Public Key Research Articles

Role of Linear Diophantine Equations in RSA Encryption

Abstract. Diophantine equations are mathematical equations that include only integer solutions and two or more unknown variables. To illustrate, the most elementary form of Diophantine equations are linear Diophantine equations when two different one-degree monomials added up to a constant value. Such equations were given the name of the extraordinary Greek mathematician Diophantus who made great contribution to algebra and number theory. In addition, they help in defining concepts in algebraic geometry and contribute to the development of algorithms for cryptography. They work in the same way as public keys do in cryptocurrencies within blockchain technology to curb cyber threats and scams targeting public systems. They serve as a means of securing transactions on a computer network when using cryptocurrencies such as bitcoins. These encryption techniques also permit cryptographers and mathematicians to create new ideas in relation to these number systems, thus making it possible for further cryptographic techniques to be put into place.

An Enhanced Learning with Error-Based Cryptosystem: A Lightweight Quantum-Secure Cryptography Method

Quantum-secure cryptography is a dynamic field due to its crucial role in various domains. This field aligns with the ongoing efforts in data security. Post-quantum encryption (PQE) aims to counter the threats posed by future quantum computers, highlighting the need for further improvement. Based on the learning with error (LWE) system, this paper introduces a novel asymmetric encryption technique that encrypts entire messages of n bits rather than just 1 bit. This technique offers several advantages including an additive homomorphic cryptosystem. The robustness of the proposed lightweight public key encryption method, which is based on a new version of LWE, ensures that private keys remain secure and that original data cannot be recovered by an attacker from the ciphertext. By improving encryption and decryption execution time—which achieve speeds of 0.0427 ms and 0.0320 ms, respectively—and decreasing ciphertext size to 708 bits for 128-bit security, the obtained results are very promising.

Biometric CNN Model for Verification Based on Blockchain and Hyperparameter Optimization

Nowadays, fingerprints as biometrics are among the most popular means of identity verification for various applications. However, they are susceptible to theft, tampering, or alteration by attackers after storage. Hence, it is critical to guarantee the privacy of these fingerprint templates because standard privacy techniques are not secure enough. Additionally, fingerprint templates are verified using a deep learning model to distinguish between authentic and fake fingerprints, making them more protected and secure by storing them inside a blockchain, which has become the most common secure technique in recent years. This paper implements the proposed efficient and secure biometric system for verification based on blockchain technology and hyperparameter optimization. First, for the storing phase, each user’s authentic fingerprint template, private, and public keys are saved in the block and linked to the previous block in the chain by a hash function. If a hacker attempts to assault a fingerprint, all prior blocks must be changed. Second, for the authentication phase, the user logs in with his fingerprint and looks up the required template in the chain. If the required fingerprint exists, it creates a new block with the login details, and the number 1 is returned, which means that the authentication is valid; if it does not exist, it is verified to see if it is authentic or fake using the proposed biometric convolutional neural network (CNN). The proposed CNN uses the Grid Search (GS) algorithm to tune hyperparameters to distinguish between authentic and fake fingerprints. The SOCOFing dataset is used for evaluating our experiment. According to the experimental results, the proposed CNN model achieved the highest accuracy of 99.52%. As a result of the blockchain, our system can return authentication information after looking up the chain in 300 ms.

The Perils of Limited Key Reuse: Adaptive and Parallel Mismatch Attacks with Post-processing Against Kyber

The Module Learning With Errors (MLWE)-based Key Encapsulation Mechanism (KEM) Kyber is NIST's new standard scheme for post-quantum encryption. As a building block, Kyber uses a Chosen Plaintext Attack (CPA)-secure Public Key Encryption (PKE) scheme, referred to as Kyber.CPAPKE. In this paper we study the robustness of Kyber.CPAPKE against key mismatch attacks. We demonstrate that Kyber's security levels can be compromised if having access to a few mismatch queries of Kyber.CPAPKE, by striking a balance between the parallelization level and the cost of lattice reduction for post-processing. This highlights the imperative need to strictly prohibit key reuse in Kyber.CPAPKE. We further propose an adaptive method to enhance parallel mismatch attacks, initially proposed by Shao et al. at AsiaCCS 2024, thereby significantly reducing query complexity. This method combines the adaptive attack with post-processing via lattice reduction to retrieve the final secret key entries. Our method proves its efficacy by reducing query complexity by 14.6 % for Kyber512 and 7.5 % for Kyber768/Kyber1024. Furthermore, this approach has the potential to improve multi-value Plaintext-Checking (PC) oracle-based side-channel attacks and fault-injection attacks against Kyber itself.

