Public Key Cryptography Research Articles

Attacking cryptosystems by means of virus machines

The security that resides in the public-key cryptosystems relies on the presumed computational hardness of mathematical problems behind the systems themselves (e.g. the semiprime factorization problem in the RSA cryptosystem), that is because there is not known any polynomial time (classical) algorithm to solve them. The paper focuses on the computing paradigm of virus machines within the area of Unconventional Computing and Natural Computing. Virus machines, which incorporate concepts of virology and computer science, are considered as number computing devices with the environment. The paper designs a virus machine that solves a generalization of the semiprime factorization problem and verifies it formally.

A Post-Quantum Digital Signature Using Verkle Trees and Lattices

Research on quantum computers has advanced significantly in recent years. If humanity ever creates an effective quantum computer, many of the present public key cryptosystems can be compromised. These cryptosystems are currently found in many commercial products. We have devised solutions that seem to protect us from quantum attacks, but they are unsafe and inefficient for use in everyday life. In the paper, hash-based digital signature techniques are analyzed. A Merkle-tree-based digital signature is assessed. Using a Verkle tree and vector commitments, the paper explores novel ideas. The authors of this article present a unique technology for developing a post-quantum digital signature system using state-of-the-art Verkle tree technology. A Verkle tree, vector commitments, and vector commitments based on lattices for post-quantum features are used for this purpose. The concepts of post-quantum signature design utilizing a Verkle tree are also provided in the paper.

A comparative analysis of public key cryptographic algorithms: RSA, ELGamal, and elliptic curve encryption

Cryptography stands as an indispensable and efficient facet within the expansive field of information security. It offers a reliable method for ensuring the confidentiality and integrity of data during the complex process of information transmission between a sender and a recipient. Beyond this, exclusive decryption privileges are meticulously reserved for the designated recipient. This individual holds the exclusive authority to decipher the transmitted information, which has been encrypted by the key holder beforehand. This scholarly investigation introduces and delves into three prevalent cryptographic algorithms: RSA, El-Gamal, and Elliptic Curve Cryptography. It offers a discerning examination and contrast of the underlying mathematical challenges associated with each sophisticated method. The discourse unfolds a detailed comparative analysis of these three pivotal algorithms, zeroing in on their crucial aspects such as key size length and operational running time. The in-depth exploration within this study aims to shed light on the intricate workings, strengths, and potential limitations of RSA, El-Gamal, and Elliptic Curve Cryptography. By unraveling these aspects, the study contributes to a richer understanding and more informed choices in the practical application of cryptographic algorithms, enhancing the overarching realm of information security in an increasingly digital and interconnected world.

Machine to Machine Authenticated Key Agreement with Forward Secrecy for Internet of Things

Internet of things (IoT), is the interconnection via the Internet of computing devices embedded in everyday objects, enabling them to send and receive data. The communication is through the internet hence susceptible to security and privacy attacks. Consequently, authenticated key agreement (AKA) of communicating entities in IoT is of paramount importance as a security and privacy credential. However, IoT devices have resource-constrained feature, hence implementation of heavy security and privacy features becomes a challenge. Research on AKA in IoT has been done since year 2006. Current research trends on AKA are together with forward secrecy (FS) feasibility, which ensures that future SKs remain safe even if the long-term master keys get compromised. However, most of researches use public key cryptosystems to achieve FS, which requires heavy computations that is not good for the resource-constrained IoT environment. The main purpose of this Thesis is to devise a new machine AKA with FS for IoT, denoted as M2MAKA-FS. To design M2MAKA-FS, we devise a new lightweight FS framework first, which does not rely on the public key cryptosystem but based on a hash chain. The security and privacy building blocks of M2MAKA-FS and the FS framework are symmetric key cryptosystem, one-way hash function, fuzzy commitment and challenge-response mechanism. Results of formal security and privacy analysis show that M2MAKA-FS provides mutual authentication, SK agreement with FS, anonymity and unlinkability and is resilient against various active attacks. Performance analysis shows that M2MAKA-FS achieves the lightweight requirements for IoT environments compared to the related protocols.

