Public Key Cryptography System Research Articles

A Study of Elliptic Curve Cryptography and Its Applications

This paper aims to provide a comprehensive review on Elliptic Curve Cryptography (ECC), a public key cryptographic system and its applications. The paper discusses important mathematical properties and operations of elliptic curves, like point addition and multiplication operations and its implementation in cryptographic methods such as encryption and decryption. This paper provides a detailed workout on important mathematical problems on elliptic curves and ECC which provides insight into working of essential cryptographic techniques in ECC. And the paper also provides a literature review of research works based on ECC in various fields such as Internet of Things (IoT), Cloud computing, Blockchain and Image Security. And the paper further provides insight into the recent applications of ECC in fields like IoT and Blockchain by comprehensively discussing the proposed mechanism for each of the recent applications and also briefly discussing the security of the proposed mechanism.

An Improved Public Key Cryptographic Algorithm Based on Chebyshev Polynomials and RSA

Due to its very desirable properties, Chebyshev polynomials are often used in the design of public key cryptographic systems. This paper discretizes the Chebyshev mapping, generalizes the properties of Chebyshev polynomials, and proposes an improved public key encryption algorithm based on Chebyshev chaotic mapping and RSA, i.e., CRPKC−Ki. This algorithm introduces alternative multiplication coefficients Ki, the selection of which is determined by the size of TrTdxmod N=TdTrxmod N, and the specific value selection rules are shared secrets among participants, overcoming the shortcomings of previous schemes. In the key generation and encryption/decryption stages, more complex intermediate processes are used to achieve higher algorithm complexity, making the algorithm more robust against ordinary attacks. The algorithm is also compared with other RSA-based algorithms to demonstrate its effectiveness in terms of performance and security.

Edge-Cloud-Assisted Certificate Revocation Checking: An Efficient Solution Against Irresponsible Service Providers

Certificate revocation checking (CRC) is a fundamental requirement in certificate-based public-key cryptographic systems. Most existing CRC schemes are not tailored for edgecloud computing systems, and directly applying these schemes would cause security and efficiency problems. In this paper, we first propose a two-layer edge-cloud-assisted CRC framework, dubbed ECA-CRC, where edge nodes utilizing a probabilistic checking algorithm serve as a first layer, and the cloud server utilizing a deterministic checking algorithm serves as a second layer. Both the edge nodes and the cloud server collaboratively provide verifiable CRC services for devices. The most prominent manifestations of ECA-CRC are that (1) most CRC requests can be processed with the probabilistic checking layer, which reduces the checking delay significantly while providing an accurate CRC service; (2) devices can detect the irresponsible behavior of the service provider, including using an incorrect revoked certificate set (RCS) to compute checking results or procrastinating on updating the RCS, as soon as possible.We then propose an efficient instantiation of ECA-CRC, dubbed eECACRC, by utilizing a Merkle hash tree (MHT) based homomorphic signature, Cuckoo filter, and Othello. We formally prove the security of eECA-CRC against the irresponsible service provider under the random oracle model. We implement an eECA-CRC prototype and conduct a comprehensive performance evaluation based on a public certificate database. Our results show that 95% of CRC requests are completed on the edge nodes, and only 5% of CRC requests need to be handled by the cloud server.

A Low-Cost High-Performance Montgomery Modular Multiplier Based on Pipeline Interleaving for IoT Devices

Modular multiplication is a crucial operation in public-key cryptography systems such as RSA and ECC. In this study, we analyze and improve the iteration steps of the classic Montgomery modular multiplication (MMM) algorithm and propose an interleaved pipeline (IP) structure, which meets the high-performance and low-cost requirements for Internet of Things devices. Compared to the classic pipeline structure, the IP does not require a multiplexing processing element (PE), which helps shorten the data path of intermediate results. We further introduce a disruption in the critical path to complete an iterative step of the MMM algorithm in two clock cycles. Our proposed hardware architecture is implemented on Xilinx Virtex-7 Series FPGA, using DSP48E1, to realize the multiplier. The implemented results show that the modular multiplication of 1024 bits by 2048 bits requires 1.03 μs and 2.13 μs, respectively. Moreover, our area–time–product analysis reveals a favorable outcome compared to the state-of-the-art designs across a 1024-bit and 2048-bit modulus.