Small Public Exponent Brings More: Improved Partial Key Exposure Attacks against RSA

Let (N,e) be a public key of the RSA cryptosystem, and d be the corresponding private key. In practice, we usually choose a small e for quick encryption. In this paper, we improve partial private key exposure attacks against RSA with a small public exponent e. The key idea is that under such a setting we can usually obtain more information about the prime factor of N and then by solving a univariate modular polynomial with Coppersmith's method, N can be factored in polynomial time. Compared to previous results, we reduce the number of d's leaked bits needed to mount the attack by log_2 (e) bits. Furthermore, our experiments show that for 1024-bit N, our attack can achieve the theoretical bound on a personal computer, which verified our attack.

The Security of SSH Protocol Public Key Sharing in the Post-Quantum Era

The security of traditional cryptographic schemes is based on mathematical puzzles that cannot be cracked by current computers. However, the rapid development of quantum computers has the potential to greatly reduce the time and resources required to crack these encryption schemes. Although true quantum supremacy may still be years away, it is imperative to adopt anti-quantum algorithms proactively. This preemptive approach aims to thwart "catch first, decrypt later" attacks, wherein attackers intercept and store encrypted data with the intent of decrypting it once quantum computing becomes sufficiently advanced. This threat is particularly critical for protocols like Secure Shell (SSH), which is widely used for secure communication over unsecured networks. In this paper, we propose an innovative approach to enhance the security of public-key distribution within the SSH protocol. Our method integrates quantum-resistant algorithms to ensure that even with the advent of quantum computing, the confidentiality and integrity of SSH sessions are maintained. We emphasize the importance of using cryptographic protocols that operate over open channels, which, while not necessarily confidential, must be authenticated to prevent tampering. In such scenarios, attackers may be able to intercept and even extract information, but they should not be able to alter the data.

Enhancing the Vehicular Public Key Infrastructure to Develop Privacy-Preserving Authentication Scheme for Vanet by Using PCM and MSS Scheme

This article proposes a security-based authentication as well as efficient certificate management approach for VANET to detect fraudulent nodes with better precision, less latency and overhead. The primary purpose of the developed system is to establish effectual and heftiness of VANET security that lead to the stability of overall network. VANETs are composed of vehicles and Road Side Units (RSUs) assisting with network management and the vehicles connect with one another and RSUs to furnish roadside information and safety solutions. Security is an essential factor in VANETs because the confidentiality of humans (passengers) is paramount; hence, Vehicular Public Key Infrastructure (VPKI) is utilised to offer authentication and safety services in VANETs. The developed structure provides an encrypted VANET transmission infrastructure by utilising the concepts of Merkle Signature Scheme (MSS) and Pseudo-code Certificate Management (PCM) to minimise overhead for communication and latency while ensuring entity authenticity. Messages are authenticated by sender, encoded with a vehicular public key distributed by a PCM-MSS and decrypted by the destination, resulting in every transmission including a certification from a reliable authority. During that verification, the transmitter and receiver of message’s authentication and validation is accomplished. Simulation findings show that the proposed approach improves the reliability of identifying hostile nodes and PDR while reducing authentication delays and overhead.

Privately Generated Key Pairs for Post Quantum Cryptography in a Distributed Network

In the proposed protocol, a trusted entity interacts with the terminal device of each user to verify the legitimacy of the public keys without having access to the private keys that are generated and kept totally secret by the user. The protocol introduces challenge–response–pair mechanisms enabling the generation, distribution, and verification of cryptographic public–private key pairs in a distributed network with multi-factor authentication, tokens, and template-less biometry. While protocols using generic digital signature algorithms are proposed, the focus of the experimental work was to implement a solution based on Crystals-Dilithium, a post-quantum cryptographic algorithm under standardization. Crystals-Dilithium generates public keys consisting of two interrelated parts, a matrix generating seed, and a vector computed from the matrix and two randomly picked vectors forming the secret key. We show how such a split of the public keys lends itself to a two-way authentication of both the trusted entity and the users.

Unlinkable Policy-Compliant Signatures for Compliant and Decentralized Anonymous Payments