Decentralised IOTA-Based Concepts of Digital Trust for Securing Remote Driving in an Urban Environment

The novel contribution of this research is decentralised IOTA-based concepts of digital trust for securing remote driving in an urban environment. The conceptual solutions are studied and described, and respective experimental solutions are developed relying on digital identities, public key cryptography with a decentralised approach using decentralised identifiers (DIDs) and verifiable credentials (VCs), and an IOTA-based distributed ledger. The provided digital trust solutions were validated by executing them according to the remote driving scenario but with a simulated vehicle and simulated remote driving system. The hybrid simulation mainly focused on the validation of functional, causal temporal correctness, feasibility, and capabilities of the provided solutions. The evaluations indicate that the concepts of digital trust fulfil the purpose and contribute towards making remote driving more trustable. A supervisory stakeholder was used as a verifier, requiring a set of example verifiable credentials from the vehicle and the remote driver, and accepting them to the security control channel. The separation of control and data planes from each other was found to be a good solution because the delays caused by required security control can be limited to the initiation of the remote driving session without causing additional delays in the actual real-time remote driving control data flow. The application of the IOTA Tangle as the verifiable data registry was found to be sufficient for security control purposes. During the evaluations, the need for further studies related to scalability, application of wallets, dynamic trust situations, time-sensitive behaviour, and autonomous operations, as well as smart contract(s) between multiple stakeholders, were detected. As the next step of this research, the provided digital trust solutions will be integrated with a vehicle, remote driving system and traffic infrastructure for evaluation of the performance, reliability, scalability, and flexibility in real-world experiments of remote driving of an electric bus in an urban environment.

Post-quantum distributed ledger technology: a systematic survey

Blockchain technology finds widespread application across various fields due to its key features such as immutability, reduced costs, decentralization, and transparency. The security of blockchain relies on elements like hashing, digital signatures, and cryptography. However, the emergence of quantum computers and supporting algorithms poses a threat to blockchain security. These quantum algorithms pose a significant threat to both public-key cryptography and hash functions, compelling the redesign of blockchain architectures. This paper investigates the status quo of the post-quantum, quantum-safe, or quantum-resistant cryptosystems within the framework of blockchain. This study starts with a fundamental overview of both blockchain and quantum computing, examining their reciprocal influence and evolution. Subsequently, a comprehensive literature review is conducted focusing on Post-Quantum Distributed Ledger Technology (PQDLT). This research emphasizes the practical implementation of these protocols and algorithms providing extensive comparisons of characteristics and performance. This work will help to foster further research at the intersection of post-quantum cryptography and blockchain systems and give prospective directions for future PQDLT researchers and developers.

A Programmable Crypto-Processor for National Institute of Standards and Technology Post-Quantum Cryptography Standardization Based on the RISC-V Architecture

The advancement of quantum computing threatens the security of conventional public-key cryptosystems. Post-quantum cryptography (PQC) was introduced to ensure data confidentiality in communication channels, and various algorithms are being developed. The National Institute of Standards and Technology (NIST) has initiated PQC standardization, and the selected algorithms for standardization and round 4 candidates were announced in 2022. Due to the large memory footprint and highly repetitive operations, there have been numerous attempts to accelerate PQC on both hardware and software. This paper introduces the RISC-V instruction set extension for NIST PQC standard algorithms and round 4 candidates. The proposed programmable crypto-processor can support a wide range of PQC algorithms with the extended RISC-V instruction set and demonstrates significant reductions in code size, the number of executed instructions, and execution cycle counts of target operations in PQC algorithms of up to 79%, 92%, and 87%, respectively, compared to RV64IM with optimization level 3 (-O3) in the GNU toolchain.

Feasibility Analysis of Cracking RSA with Improved Quantum Circuits of the Shor’s Algorithm

Since the RSA public key cryptosystem was proposed, it has been widely used because of its strong security. Although the proposal of the Shor’s algorithm offers hope for cracking RSA, it is debatable whether the algorithm can actually pose a threat in practice. From the perspective of the quantum circuit of the Shor’s algorithm, we analyse the feasibility of cracking RSA with improved quantum circuits using an ion-trap quantum computer. We present an improved quantum circuit for the modular exponentiation of a constant, which is the most expensive operation in Shor’s algorithm for integer factorization. Whereas previous studies mostly focused on minimizing the number of qubits or the depth of the circuit, we minimize the number of CNOTs, which greatly affects the time to run the algorithm on an ion-trap quantum computer. First, we give the implementation of the basic arithmetic with the lowest known number of CNOTs and the construction of an improved modular exponentiation of a constant by accumulating intermediate data and using a windowing technique. Then, we precisely estimate the number of improved quantum circuits needed to perform the Shor’s algorithm for factoring an n -bit integer, which is 217 n 3 / log 2 n + 4 n 2 + n . We analyse the running time and feasibility of the Shor’s algorithm on an ion-trap quantum computer according to the number of CNOTs. Finally, we discussed the lower bound of the number of CNOTs needed to implement the Shor’s algorithm.

