Public Key Cryptography Research Articles

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

Diffie-Hellman (DH) is the reason for the existence of a solution to the key distribution problem, where two parties can mutually set up a shared secret key over an insecure channel without any previous communication. In this study, a novel key exchange protocol based on the difficulty of the Discrete Logarithm Problem with Factor Problem (DLPFP) utilizing matrices in non-commutative semigroup over semiring is proposed. The security and complexity analyses of the protocol are discussed. Also, an ElGamal cryptosystem based on a group of invertible matrices and DLPFP over a semiring to encrypt the Sensitive Health Information (SHI) in healthcare systems is suggested.

Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers

Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05. Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers

IoT cryptography with privacy-preserving ElGamal public key cryptosystem using oppositional artificial flora optimization algorithm

IoT cryptography with privacy-preserving ElGamal public key cryptosystem using oppositional artificial flora optimization algorithm

Software implementation of systematic polar encoding based PKC-SPE cryptosystem for quantum cybersecurity

The ever-growing threats in cybersecurity growing with the rapid development of quantum computing, necessitates the development of robust and quantum-resistant cryptographic systems. This paper introduces a novel cryptosystem, Public Key Cryptosystem based on Systematic Polar Encoding (PKC-SPE), based on the combination of systematic polar encoding and public-key cryptographic principles. The Systematic Polar Encoding (SPE), derived from the well-established field of polar codes, serves as the foundation for this proposed cryptographic scheme. Here, we have used MATLAB Software to introduce and implement the PKC-SPE Cryptosystem. The paper examines key generation, encryption, and decryption algorithms, providing insights into the adaptability and efficiency of systematic polar encoding in public-key cryptography. We assess the efficiency of the PKC-SPE Cryptosystem in three aspects: key size, computational complexity, and system implementation timings. In addition, we compare the PKC-SPE Cryptosystem with PKC-PC cryptosystem and find that it has reduced key sizes (Pr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{r}$$\\end{document} = 0.8436 kbytes). The results obtained through simulations validate the effectiveness of the proposed cryptosystem and highlighting its potential for integration into real-world communication systems. Thus, in the paradigm shift to quantum computing, the PKC-SPE cryptosystem emerges as a promising candidate to secure digital communication in the quantum computing era.

MAN[sbnd]C: A masked autoencoder neural cryptography based encryption scheme for CT scan images

Sharing medical images securely is very important towards keeping patients’ data confidential. In this paper we propose MANC: a Masked Autoencoder Neural Cryptography based encryption scheme for sharing medical images. The proposed technique builds upon recently proposed masked autoencoders. In the original paper, the masked autoencoders are used as scalable self-supervised learners for computer vision which reconstruct portions of originally patched images. Here, the facility to obfuscate portions of input image and the ability to reconstruct original images is used an encryption-decryption scheme. In the final form, masked autoencoders are combined with neural cryptography consisting of a tree parity machine and Shamir Scheme for secret image sharing. The proposed technique MANC helps to recover the loss in image due to noise during secret sharing of image.•Uses recently proposed masked autoencoders, originally designed as scalable self-supervised learners for computer vision, in an encryption-decryption setup.•Combines autoencoders with neural cryptography - the advantage our proposed approach offers over existing technique is that (i) Neural cryptography is a new type of public key cryptography that is not based on number theory, requires less computing time and memory and is non-deterministic in nature, (ii) masked auto-encoders provide additional level of obfuscation through their deep learning architecture.•The proposed scheme was evaluated on dataset consisting of CT scans made public by The Cancer Imaging Archive (TCIA). The proposed method produces better RMSE values between the input the encrypted image and comparable correlation values between the input and the output image with respect to the existing techniques.

Proposed Development of NTRU Public Key Cryptosystem

As life progresses and develops, cryptography has become an indispensable science. The development of this science has given flexibility and security in exchanging information and data of various kinds by making it difficult for unauthorized persons to access them. In this paper, we proposed a new NTRU-like encryption scheme using a different mathematical structure for the public key, as well as for text encryption and decryption to have more resistance to attacks, which makes this method suitable for many applications.

