Public Key Cryptography Research Articles

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.

The main features of the public key infrastructure

Trust is the basis of any communication, whether it is built in the physical world or in the digital environment. Establishing trust in the physical world does not pose any particular challenges because communication subjects can identify each other through biometric features, identity card or other identification documents. In the digital environment, a number of difficulties arise for the identification and authentication procedure. The communicating parties do not meet face-to-face and can be at a significant distance from each other. As a result, they cannot identify uniquely and verify each other's identity using the identity verification methods used in the material world. To ensure the security of electronic communications, it is necessary for communication systems to be equipped with technical means of information protection and an additional mechanism that will contribute to the establishment of trust between the parties to the communication. The Public Key Infrastructure is used to solve problems related to trust, authentication, identity, and security on a network. A digital certificate is a fundamental element for establishing trust in the digital world. It plays a crucial role in ensuring security and identification on the Internet and when working with electronic resources. The Public Key Infrastructure is a trusted system used to ensure the security and privacy of information across networks and platforms. This system is based on public key cryptography. It implements the management of public keys and digital certificates of various entities, such as companies, corporations, organizations, individuals, websites, servers, etc. The Public Key Infrastructure is widely deployed in government portals and systems. It is used in the electronic government system to guarantee the transparency of the provision of electronic services and to ensure the security of communication links between authorities and society. The Public Key Infrastructure represents a multifaceted structure that includes a set of standards, technologies, and procedures for managing, storing, and distributing keys and digital certificates. A certificate authority is a key component of a public key infrastructure and is an independent third party that manages digital certificates. Various technical and cryptographic means of information security are used in the Public Key Infrastructure, such as digital signatures, encryption, hash functions, hardware security modules, key management software, etc. The main purpose of this article is to analyze the main features and aspects of public key infrastructure.

Lattice attacks on pairing-based signatures

ABSTRACT Practical implementations of cryptosystems often suffer from critical information leakage through side-channels (such as their power consumption or their electromagnetic emanations). For public-key cryptography on embedded systems, the core operation is usually group exponentiation – or scalar multiplication on elliptic curves – which is a sequence of group operations derived from the private-key that may reveal secret bits to an attacker (on an unprotected implementation). We present lattice-based polynomial-time (heuristic) algorithms that recover the signer’s secret in popular pairing-based signatures when used to sign several messages under the assumption that blocks of consecutive bits of the corresponding exponents are known by the attacker. Our techniques rely upon Coppersmith's method and apply to many signatures in the so-called exponent-inversion framework in the standard security model (i.e. Boneh-Boyen, Gentry and Pontcheval-Sanders signatures) as well as in the random oracle model (i.e. Sakai-Kasahara signatures).

Quantum spider prioritized routing and Cramer Shoup cryptosecured data transmission in wireless body area network

The wireless body area network (WBAN) offers healthcare applications for remote patient monitoring. In healthcare, prioritizing patient data has a high impact on the energy usage, delays, and congestion involved in routing. Energy usage, battery life, and absorption rates are current research obstacles in WBAN. The path loss ratio and residual energy were generally the focus of attention during data transfer. Despite this, compromised transaction security caused serious problems with the delivery of vital health data. The Quantum Spider Cramer Shoup Public Key Cryptosystem (QS-CSPKC), which is proposed in this study, is an optimized priority-aware (for many patients) and transaction security technique for vital sensed data in WBAN, selects the optimum energy efficient and reliable path to assure secure data transfer. The proposed QS-CSPKC method employs Dual Contention Access Periods (DCAPs) for managing regular data (i.e., normal sensed or low priority data) and life-threatening data (i.e., abnormal sensed data or high priority data). After prioritizing, the Quantum Spider Monkey Optimized Routing algorithm is used to allocate an optimal shortest route for normal low priority data (i.e., with 0 as the quantum value) and an energy-efficient emergency route for critical high priority data (i.e., with 1 as the quantum value). In addition, to prevent illegal access during transmission, security keys are generated using the Cramer Shoup public key cryptosystem. By using this model, only legitimate users have access to information for which they are authorized. The evaluation results were validated through simulations, showing that the proposed QS-CSPKC method performs efficient routing and secure data transmission better than conventional techniques in terms of throughput, packet loss, average power consumption, and energy use.