An Analysis of the Performance and Randomness of Lattice-based Public Key Cryptography Algorithms

An Analysis of the Performance and Randomness of Lattice-based Public Key Cryptography Algorithms

A full privacy-preserving distributed batch-based certificate-less aggregate signature authentication scheme for healthcare wearable wireless medical sensor networks (HWMSNs)

AbstractThe dynamic connectivity and functionality of sensors has revolutionized remote monitoring applications thanks to the combination of IoT and wireless sensor networks (WSNs). Wearable wireless medical sensor nodes allow continuous monitoring by amassing physiological data, which is very useful in healthcare applications. These text data are then sent to doctors via IoT devices so they can make an accurate diagnosis as soon as possible. However, the transmission of medical text data is extremely vulnerable to security and privacy assaults due to the open nature of the underlying communication medium. Therefore, a certificate-less aggregation-based signature system has been proposed as a solution to the issue by using elliptic curve public key cryptography (ECC) which allows for a highly effective technique. The cost of computing has been reduced by 93% due to the incorporation of aggregation technology. The communication cost is 400 bits which is a significant reduction when compared with its counterparts. The results of the security analysis show that the scheme is robust against forging, tampering, and man-in-the-middle attacks. The primary innovation is that the time required for signature verification can be reduced by using point addition and aggregation. In addition, it does away with the reliance on a centralized medical server in order to do verification. By taking a distributed approach, it is able to fully preserve user privacy, proving its superiority.

Analysis of Elliptic Curve Cryptography & RSA

In today’s digital world, the Internet is an essential component of communication networks. It provides a platform for quickly exchanging information among communicating parties. There is a risk of unauthorized persons gaining access to our sensitive information while it is being transmitted. Cryptography is one of the most effective and efficient strategies for protecting our data and it are utilized all around the world. The efficiency of a cryptography algorithm is determined by a number of parameters, one of which is the length of the key. For cryptography, key (public/private) is an essential part. To provide robust security, RSA takes larger key size. If we use larger key size, the processing performance will be slowed. As a result, processing speed will decrease and memory consumption will increase. Due to this, cryptographic algorithms with smaller key size and higher security are becoming more popular. Out of the cryptographic algorithms, Elliptic Curve Cryptography (ECC) provides equivalent level of safety which RSA provides, but it takes smaller key size. On the basis of key size, our work focused on, studied, and compared the efficacy in terms of security among the well-known public key cryptography algorithms, namely ECC (Elliptic Curve Cryptography) and RSA (Rivets Shamir Adelman).

General analysis on essential mathematical principles of elliptic curve cryptography

Prevalent is the practical application of Elliptic Curve Cryptography (ECC) in the modern public-key cryptosystem, especially the implementation of ECC algorithm in Bitcoin source code. With the thorough introduction of discrete logarithm and Diffie-Hellman key exchange, ECC has gradually progressed to be sophisticated and efficient simultaneously. Therefore, it currently has been widely regarded as the successor of RSA algorithm in terms of inheritance for its shorter lengths of keys, faster speed and higher safety under the same encryption strength. Due to the potential safety and complexity of Elliptic Curve Cryptosystem, it is apparently noticed that there is included a large volume of Maths principles related to the establishment of ECC algorithm. As a consequence, this paper will mainly focus on qualitative research and exemplary analysis to specifically elucidate the general knowledge on essential mathematical principles of ECC, including the Law of Addition, the Elliptic Curve Discrete Logarithm Problems (ECDLP) and the Elliptic Curve ElGamal (EC ElGamal), together with the corresponding applications combined with their deprivation processes.