Solving systems of algebraic equations over finite commutative rings and applications

AbstractSeveral problems in algebraic geometry and coding theory over finite rings are modeled by systems of algebraic equations. Among these problems, we have the rank decoding problem, which is used in the construction of public-key cryptosystems. A finite chain ring is a finite ring admitting exactly one maximal ideal and every ideal being generated by one element. In 2004, Nechaev and Mikhailov proposed two methods for solving systems of polynomial equations over finite chain rings. These methods used solutions over the residue field to construct all solutions step by step. However, for some types of algebraic equations, one simply needs partial solutions. In this paper, we combine two existing approaches to show how Gröbner bases over finite chain rings can be used to solve systems of algebraic equations over finite commutative rings. Then, we use skew polynomials and Plücker coordinates to show that some algebraic approaches used to solve the rank decoding problem and the MinRank problem over finite fields can be extended to finite principal ideal rings.

Decentralized Identity Authentication Mechanism: Integrating FIDO and Blockchain for Enhanced Security

FIDO (Fast Identity Online) is a set of network identity standards established by the FIDO Alliance. It employs a framework based on public key cryptography to facilitate multi-factor authentication (MFA) and biometric login, ensuring the robust protection of personal data associated with cloud accounts and ensuring the security of server-to-terminal device protocols during the login process. The FIDO Alliance has established three standards: FIDO Universal Second Factor (FIDO U2F), FIDO Universal Authentication Framework (FIDO UAF), and the Client to Authenticator Protocols (CTAP). The newer CTAP, also known as FIDO2, integrates passwordless login and two-factor authentication. Importantly, FIDO2’s support for major browsers enables users to authenticate their identities via FIDO2 across a broader range of platforms and devices, ushering in the era of passwordless authentication. In the FIDO2 framework, if a user’s device is stolen or compromised, then the private key may be compromised, and the public key stored on the FIDO2 server may be tampered with by attackers attempting to impersonate the user for identity authentication, posing a high risk to information security. Recognizing this, this study aims to propose a solution based on the FIDO2 framework, combined with blockchain technology and access control, called the FIDO2 blockchain architecture, to address existing security vulnerabilities in FIDO2. By leveraging the decentralized nature of the blockchain, the study addresses potential single points of failure in FIDO2 server centralized identity management systems, thereby enhancing system security and availability. Furthermore, the immutability of the blockchain ensures the integrity of public keys once securely stored on the chain, effectively reducing the risk of attackers impersonating user identities. Additionally, the study implements an access control mechanism to manage user permissions effectively, ensuring that only authorized users can access corresponding permissions and preventing unauthorized modifications and abuse. In addition to proposing practical solutions and steps, the study explains and addresses security concerns and conducts performance evaluations. Overall, this study brings higher levels of security and trustworthiness to FIDO2, providing a robust identity authentication solution.

Investigating CRYSTALS-Kyber Vulnerabilities: Attack Analysis and Mitigation

Significant advancements have been achieved in the field of quantum computing in recent years. If somebody ever creates a sufficiently strong quantum computer, many of the public-key cryptosystems in use today might be compromised. Kyber is a post-quantum encryption technique that depends on lattice problem hardness, and it was recently standardized. Despite extensive testing by the National Institute of Standards and Technology (NIST), new investigations have demonstrated the effectiveness of CRYSTALS-Kyber attacks and their applicability in non-controlled environments. We investigated CRYSTALS-Kyber’s susceptibility to side-channel attacks. In the reference implementation of Kyber512, additional functions can be compromised by employing the selected ciphertext. The implementation of the selected ciphertext allows the attacks to succeed. Real-time recovery of the entire secret key is possible for all assaults.