Combining Beaufort cipher and RSA-CRT algorithm in a hybrid scheme to secure images

RSA algorithm is one type of algorithms in public-key cryptographic systems where the private keys are kept secret and the public keys can be disseminated. Beaufort Cipher algorithm is a type of classical symmetric algorithm. Meanwhile, the RSA-CRT is one variant of RSA cryptosystem. The RSA-CRT is not efficient for encrypting large files such as image files, since it uses modular exponentiation, which is slow, and the resulting ciphertext would be very much larger than the message. To avoid this problem, a hybrid cryptosystem scheme using RSA-CRT and Beaufort algorithm is designed to encrypt images. Beaufort Cipher algorithm is used for encryption and decryption of digital images, while RSA-CRT algorithm for decryption and decryption of beaufort cipher keys. The results showed that the size of the image (*.BMP) files and the encrypted image files are the same.

Encrypted chat application using RSA Algorithm

In some ways, the potency and effectiveness of the knowledge systems rely upon its design and the way the knowledge area unit is transmitted among totally different parties. Similarly, a crucial side of computer code development is the security of the knowledge that flows through open communication channels. One of the foremost widespread designs is User/server design which creates the centralization of knowledge storage and process modification, and supply flexibility for applying authentication strategies and coding algorithms inside info systems. whereas the number of users increases, it needs to increase the authentication and coding levels as high as possible. users/servers could be a technology that enables the opening of an associate degree interactive session between the user's browser and also the server. during this study, we tend to use users/server design to accomplish secure messaging/chat between users while not the server having the ability to decode the message. During this manner, a Server Cryptography- based mostly Secure electronic messaging System mistreatment RSA (Rivest- Shamir Adelman), it is a widely used public-key cryptography and authentication system for encryption of digital electronic messaging transactions like email over the computer network, extranet, and net, to write in code and decipher messages is developed using Java Web Application.

Improving Security of Internet of Vehicles Based on Post-quantum Signatures with Systolic Divisions

Internet of Things (IoT) techniques have been employed in many areas, e.g., vehicles, smart home, and medicine. Among the applications of IoTs, the Internet of Vehicles (IoV) is one of the most popular techniques. IoVs are protected by public key cryptographic systems, such as RSA and ECC. However, such systems are vulnerable to quantum computer attacks. Thus, we improve the security of IoV-based post-quantum signatures, which can resist quantum computer attacks. The key operations are divisions in a finite field. Hence, we improve the security of IoV-based post-quantum signatures with division by employing systolic architectures. We propose a systolic architecture for computing division in composite fields. After that, we improve the IoT security-based post-quantum signatures with systolic divisions. We test and verify our design on a Field-Programmable Gate Array (FPGA); the experimental results confirm our estimates. Furthermore, the optimized method proposed can be further applied to various applications like solving system of linear equations and cryptographic applications for IoT security.

A Scalable Montgomery Modular Multiplication Architecture with Low Area-Time Product Based on Redundant Binary Representation

The Montgomery modular multiplication is an integral operation unit in the public key cryptographic algorithm system. Previous work achieved good performance at low input widths by combining Redundant Binary Representation (RBR) with Montgomery modular multiplication, but it is difficult to strike a good balance between area and time as input bit widths increase. To solve this problem, based on the redundant Montgomery modular multiplication, in this paper, we propose a flexible and pipeline hardware implementation of the Montgomery modular multiplication. Our proposed structure guarantees a single-cycle delay between two-stage pipeline units and reduces the length of the critical path by redistributing the data paths between the pipelines and preprocessing the input in the loop. By analyzing the structure and comparing the related work in this paper, our structure ensures a lower area-time product while achieving a controllable and small area consumption. The comprehensive results under different Taiwan Semiconductor Manufacturing Company (TSMC) processes demonstrate the advantages of our structure in terms of flexibility and area-time product.