A New Idea for RSA Backdoors

This article proposes a new method to inject backdoors in RSA (the public-key cryptosystem invented by Rivest, Shamir, and Adleman) and other cryptographic primitives based on the integer factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the semi-primes based on a large prime number, which acts as a “designer key” or “escrow key”. In particular, two different backdoors are proposed, one targeting a single semi-prime and the other one a pair of semi-primes. This article also describes the results of tests performed on a SageMath implementation of the backdoors.

Verifiable and Searchable Symmetric Encryption Scheme Based on the Public Key Cryptosystem

With the rapid development of Internet of Things technology and cloud computing technology, all industries need to outsource massive data to third-party clouds for storage in order to reduce storage and computing costs. Verifiable and dynamic searchable symmetric encryption is a very important cloud security technology, which supports the dynamic update of private data and allows users to perform search operations on the cloud server and verify the legitimacy of the returned results. Therefore, how to realize the dynamic search of encrypted cloud data and the effective verification of the results returned by the cloud server is a key problem to be solved. To solve this problem, we propose a verifiable dynamic encryption scheme (v-PADSSE) based on the public key cryptosystem. In order to achieve efficient and correct data updating, the scheme designs verification information (VI) for each keyword and constructs a verification list (VL) to store it. When dynamic update operations are performed on the cloud data, it is easy to quickly update the security index through obtaining the latest verification information in the VL. The safety and performance evaluation of the v-PADSSE scheme proved that the scheme is safe and effective.

A Novel and Secure Fake-Modulus Based Rabin-Ӡ Cryptosystem

Electronic commerce (E-commerce) transactions require secure communication to protect sensitive information such as credit card numbers, personal identification, and financial data from unauthorized access and fraud. Encryption using public key cryptography is essential to ensure secure electronic commerce transactions. RSA and Rabin cryptosystem algorithms are widely used public key cryptography techniques, and their security is based on the assumption that it is computationally infeasible to factorize the product of two large prime numbers into its constituent primes. However, existing variants of RSA and Rabin cryptosystems suffer from issues like high computational complexity, low speed, and vulnerability to factorization attacks. To overcome the issue, this article proposes a new method that introduces the concept of fake-modulus during encryption. The proposed method aims to increase the security of the Rabin cryptosystem by introducing a fake-modulus during encryption, which is used to confuse attackers who attempt to factorize the public key. The fake-modulus is added to the original modulus during encryption, and the attacker is unable to distinguish between the two. As a result, the attacker is unable to factorize the public key and cannot access the sensitive information transmitted during electronic commerce transactions. The proposed method’s performance is evaluated using qualitative and quantitative measures. Qualitative measures such as visual analysis and histogram analysis are used to evaluate the proposed system’s quality. To quantify the performance of the proposed method, the entropy of a number of occurrences for the pixels of cipher text and differential analysis of plaintext and cipher text is used. When the proposed method’s complexity is compared to a recent variant of the Rabin cryptosystem, it can be seen that it is more complex to break the proposed method—represented as O(ɲ× τ) which is higher than Rabin-P (O(ɲ)) algorithms.

Integration of an RSA-2048-bit public key cryptography solution in the development of secure voice recognition processing applications

The authors initially employs the fast Fourier transform (FFT) approach to transforming voice inputs into digital signals before integrating a speech recognition solution (which includes two models: the hidden Markov model (HMM) and the artificial neural network (ANN)). To achieve standard-tone identification of voice signals and digitally store speech, the authors then incorporated a 2048-bit Rivest-Shamir-Adleman (RSA) encryption method to encrypt and decrypt digital speech. The authors’ building team constructed the program using a 256-bit advanced encryption standard - Galois counter mode (AES-GCM) encryption method to assure the application’s effectiveness. The authors successfully created a voice recognition application according to the HMM of ANN. The collected findings suggest that the authors’ secure speech recognition program (named soft voice - RSA) has improved in terms of safety, keeping speech material secret, and speed. It takes roughly 0.2 s to generate a 2048-bit RSA key pair that exceeds the National Institute of Standards and Technology (NIST) standard, 700-1070 ms to process speech, 1-4 ms to encrypt 2048-bit RSA, 6-8 ms to decrypt 2048-bit RSA.