Secure Data in the Cloud with a Robust Hybrid Cryptographic Approach

Cloud security combines hybrid symmetric encryption and key management to protect user privacy. Our approach can be easily scaled to meet growing cloud data security needs. Cloud computing's basic tenet is resource sharing, which is used for data storage, analysis, and management. Since many people use cloud services and are spread out across the internet, they present many security risks. Hybrid clouds, which can be accessed from anywhere, provide numerous advantages. The security solution (infrastructure as a service) is compatible with many PaaS, SaaS, and even IaaS cloud services. Furthermore, it is consistent with the vast majority of existing cloud solutions. Cloud computing security can be strengthened by using hybrid public key cryptosystems. Concerns about data security have made many businesses wary of cloud computing. The study aims to secure cloud computing by combining the Rabin and Rivest-Shamir-Adleman (RSA) cryptographic models. Analyzing how well a combination of methods generates secure encryption and decryption keys for data. The pure RSA system has longer response times and requires fewer computations compared to the hybrid system.

Beyond Bitcoin the Future of Blockchain in Secure Communications

This research paper discusses the possibilities blockchain has for being used beyond its cryptocurrencies (e.g., Bitcoin) to provide better communication security, privacy, and dependability. The use of blockchain seals out the so-called single-collapsar points where failure is possible and from the attacks that are targeted on the centralized systems. Blockchain ensures the continuity, anonymity, and accessibility of data attacks through the use of modern cryptography which comprises, among other things, public-key cryptography. Discovering the potential and making it available is the power of this technology. It makes it safe from unauthorized access, preventing manipulation and addressing the issue of privacy with pseudonymity. It gives a longer path that can be used as an alternative to existing social platforms. Some issues facing blockchain's scalability, user experience, and regulatory questions are deterring its wider use in secure communications activities in the report. However, blockchain technology has its scaling solutions, aversion to privacy and security issues, adaptation to regulation, and integration with emerging technologies could be the basis for a massive transformation in security communications

Hazardous Chemicals Logistics Internet of Vehicles Based on Encryption Algorithm

With the advancement of information and communication technology, vehicles role in people's lives is not just for transportation but also equipment for the carrier of mobile communication. The new direction is provided by the Internet for the automobiles development and upgrading. Internet of Vehicles (IoVs) includes smart vehicles, Autonomous Vehicles (AVs) as well as roadside units (RSUs) that communicate for providing the enhanced transportation services such as high traffic efficiency and reduced congestion and accidents. In the hazardous chemical logistics sector, the integration of Internet of Vehicles (IoVs) introduces significant security, privacy, and trust challenges. Vulnerabilities to cyberattacks, such as hacking and data manipulation, threaten the integrity of sensitive information regarding hazardous cargo, while concerns about location privacy and data minimization arise due to the tracking of vehicle movements. Ensuring authentication, authorization, and compliance with regulatory standards is essential for building trust within the IoV ecosystem, as any compromise in supply chain integrity could lead to safety hazards or legal liabilities. Robust encryption algorithms like AES and RSA play a crucial role in securing data transmission, but proper implementation and key management practices are necessary to prevent cryptographic weaknesses. Addressing these issues comprehensively is vital for safeguarding the transportation of hazardous chemicals and ensuring the safety of both the environment and the public. IoVs, suffer from security, privacy and trust issues. In order to solve the problem of hazardous chemical logistics of encryption algorithm, the author proposed a research on the information security of the Internet of Vehicles. Firstly, the information characteristics of dangerous chemicals vehicles are analyzed, then analyze the Data Encryption Standard (DES) algorithm. Advanced Encryption Standard (AES) algorithm is analyzed in the symmetric cryptosystem and then RSA algorithm is analyzed in the public key cryptosystem. Finally, the performance of the algorithm and the characteristics of vehicle information are comprehensively analyzed. The security of Internet of Vehicle's data transmission is efficiently improved by the proposed method.