Privacy-preserving payment systems face the difficult task of balancing privacy and accountability: on one hand, users should be able to transact privately and anonymously, on the other hand, no illegal activities should be tolerated. The challenging question of finding the right balance lies at the core of the research on accountable privacy that stipulates the use of cryptographic techniques for policy enforcement. Current state-of-the-art systems are only able to enforce rather limited policies, such as spending or transaction limits, or assertions about single participants, but are unable to enforce more complex policies that for example jointly evaluate both, the private credentials of sender and recipient, situations that occur in cross-border payments, let alone to do this without auditors in the loop during payment. This severely limits the cases where decentralized virtual assets can be used in accordance with regulatory compliance such as the Financial Action Task Force (FATF) travel rule, while retaining strong privacy features. We present unlinkable Policy-Compliant Signatures (ul-PCS), an enhanced cryptographic primitive extending the work of Badertscher et al.~(TCC 21). We give rigorous definitions, formally proven constructions, and benchmarks using our prototype developed using CharmCrypto which gives the first insights into feasibility of PCS. Unlinkable PCS has the following unique combination of features: 1) It is an enhanced signature scheme where the public key encodes in a privacy-preserving way the user's verifiable credentials (obtained from a credential authority). 2) Signatures can be created (and later publicly verified) by additionally specifying a recipient's public key aside of the to-be-signed message. A valid signature can only ever be created if the attributes $x_S$ of the signer and the attributes $x_R$ of the receiver fulfill some global policy $F(x_S,x_R)$. 3) The signature can be created by the signer just knowing the recipient's public key; there is no further interaction needed and no information is leaked (beyond the validity of the policy). 4) Once credentials are obtained, a user can generate fresh public keys without interacting with the credential authority. By merging the act of signing a transaction with the act of providing an assurance about the involved participants being compliant with complex policies, yet retain that participants are able to change public keys without the involvement of an authority, we formally show how ul-PCS is a step towards improving regulatory compliance of privacy coins such as Monero or Zcash.

Private Blockchain-Assisted Certificateless Public Key Encryption With Multikeyword Search for Fog-Based IIoT Environments

Private Blockchain-Assisted Certificateless Public Key Encryption With Multikeyword Search for Fog-Based IIoT Environments

CLLS: Efficient certificateless lattice-based signature in VANETs

The rapid development of Vehicular Ad-hoc Network (VANETs) has improved road safety and traffic management, and brought great convenience to intelligent transportation system (ITS). However, the transmission of data over open channels caused many security issues. Certificateless cryptography solves the certificate management and key escrow problems, which makes it the primary method for message authentication in VANETs. However, with the emergence of quantum computing, traditional cryptography faces a significant challenge. Lattice-based cryptography are regarded as effective post-quantum ciphers. Nevertheless, nearly all existing lattice-based certificateless signature schemes rely on Gaussian sampling or trapdoor techniques, resulting in computational inefficiencies and large key and signature sizes that are impractical for VANETs. To address these issues, we proposed the first efficient algebraic lattice-based certificateless signature scheme in VANETs based on the Dilithium signature algorithm. The security of our certificateless lattice-based signature(CLLS) scheme is based on the MSIS and MLWE hardness assumption, which makes the scheme resistant to quantum attacks and easy to implement. Our scheme did not use Gaussian sampling or trapdoor techniques, which improve the computational and storage efficiency. As a result, the public key of our scheme is 1X smaller than the previous scheme and the size of signature is 2X smaller than the previous efficient algebraic lattice scheme. In addition, compared to the most efficient existing CLLS scheme, the signing and verification computation cost of our scheme are reduced by 20% and 55% respectively and our proposed CLLS scheme has low power consumption. Furthermore, the security of our scheme achieves strong unforgeability against chosen-message attacks(SUF-CMA) in the random oracle model(ROM), which surpasses that of existing lattice-based certificateless signature schemes.

Improving Security and Compliance for Medical Devices With Public Key Infrastructure

Improving Security and Compliance for Medical Devices With Public Key Infrastructure

A practical convertible quantum signature scheme with public verifiability into universal quantum designated verifier signature using self-certified public keys

A practical convertible quantum signature scheme with public verifiability into universal quantum designated verifier signature using self-certified public keys

Homomorphic Polynomial Public Key with Barrett Transformation for Digital Signature

Homomorphic Polynomial Public Key with Barrett Transformation for Digital Signature

RPKI Defense Capability Simulation Method Based on Container Virtualization

As the main inter-domain routing protocol in today’s internet, the Border Gateway Protocol (BGP) faces serious security risks during actual usage. Research on BGP malicious attack methods requires a realistic network environment, and evaluation methods based on physical networks often suffer from high costs and insufficient flexibility. Thus, we propose an efficient BGP simulated network deployment system based on a virtualization technology called the SOD–BGP. This system, combining cloud computing and virtualization technologies, creates a scalable, highly flexible basic network environment that allows for the automated simulation and evaluation of actual BGP prefix hijacking attack scenarios. A Resource Public Key Infrastructure (RPKI) simulation suite is introduced into the system, emulating a certificate issuance system, certificate storage, and a certificate synchronization verification mechanism, thus aligning the simulation environment with real-world usage scenarios. Finally, we propose a data collection and performance evaluation technique to evaluate BGP networks deploying RPKI under different attack scenarios and to explore the effectiveness of RPKI defense mechanisms at various deployment rates. A comparative analysis with other simulation techniques demonstrates that our approach achieves a balanced performance in terms of deployment speed, complexity, and RPKI integrity, providing a solid simulation technology foundation for large-scale BGP security defense strategies.