Development of RSA and some attack points

Currently, the relatively popular public key encryption is RSA. It was officially launched in 1978 and given their initials as a name. Different encryption and decryption keys are used in the RSA public-key cryptosystem. Deriving decryption keys from known encryption keys is computationally difficult. Rsa has emerged in various forms since its development. Since the development of RSA, there have been various forms, which means there are various loopholes. Next, we will summarize several interesting attack methods of rsa. It will involve continued fractions and CRT and so on. Through this paper, one can learn a series of knowledge about rsa. As a classic asymmetric password, the value of rsa's existence is relatively high, and exploring its value is something that every password learner should experience. Through this article, one will learn about the most basic attack methods of rsa.

Lightweight authentication scheme based on Elliptic Curve El Gamal

ABSTRACT Elliptic Curve Cryptography (ECC) is a promising cryptosystem as it presents the ideal choice for implementing public-key cryptography in resource-limited devices, such as those found in envisioned Internet of Things applications, e.g. wireless sensors. Elliptic Curve ElGamal (ECEG) is a renowned member of the ECC family. However, it requires encoding the message before encryption and decoding it after decryption. To better improve the processing time and to avoid sharing a lookup table, we propose, in this document, a new method that exchanges encoding parameters and authenticates endpoints at the same time. So, our new protocol ensures the authentication of communication parties and integrity of ephemeral encoding parameters. The robustness of our solution is proven by the Scyther tool. Experimental tests have been carried out, and the performance of the new methods is provided and compared with RSA and related work. Security and performance analysis show that our new scheme has achieved improved functionality and higher security while maintaining low computational.

Quantum-resistant Transport Layer Security

The reliance on asymmetric public key cryptography (PKC) and symmetric encryption for cyber-security in current telecommunication networks is threatened by the emergence of powerful quantum computing technology. This is due to the ability of quantum computers to efficiently solve problems such as factorization or discrete logarithms, which are the basis for classical PKC schemes. Thus, the assumption that communications networks are secure no longer holds true. Quantum Key Distribution (QKD) and post-quantum cryptography (PQC) are the first cyber-security technologies that allow communications to resist the attacks of a quantum computer. To achieve quantum-resistant communications, the aforementioned technologies need to be incorporated into a network security protocol such as Transport Layer Security (TLS). In this paper, we describe and implement two novel, hybrid solutions in which QKD and PQC are combined inside TLS for achieving quantum-resistant authenticated key exchange: Concatenation and Exclusively-OR (XOR). We present the results, in terms of complexity and security enhancement, of integrating state-of-the-art QKD and PQC technologies into a practical, industry-ready TLS implementation. Our findings demonstrate that the adoption of a PQC-only approach enhances the TLS handshake performance by approximately 9% compared to classical methods. Furthermore, our hybrid PQC-QKD quantum-resistant TLS comes at a performance cost of approximately 117% during the key establishment process. In return, we substantially augment the security of the handshake, paving the road for the development of future-proof quantum-resistant communication systems based on QKD and PQC.

Polar code-based cryptosystem: comparative study and analysis of efficiency

<p><span>This review paper aims to examine the use of polar codes in public key cryptosystems, providing a comprehensive overview of the state-of-the-art in this field at present. This study thoroughly searches databases such as IEEE Xplore, Scopus, and the ACM digital library to locate relevant research articles. In this study, we demonstrate the use of polar codes in public key cryptography and provide valuable insights for researchers interested in this field of research. The paper identifies several areas for further research and development, such as improved security and reliability of polar code-based cryptosystems. An analysis of the review highlights the major challenges and open research questions in this area, including the need for efficient key generation algorithms and the trade-offs between security and performance. An analysis of various existing encryption techniques as well as their security proofs is provided in the tables.</span></p>

Kyber, Saber, and SK-MLWR Lattice-Based Key Encapsulation Mechanisms Model Checking with Maude

Facing the potential threat raised by quantum computing, a great deal of research from many groups and industrial giants has gone into building public-key post-quantum cryptographic primitives that are resistant to the quantum attackers. Among them, there is a large number of post-quantum key encapsulation mechanisms (KEMs), whose purpose is to provide a secure key exchange, which is a very crucial component in public-key cryptography. This paper presents a formal security analysis of three lattice-based KEMs including Kyber, Saber, and SK-MLWR. We use Maude, a specification language supporting equational and rewriting logic and a high-performance tool equipped with many advanced features, such as a reachability analyzer that can be used as a model checker for invariant properties, to model the three KEMs as state machines. Because they all belong to the class of lattice-based KEMs, they share many common parts in their designs, such as polynomials, vectors, and message exchange patterns. We first model these common parts and combine them into a specification, called base specification. After that, for each of the three KEMs, by extending the base specification, we just need to model some additional parts and the mechanism execution. Once completing the three specifications, we conduct invariant model checkings with the Maude search command, pointing out a similar man-in-the-middle attack. The occurrence of this attack is due to the fact that authentication is not part of the KEMs, and therefore an active attacker can modify all communication between two honest parties.