Post-quantum cryptography Algorithm's standardization and performance analysis

-Quantum computer is no longer a hypothetical idea. It is the world's most important technology and there is a race among countries to get supremacy in quantum technology. It is the technology that will reduce the computing time from years to hours or even minutes. The power of quantum computing will be a great support for the scientific community. However, it raises serious threats to cybersecurity. Theoretically, all the cryptography algorithms are vulnerable to attack. The practical quantum computers, when available with millions of qubits capacity, will be able to break nearly all modern public-key cryptographic systems. Before the quantum computers arrive with sufficient ‘qubit’ capacity, we must be ready with quantum-safe cryptographic algorithms, tools, techniques, and deployment strategies to protect the ICT infrastructure. This paper discusses in detail the global effort for the design, development, and standardization of various quantum-safe cryptography algorithms along with the performance analysis of some of the potential quantum-safe algorithms. Most quantum-safe algorithms need more CPU cycles, higher runtime memory, and a large key size. The objective of the paper is to analyze the feasibility of the various quantum-safe cryptography algorithms.

Post‐quantum cryptography techniques for secure communication in resource‐constrained Internet of Things devices: A comprehensive survey

AbstractAs the number and characteristics of smart devices change, the concept of the Internet of Things (IoT) emerges. The IoT provides the connected devices with a variety of resources that enable effective communication. At this point, several security issues arise to get the sensitive information behind every communication in the IoT. To provide users with security and privacy, cryptographic schemes are adopted, the most popular being public key cryptographic systems (PKC). However, with the advent of quantum computing, the level of security that can be provided by the PKC schemes is a big question. Another important issue is that the IoT environment is resource‐constrained, which necessitates the implementation of lightweight cryptographic algorithms for better security. In response to these issues, the post‐quantum cryptographic (PQC) schemes are one of the significant developments contributing to IoT security in the post‐quantum world. This article examines the key security issues in the IoT environment and examines the effective solutions found in the literature. The problems in IoT in the quantum era are discussed and appropriate solutions by PKC schemes under limited resources in IoT are focused. As the lattice‐based cryptosystems are more effective, the importance of these schemes in the resource‐constrained IoT is highlighted. This survey also leads to feasible future directions that can support developers and researchers in this field.

Knapsack Cipher-based metaheuristic optimization algorithms for cryptanalysis in blockchain-enabled internet of things systems

The integration of the Internet of Things (IoT) and blockchain demand the use of public-key cryptography systems to secure network communications. In this study, one of those public-key algorithms, known as Merkle–Hellman Knapsack Cryptosystem (MHKC), is employed to cryptographically analyze its utilization for blockchain technology using a metaheuristic algorithm. To do so, eight well-known metaheuristic algorithms are employed to determine the trustworthiness of MHKC against cryptoanalysis attacks using various knapsack lengths, ranging from 8 to 32 bits. The experimental findings showed that pathfinder algorithm (PFA) and slime mold optimizer (SMA) could exploit MHKC under 8-bit ASCII code, and their performance gradually deteriorates with higher bit representations, while the performance of manta ray foraging optimization (MRFO) could be superior for the knapsack lengths higher than 8-bit. Additionally, MRFO would not attack MHKC under 32-bit; thus, some genetic operators have been integrated to manipulate the binary solutions obtained by this algorithm to promote its exploration capability in a variant, namely HMRFO. The experimental findings revealed that HMRFO is a better alternative to the existing ones for attacking the MHKC with knapsack lengths higher than 8-bit to appear their fragility points, while both SMA and PFA are competitive for 8-bit ASCII code and superior to the other algorithms.

Non-Restoring Array Divider Using Optimized CAS Cells Based on Quantum-Dot Cellular Automata with Minimized Latency and Power Dissipation for Quantum Computing.

Many studies have addressed the physical limitations of complementary metal-oxide semi-conductor (CMOS) technology and the need for next-generation technologies, and quantum-dot cellular automata (QCA) are emerging as a replacement for nanotechnology. Meanwhile, the divider is the most-used circuit in arithmetic operations with squares and multipliers, and the development of effective dividers is crucial for improving the efficiency of inversion and exponentiation, which is known as the most complex operation. In most public-key cryptography systems, the corresponding operations are used by applying algebraic structures such as fields or groups. In this paper, an improved design of a non-restoring array divider (N-RAD) is proposed based on the promising technology of QCA. Our QCA design is focused on the optimization of dividers using controlled add/subtract (CAS) cells composed of an XOR and full adder. We propose a new CAS cell using a full adder that is designed to be very stable and compact so that power dissipation is minimized. The proposed design is considerably improved in many ways compared with the best existing N-RADs and is verified through simulations using QCADesigner and QCAPro. The proposed full adder reduces the energy loss rate by at least 25% compared to the existing structures, and the divider has about 23%~4.5% lower latency compared to the latest coplanar and multilayer structures.