An Approach for Cipher Communication Utilizing the Concepts of Elliptic Curve Cryptography

Message encryption is a process of protection of the original data in transmission. Several cryptosystems were designed in the history for different environments. Public key or Asymmetric cryptosystem has become more popular in recent era where the key space consists both public and private keys. Elliptic curve cryptography dominates public key cryptosystems like Diffie Hellman key exchange and RSA. ECC is more powerful and alternative technique of RSA, with a simple replacement of exponent calculations of large prime numbers to mathematical representation of Elliptic curve points. Besides the computation ECC works with shorter key length than RSA. The present paper describes an encryption algorithm using elliptic curves over finite fields. Here a group of authentic users transmit.

Four-qubit photonic system for publicly verifiable quantum random numbers and generation of public and private key

Four-qubit photonic system for publicly verifiable quantum random numbers and generation of public and private key

An Improved Multi-Chaotic Public Key Algorithm Based on Chebyshev Polynomials

Due to the similar characteristics of chaotic systems and cryptography, public key encryption algorithms based on chaotic systems are worth in-depth research and have high value for the future. Chebyshev polynomials have good properties and are often used in the design of public key algorithms. This paper improves the Bose Multi-Chaotic Public Key Cryptographic Algorithm (BMPKC) by applying Chebyshev polynomials. The proposed algorithm (CMPKC-) introduces the selective coefficient based on the properties of Chebyshev polynomials, allowing the special functions that need to be negotiated in the original system to be freely and randomly chosen as Chebyshev polynomials, and can also be expanded to m levels. The improved cryptographic algorithm also utilizes chaotic hash functions and logistic mapping to generate pseudo-random sequences and overcomes shortcomings of the Bose algorithm by iteratively iterating the selected Chebyshev polynomials based on the number of 0s or 1s in the pseudo-random sequence, thus providing better security. Analysis and software testing results indicate that this algorithm has strong robustness against brute force attacks, achieving a higher attack time for breaking the private key compared to the CEPKC, BMPKC, and CMPKC algorithms. Compared to the CMPKC algorithm, our proposal algorithm achieves better performance in the encryption and decryption phases. Furthermore, we combine this Multi-Chaotic System Key Exchange Protocol with the Advanced Encryption Standard (AES) algorithm, while providing a demonstration, offering more possibilities for practical applications of this system.

The Impact of Technology on Testate Succession in South Africa

One advantage of the Fourth Industrial Revolution (4IR) era is the expedient exchange of goods and services via the Internet. The Electronic Communications and Transactions Act 25 of 2002 (ECTA) plays a critical role in regulating transactions and communications. However, ECTA excludes the provisions of the Wills Act 7 of 1953 from its ambit. Inevitably, this creates difficulties for the recognition and/or validity of electronic wills in South Africa. If technology is not acknowledged and applied in the space of testate succession, enhanced 4IR innovations threaten the Wills Act with obsolescence. We argue in this contribution that the rapid changes brought about by the 4IR and the exclusion of the Wills Act from the ambit of ECTA mean that testate succession is not responding to the current impact of technology on people. In this contribution we seek to create a synergy between the two statutes with a view to ensuring the relevance of the Wills Act in the 4IR. Ultimately we propose that both statutes be amended to cater for electronic wills. This can be achieved by combining the use of digital signatures and Public Key Infrastructure (PKI) technology. In reaching this conclusion we draw some lessons from the statutory changes in the United States of America (USA).

Blockchain and Cryptography Framework of E-Apps with Big Data

With the tremendous and rapid evolution taking place in the field of technology and considering the rise in data volume that is dealt with daily, managing this data, whether in terms of security or terms of storage especially if the data is huge, is considered a necessary issue. Therefore, in this research, we established a framework that provides both security and storage/repository management. Where the security issue in the suggested framework is supported by the use of lightweight hash functions and public-key encryption algorithms represented by SPONGENT and elliptic curve cryptography (ECC). Additionally, the fast random number generator is also used to support the security algorithms included in the framework, while managing the repository storage is controlled by the use of a hybrid Blockchain to manage storage for this type of big data. The process of storing this data in databases or any of the traditional centralized methods exposes the data to loss or penetration. After analyzing the proposed framework, it successfully addressed the prevention of malicious within the field of proposed research attacks. Moreover, the performance analysis of the framework proposed was quite effective with the lightweight SPONGENT and ECC results, while the creation of blocks in the storage phase was not more than 0.18 ns. Thus, we obtained an effective framework in terms of security, performance, and terms of data repository management and control.