A novel homomorphic polynomial public key encapsulation algorithm

Background: One of the primary drivers in development of novel quantum-safe cryptography techniques is the ongoing National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) competition, which aims to identify quantum-safe algorithms for standardization. Although NIST has recently announced candidates to be standardized, the development of novel PQC algorithms remains desirable to address the challenges of quantum computing. Furthermore, to enhance security and improve performance. Methods: This paper introduces a novel public key encapsulation algorithm that incorporates an additional layer of encryption during key construction procedure, through a hidden ring. This encryption involves modular multiplication over the hidden ring using a homomorphism operator that is closed under addition and scalar multiplication. The homomorphic encryption key is comprised of two values - one used to create the hidden ring and the other to form an encryption operator. This homomorphic encryption can be applied to any polynomials during key construction over a finite field with their coefficients considered private. Particularly, the proposed homomorphic encryption operator can be applied to the public key of the Multivariate Public Key Cryptography schemes (MPKC) to hide the structure of its central map construction. Results: This paper presents a new variant of the MPKC with its public key encrypted using the proposed homomorphic operator. This novel scheme is called the Homomorphic Polynomial Public Key (HPPK) algorithm, which simplifies MPKC central map to two multivariate polynomials constructed from polynomial multiplications. The HPPK algorithm employs a single polynomial vector for the plaintext and a multi-variate noise vector associated with the central map. In contrast, in MPKC, a single multivariate vector is created by segmenting the secret plaintext over a small finite field. The HPPK algorithm is Indistinguishability Under Chosen-Plaintext Attack (IND-CPA) secure, and its classical complexity for cracking is exponential in the size of the prime field GF(p).

Lightweight Authentication Scheme for Healthcare With Robustness to Desynchronization Attacks

Remote healthcare monitoring systems are gaining a lot of interest as they enable doctors to use public channels to get real-time data from the sensors placed in/on the patient’s body. This necessitates the implementation of a robust authentication scheme to ensure secure communication between trusted healthcare providers and sensors which are usually low in resources. To address these issues, in 2021, Masud et al. presented a lightweight anonymous user authentication scheme for securely obtaining patient’s real-time data. Their protocol is considered practical for deployment on sensor nodes as it only utilizes hash functions and does not require any public key cryptography. In this work, we demonstrate how their protocol loses synchronization when a message is blocked/jammed and how in some scenarios, the protocol is exposed to the risk of session key disclosure and cannot ensure forward secrecy. To overcome these threats, we propose, a Lightweight mutual Authentication Protocol that provides Robustness to Desynchronization attacks. The proposed scheme uses a one-way hash chain technique to ensure forward secrecy and enable resynchronization between the protocol entities in the event of a desynchronization attack. also achieves user and sensor node anonymity, thus ensuring privacy of the communicating entities. With the demonstration of both formal and informal analysis, the proposed protocol is ensured to withstand the identified attacks in Masud et al.’s scheme. The comparative analysis in terms of security and performance with relevant protocols indicates that the proposed protocol ensures higher security with considerably low computation and communication overheads, making it suitable for practical implementation in a lightweight healthcare environment.

On Multiple Encryption for Public-Key Cryptography

Using multiple, individual encryption schemes is a well-established method to increase the overall security of encrypted data. These so-called multiple encryption or hybrid schemes have regained traction in the context of public-key cryptography due to the rise of quantum computers, since it allows the combination of well-known classical encryption schemes with novel post-quantum schemes. In this paper, we conduct a survey of the state-of-the-art public-key multiple encryption (M-PKE) schemes. For the first time, we describe the most relevant M-PKE schemes in detail and discuss their security in a unified model, which allows better comparison between the schemes. Hence, we compare the security, efficiency, and complexity of the schemes and offer recommendations for usage based on common use cases. Our survey emphasizes the importance of being deliberate when combining encryption schemes, as small nuances can easily break security.