Upgrading strategies for long-haul quantum key distribution networks

Quantum key distribution (QKD) has become a promising option for transmitting sensitive data due to the increased maturity of QKD devices and the threat scalable quantum computers imposes on asymmetric public-key cryptosystems. By utilizing existing infrastructure, e.g., amplifier huts and dark fibers, the cost and complexity of deploying QKD networks (QKDNs) can be reduced. In this study, we develop a topology optimization algorithm that minimizes the cost of the QKDN deployment and maximizes the key capacity between any pair of nodes. We present three deployment upgrade strategies for facilitating the encryption of increasing throughput of QKD-secured optical transport networks and enabling a pay-as-you-grow approach. Comparing different strategies in a capacity-planning study allows operators to assess the scalability of deployments and upgrades. Depending on the availability requirements, our results compare the cost of protection measures. We confirm that adding trusted nodes is the most cost-efficient upgrading strategy based on our analysis.

Blockchain-Enhanced Sensor-as-a-Service (SEaaS) in IoT: Leveraging Blockchain for Efficient and Secure Sensing Data Transactions

As the Internet of Things (IoT) continues to revolutionize value-added services, its conventional architecture exhibits persistent scalability and security vulnerabilities, jeopardizing the trustworthiness of IoT-based services. These architectural limitations hinder the IoT’s Sensor-as-a-Service (SEaaS) model, which enables the commercial transmission of sensed data through cloud platforms. This study proposes an innovative computational framework that integrates decentralized blockchain technology into the IoT architectural design, specifically enhancing SEaaS efficiency. This research contributes to an optimized IoT architecture with decentralized blockchain operations and simplified public key encryption. Furthermore, this study introduces an advanced SEaaS model featuring innovative trading operations for sensed data among diverse stakeholders. At its core, this model presents a unique blockchain-based data-sharing mechanism that manages multiple aspects, from enrollment to validation. Evaluations conducted in a standard Python environment indicate that the proposed SEaaS model outperforms existing blockchain-based data-sharing models, demonstrating approximately 40% less energy consumption, 18% increased throughput, 16% reduced latency, and a 25% reduction in algorithm processing time. Ultimately, integrating a lightweight authentication mechanism using simplified public key cryptography within the blockchain establishes the model’s potential for efficient and secure data-sharing in IoT.

Privacy-preserving multi-party logistic regression in cloud computing

In recent years, machine learning techniques have been widely deployed in various fields. However, machine learning faces problems like high computation overhead, low training accuracy, and poor security due to data silos, privacy issues and communication limitations, especially in the environment of cloud computing. Logistic regression (LR) is a popular machine learning method used for prediction, while current LR algorithms suffer from high computation cost and communication burden due to interactions between users and cloud servers. In this paper, we propose a Privacy-Preserving Multi-party Logistic Regression (PPMLR) algorithm, which achieves privacy-preserving and non-interactive gradient descent regression training in machine learning. PPMLR uses the Distributed two Trapdoors Public-Key Cryptosystem (DT-PKC) as a main building block, which satisfies additive homomorphic encryption. Specifically, users go off-line after encrypting local private data, then the service provider (SP) trains the global logistic regression model by interacting with the cloud server (CS), so that the confidentiality and privacy of user’s private data can be guaranteed during the training process. We prove by detailed security proof that PPMLR guarantees data and model privacy. Finally, we conduct experiments on two popular medical datasets from the UCI machine learning repository. The experimental results show that PPMLR can conduct privacy-preserving training efficiently. Comparison with the stat-of-the-art Privacy-Preserving Logistic Regression Algorithm (PPLRA) shows that the model training time is reduced by about 4 times.

Survey: Recovering cryptographic keys from partial information, by example

Side-channel attacks targeting cryptography may leak only partial or indirect information about the secret keys. There are a variety of techniques in the literature for recovering secret keys from partial information. In this work, we survey several of the main families of partial key recovery algorithms for RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman, the classical public-key cryptosystems in common use today. We categorize the known techniques by the structure of the information that is learned by the attacker, and give simplified examples for each technique to illustrate the underlying ideas.

