybrid deep learning models have improved detection accuracy, but lightweight ViT fusion models lack terminal adaptability and multi-modal data fusion applications are scarce. The balance between dynamic scheduling and privacy protection in end-edge-cloud collaboration still needs to be broken through. To address the above issues, this paper proposes an IoT terminal AI security anomaly detection system based on the ViT-Transformer fusion model: adopting a three-level end-edge-cloud collaborative architecture, integrating multi-modal data such as network traffic, sensor timing, and side channel signals, and achieving cross-modal feature fusion through tokenization; combining pruning, distillation, and quantization optimization strategies to increase the model compression ratio to 70%; introducing Elliptic Curve Certificateless Encryption (CL-PKE) and Batch Listing Signature (BLS) batch authentication to ensure data security, and using federated learning to aggregate edge model updates and optimize global performance. Experiments were conducted on public datasets such as IoT-23 and UCI, as well as a self-made testbed. The results show that the model achieves an accuracy of 89.2% and an F1-score of 0.87 in multi-modal anomaly detection, with a terminal inference delay of 90ms and a memory footprint of 30MB, adapting to low-computing devices such as RPi4B and Arduino; CL-PKE resists brute force attacks for 5.2e6 seconds, and batch authentication for 100 terminals takes only 75ms; it exhibits excellent generalization across smart home, industrial IoT, and other scenarios, with a defense success rate of 85.3% against FGSM attacks. This study effectively addresses the resource bottleneck and security pain points of existing methods, providing an efficient and reliable technical solution for IoT terminal security.

The rapid growth of internet of thing (IoT) has increased the need for secure communication among resource-constrained devices using lightweight protocols such as message queuing telemetry transport (MQTT) and message queuing telemetry transport for sensor network (MQTT-SN). Traditional certificate-based solutions introduce significant computational and memory overhead for low-power devices. This paper proposes the hybrid lightweight protocol (HLP), a certificate-free approach combining elliptic-curve key exchange, hash-based message authentication code (HMAC)-based authentication, and ChaCha20-Poly1305 encryption. HLP uses pre-shared keys to reduce handshake complexity while maintaining confidentiality, integrity, and mutual authentication across MQTT and MQTT-SN environments. A Python-based implementation using paho-mqtt was evaluated in a constrained-device testbed. Experimental results show that HLP achieves lower handshake latency (-20–24 ms) and reduced bandwidth overhead (-130 bytes) compared with elliptic curve Diffie-Hellman ephemeral-pre-shared key (ECDHE-PSK) and elliptic curve Diffie-Hellman ephemeral-elliptic curve digital signature algorithm (ECDHE-ECDSA), while still supporting forward secrecy. These findings demonstrate that HLP is an efficient and practical solution for securing IoT communications on constrained devices.

Block lightweight encryption scheme for securing internet of things data and information

In Wireless Sensor Networks (WSNs), communication security and energy efficiency are the main design issues. Security can be provided using techniques for attack detection, cryptographic encryption and decryption, access control, key management, and trust management. Most of the existing secure routing algorithms focus on handling one method of security. However, a combined approach for security will ensure better security in communication. Hence, a new security model is proposed in this paper based on encryption and trust modelling for providing improved security. In the literature, many secure routing algorithms are present, but they use only one level of security. This article proposes a multi-aspect security model by using trust management and different types of algorithms for data encryption depending on the sensitivity levels of data. For less sensitive data, the sender encrypts the data using the Hill cipher. If the data are medium-sensitive, they are encrypted using the Advanced Data Encryption Standard (AES). Finally, if the data are highly sensitive, the sender uses the Modified Elliptic Curve Cryptography (MECC) for encryption. Finally, one routing algorithm named Fuzzy-Based Encrypted Data Routing Algorithm (FBEDRA) is proposed using Ant Colony Optimization (ACO) meta-heuristics with fuzzy rules for secured route discovery in WSN. The main outcomes of the proposed FBEDRA include increased packet delivery rate, security, and throughput, but a reduction in delay and energy usage.

The growing reliance upon cloud settings has rendered secure transmission of information essential. This study introduces the future-ready DNA-based cryptography (FRDNAC) paradigm, which combines DNA-based encryption with the feedback-assisted archimedes optimization algorithm to achieve efficient key generation and improved security. FRDNAC was assessed in comparison to contemporary optimization approaches such as the feedback artificial tree, the archimedes optimization algorithm, the blue monkey optimization, the coot optimization algorithm, the butterfly optimization algorithm, the shark smell optimization, the whale optimization algorithm, and the lightweight encryption system, as well as traditional encryption methods such as DNA encryption, Blowfish, Rivest-Shamir-Adleman (RSA), the advanced encryption system, and the elliptic curve cryptography. Experimental findings demonstrate FRDNAC's exceptional encryption and decryption efficacy, achieving an encryption duration of 0.11s (key length 4.0), surpassing rivals like FAT (0.29s) and LES (0.20s). Furthermore, FRDNAC markedly enhanced memory efficiency, rendering it suitable for resource-limited cloud settings. Security evaluations indicate its robustness against cryptographic threats, encompassing known-plaintext attack, chosen-plaintext attack, and brute force attack. Despite obstacles in real-time key generation and computational cost, FRDNAC presents itself as a highly safe and efficient cryptographic framework appropriate for cloud-based applications. Its strong security framework establishes it as a viable solution for sectors requiring high-performance encryption in evolving digital environments.

Device-to-device (D2D) communication is expected to become a key component of 6G and IoT systems, enabling low-latency and infrastructure-independent connectivity. A major challenge is to establish secure session keys between previously unknown devices without relying on an online trusted third party, while also ensuring resilience against future quantum adversaries. This paper proposes a lightweight hybrid authentication and key agreement protocol for decentralized D2D communication. The approach combines IPFS-assisted distributed key discovery with a two-message protocol that uses post-quantum key encapsulation for long-term confidentiality, while retaining elliptic curve cryptography (ECC) for efficient real-time authentication under classical security assumptions.This design reflects the different temporal security requirements of confidentiality and authentication and provides a practical trade-off between quantum resilience and computational efficiency. The proposed scheme achieves mutual authentication under classical ECC assumptions, secure session key establishment, and resistance against common attacks, while providing post-quantum confidentiality protection against future quantum adversaries and removing the need for an online trusted third party (TTP) during protocol execution. The results demonstrate that the protocol offers a competitive and practical solution for secure decentralized D2D communication in IoT and future 6G environments.

With the widespread adoption of cryptocurrencies, the ability to conduct continuous offline payments has increasingly become a critical technological requirement. In network-constrained scenarios, current dual-offline payment technologies are useful for single transactions. However, their limitations in continuous payment scenarios have become increasingly evident, making them unable to meet real-world application needs. This has prompted the industry to demand more urgent innovations in research on continuous offline payment capabilities. To address these challenges, this paper proposes a continuous dual-offline payment system capable of supporting multiple continuous payments. The system integrates elliptic curve cryptography (ECC) and zero-knowledge proof (ZKP) technology to generate secure asset credentials, ensuring both immutability and privacy credentials throughout the offline payment lifecycle. A dynamic credential decomposition mechanism enables the splitting of input credentials into change credentials and receipt credentials, facilitating uninterrupted dual-offline payments between hardware wallets. Additionally, it incorporates a batch verification scheme based on smart contracts, utilizing zero-balance verification and chained hash tracing to ensure payment uniqueness and prevent double-spending attacks, thereby guaranteeing the verifiability and validity of payment settlements. Experimental evaluations demonstrate that the proposed system reduces gas consumption per payment and improves execution efficiency during batch processing, combining high security with strong performance. This research provides a feasible solution for the application of digital currencies in offline scenarios, carrying significant theoretical value and practical significance for driving technological innovation and application expansion in the cryptocurrency field. In addition to cryptocurrency payments, the proposed system is also applicable to IoT and sensor network environments. Many IoT devices operate in disconnected or network-limited areas and require secure micro-transactions. Our dual-offline payment mechanism supports such scenarios, as the main cryptographic operations are lightweight enough for typical IoT hardware. This further extends the practical value of our system beyond traditional cryptocurrency payments.

An innovative image encryption scheme combining Vigenere-Affine and elliptic curve over a finite body

The rapid growth of Intelligent Transportation Systems (ITSs) necessitates secure and efficient Vehicle-to-Everything (V2X) communication. However, existing Physical Unclonable Function (PUF)-based schemes often suffer from modeling vulnerabilities and high overheads. This paper proposes a decentralized, dynamic, anonymous authentication protocol tailored for Vehicular Ad Hoc Networks (VANETs). By integrating Elliptic Curve Cryptography (ECC) with highly reliable Self-Adaption Deviation Locking PUFs (SDL PUFs), we design a dynamic Challenge–Response Pair (CRP) obfuscation mechanism. This mechanism effectively mitigates modeling threats, reducing the prediction success rate of machine learning (ML) and deep learning (DL) attacks by approximately 35% compared to raw SDL PUFs. The protocol ensures identity untraceability and forward secrecy through anonymous identifiers and ephemeral session keys. Security is formally verified under the Real-or-Random (ROR) model and validated using the AVISPA tool. Simulations in SUMO and Omnetpp demonstrate that the protocol is highly efficient, achieving a low computational overhead of 6.77 ms per entity and a communication cost of 192 bytes. Compared to state-of-the-art approaches, our solution provides superior robustness against advanced modeling attacks and significantly reduces latency, making it suitable for resource-constrained V2X environments.