Secure data aggregation using quantum key management in IoT networks

The Internet of Things and Quantum Computing raise concerns, as Quantum IoT defines security that exploits quantum security management in IoT. The security of IoT is a significant concern for ensuring secure communications that must be appropriately protected to address key distribution challenges and ensure high security during data transmission. Therefore, in the critical context of IoT environments, secure data aggregation can provide access privileges for accessing network services. "Most data aggregation schemes achieve high computational efficiency; however, the cryptography mechanism faces challenges in finding a solution for the expected security desecration, especially with the advent of quantum computers utilizing public-key cryptosystems despite these limitations. In this paper, the Secure Data Aggregation using Quantum Key Management scheme, named SDA-QKM, employs public-key encryption to enhance the security level of data aggregation. The proposed system introduces traceability and stability checks for the keys to detect adversaries during the data aggregation process, providing efficient security and reducing authentication costs. Here the performance has been evaluated by comparing it with existing competing schemes in terms of data aggregation. The results demonstrate that SDA-QKM offers a robust security analysis against various threats, protecting privacy, authentication, and computation efficiency at a lower computational cost and communication overhead than existing systems.

Effective privacy preserving in cloud computing using position aware Merkle tree model

In this research manuscript, a new protocol is proposed for predicting the available space in the cloud and verifying the security of stored data. The protocol is utilized for learning the available data, and based on this learning, the available storage space is identified, after which the cloud service providers allow for data storage. The Integrity verification separates the private and the public data, which avoids privacy issues. The integration of the private data is done with the help of cloud service providers with respect to the third-party auditing (TPA). Earlier, public key cryptography and bilinear map technologies have been combined by the researchers, but the computation time and costs were high. To secure the integrity of the data storage, the client should execute several computations. Therefore, this research suggests a reliable and effective method called position-aware Merkle tree (PMT), which is implemented for ensuring data integrity. The proposed system uses a PMT that enables the TPA to perform multiple auditing tasks with high efficiency, less computational cost and computation time. Simulation results clearly shows that the developed PMT method consumed 0.00459 milliseconds of computation time, which is limited when compared to the existing models.

Vector finite fields of characteristic two as algebraic support of multivariate cryptography

The central issue of the development of the multivariate public key algorithms is the design of reversible non-linear mappings of $n$-dimensional vectors over a finite field, which can be represented in a form of a set of power polynomials. For the first time, finite fields $GF\left((2^d)^m\right)$ of characteristic two, represented in the form of $m$-dimensional finite algebras over the fields $GF(2^d)$ are introduced for implementing the said mappings as exponentiation operation. This technique allows one to eliminate the use of masking linear mappings, usually used in the known approaches to the design of multivariate cryptography algorithms and causing the sufficiently large size of the public key. The issues of using the fields $GF\left((2^d)^m\right)$ as algebraic support of non-linear mappings are considered, including selection of appropriate values of $m$ and $d$. In the proposed approach to development of the multivariate cryptography algorithms, a superposition of two non-linear mappings is used to define resultant hard-to-reverse mapping with a secret trap door. The used two non-linear mappings provide mutual masking of the corresponding reverse maps, due to which the size of the public key significantly reduces as compared with the known algorithms-analogues at a given security level.

Implementation of Cryptography Using the RSA (Rivest-Shamir-Adleman) Algorithm in Encoding Text Messages and Documents

Cryptography can be used in prevent data, one of the preventive measures is by encoding messages. Cryptography is the study of encoding messages or ways of data protection. In encoding the content of messages, there is an algorithm conventionally used nowadays, the RSA (Rivest-Shamir-Adleman) algorithm. The RSA algorithm is a method that has two different keys for each encryption and decryption process but is still interrelated to maintain security in processing the data. In finding the key, the RSA algorithm utilizes the rule of prime number. The larger the prime number used as a key, the harder it is to find a large number as a factor. This research describes the process of encrypting text messages, the content of documents using the RSA algorithm, and the key generation process. Those processes are done by converting plaintext into ciphertext using ASCII code, which is 256 long, and using PKCS (Public Key Cryptography Standards) is the encryption process on the RSA algorithm. This study uses Pyhton programming language to implement the RSA algorithm on text messages and documents. As a recommendation to the subsequent studies, it is proper to use algorithms or other programming languages to secure messages.