Main conjectures for non-CM elliptic curves at good ordinary primes

Abstract A hardware-bound key management architecture is developed, which is used in digital currency system with controlled access, verifiable node identity and high reliability encryption protection. Firstly, random input generation, polynomial coefficient construction, share encapsulation and commitment verification are all limited within the isolated execution boundary of hardware security module, thus separating the key generation path from the untrusted host environment. Secondly, the distributed key generation (DKG) mechanism is combined with the threshold signature workflow of DKG aggregation based on flexible turn optimization Schnorr threshold, allowing multiple nodes to complete collaborative signature without exposing local key shares. Through layered communication, controlled state evolution and certified standby node taking over, life cycle synchronization, multi-area recovery and disaster recovery switching are realized, thus ensuring the continuity of the system under node failure and regional failure. The results show that the average entropy reaches 0.99795 bit/bit under the condition of 16 nodes and 40 independent experiments for each node, while the test pass rate according to National Institute of Standards and Technology (NIST) Special Publication (SP) 800-22 remains at 96.4%. In the case of 30% malicious coefficient injection, the hardware-bound DKG structure still maintains the verification pass rate of 89.1%. When the proportion of abnormal nodes rose to 40%, the completion rate of DKG remained at 94.1%. The blocking rates of share substitution attack and offset injection attack reach 98.7% and 97.4% respectively. In the performance evaluation, the elliptic curve cryptography operation is accelerated by 3.8 times to 4.5 times with the assistance of hardware security module, and the number of transactions per second can reach 1165 under high load conditions. The proposed architecture enhances the execution integrity, key isolation and operation continuity of multi-node digital currency infrastructure. This design provides a reproducible and fault-tolerant security path for trusted digital currency deployment.

In recent years, new energy vehicle ownership and charging loads have shown a rapid upward trend, and the amount of data on charging platforms has increased dramatically. However, the traditional centralized data storage method will be more and more difficult to cope with the increasing massive data. For this reason, blockchain technology is introduced, and a charging transaction data storage scheme is designed by using blockchain technology to select a number of charging stations as data center nodes in the new energy vehicle charging platform. In this shared charging pile cross-domain data security protection system running consensus process adopts EPBFT consensus algorithm, the data center nodes use the consensus mechanism between the encrypted data for decentralized synchronous storage. Finally, relevant experiments verify the effectiveness of the cross-domain data security protection system for shared charging piles of new energy vehicles proposed in this paper. In the security performance test experiments, the time-consuming method of this paper can meet the efficiency requirements of new energy vehicle charging data aggregation scenarios, and at the same time, it ensures that the charging data aggregation process is not tampered with and privacy protection. In the operation efficiency comparison experiments, the protocol proposed in this paper in the generation of authentication messages needed to increase the random number of four times the elliptic curve on the multiplier operation, authentication messages and other comparative schemes compared to the length of the token there is a significant reduction in the signature checking process is more efficient advantage. In the charging right allocation analysis, by adding the credit value method, this paper's method can improve the reasonableness of the charging right allocation of each charging station, and at the same time, it can incentivize each charging station to obtain a higher credit value through better quality service. This proves the superiority of the system designed in this paper.

Authentication mechanism between different parties of the Internet of Things system is significant to prevent unauthorized access, especially in the Industrial environments, where multiple factors collaborate to achieve that goal.Most traditional multifactor authentication schemes are known to be static and require equivalent verification across all devices, reducing usability to a dynamic risk context.On the other hand, the current advances in Machine Learning techniques encourage their integration in many systems where security is required, but in an efficient way.The work in this paper implements a multifactor authentication mechanism powered by a reinforcement learning technique to adjust the authentication factors based on the contextual risk level.The learning and testing phases are carried out using a modified dataset named mTON-IoT with multifactor authentication features that have been derived from the publicly known cybersecurity dataset TON-IoT.The practical implementation of the proposed system involves using the Double Q-Learning technique within a Raspberry Pi network and securely exchanging data using Elliptic Curve Cryptography over the Message Queuing Telemetry Transport protocol.The experimental results show a high decision accuracy of 99.72%, confirming the trained model's ability to obtain an intelligent balance between security and usability in resource-constrained IoT.

The rapid evolution of 5G networks introduces unprecedented high-speed communication and massive connectivity, but it also intensifies security challenges. Ensuring confidentiality, integrity, and availability of data requires robust encryption mechanisms. This study evaluates the performance and overhead of Advanced Encryption Standard (AES), Rivest–Shamir–Adleman (RSA), and Elliptic Curve Cryptography (ECC) in 5G networks using simulation-based analysis. Metrics considered include latency (ms), throughput (%), encryption/decryption time per MB, and computational cost on UE-class hardware, providing quantitative comparison across typical 5G scenarios (high mobility eMBB, URLLC, and mMTCIoT devices). Key findings: AES achieves low latency and high throughput for bulk data; ECC provides secure, lightweight key exchange; RSA is suitable only for session key establishment due to higher computational overhead. Overall, hybrid AES+ECC provides the best tradeoff between security and performance in realistic 5G environments.