A high speed processor for elliptic curve cryptography over NIST prime field

Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) operation which has the highest computational complexity in ECC. In this study, we propose a hardware processor which achieves high speed and high security for ECC. We first present a three-clock cycle, divide-and-conquer multiplication algorithm which greatly reduces the number of execution cycles of multiplication. We then propose a dedicated multiplication hardware structure which reuses the multiplier and optimizes data path delay. To keep multiplication running in non-idle status and executing in parallel with other modular operations, the operation scheduling of point addition and point doubling has been re-designed and optimized based on an effective segmentation and pipeline strategy. Finally, under the premise of similar computing and hardware overhead, we propose an improved high-security SM algorithm which involves random points to resist side-channel attacks. On a 55 nm complementary metal oxide semiconductor application specific integrated circuit platform, the processor costs 463k gates and requires 0.028 ms for one SM. Our results indicate that the ECC processor is superior to other state-of-the-art designs reported in the literature in terms of speed and area-time product metrics.

Enhancement of Security of Diffie-Hellman Key Exchange Protocol using RSA Cryptography.

Cryptography is related and referred to as the secured transmission of messages amongst the sender and the intended receiver by ensuring confidentiality, integrity, and authentication. Diffie – Hellman (DH) key exchange protocol is a well-known algorithm that would generate a shared secret key among the sender and the intended receiver, and the basis of cryptosystems for using public and private key for encryption and decryption process. But it is severely affected by the Man in the Middle (MITM) attack that would intercept and manipulate thus eavesdropping the shared secret key. This paper proposes a model of integrating the public-key RSA cryptography system with the DH key exchange to prevent the MITM attack. The performance of the proposed work has been compared to the DH Key Exchange algorithm as well as RSA Cryptosystem to conclude for effectiveness of the proposed model.

Data Security Analysis Against Chosen Ciphertext Secure Public Key Attack Using Threshold Encryption Scheme

A public key encryption cryptography system can be utilized to generate ciphertext of a message using a public key. However, this public key encryption cryptography system cannot be utilized if you want to generate ciphertext using several different keys. Solving the problems above can use the Chosen Ciphertext Secure Public Key Threshold Encryption scheme but are the securities from Threshold Encryption really strong in securing messages, therefore the above problems can be analyzed for Data Security Against Chosen Ciphertext Secure Public Key Attacks Using Threshold Encryption Schemes. The work process starts from Setup which functions to generate the server's private key and public key. Then, the process is continued with ShareKeyGen which functions to generate private keys based on the user's identity. After that, the process continues with ShareVerify which serves to verify the key generated from the ShareKeyGen process. The process will be continued again with Combine which serves to generate a private key that will be used in the decryption process. After that, the process will continue with the encryption process of the secret message. The ciphertext obtained will be sent to the recipient. The receiver verifies the ciphertext by running ValidateCT. Finally, the ciphertext is decrypted by running Decrypt. The software created can be used to display the workflow process of the Threshold schema. In addition, it makes it easier to test intercepts of ciphertext messages to other users so that generic securities analysis is carried out in testing the resulting ciphertext. The results of the implementation of Threshold Encryption algorithm scheme can protect important personal data, because it involves human rights, namely the right to access, the right to delete, the right to correct, the right to be corrected and the right to transfer personal data safely from attacks.

A Lightweight Authentication and Key Agreement Schemes for IoT Environments.

In the Internet of Things (IoT) environment, more types of devices than ever before are connected to the internet to provide IoT services. Smart devices are becoming more intelligent and improving performance, but there are devices with little computing power and low storage capacity. Devices with limited resources will have difficulty applying existing public key cryptography systems to provide security. Therefore, communication protocols for various kinds of participating devices should be applicable in the IoT environment, and these protocols should be lightened for resources-restricted devices. Security is an essential element in the IoT environment, so for secure communication, it is necessary to perform authentication between the communication objects and to generate the session key. In this paper, we propose two kinds of lightweight authentication and key agreement schemes to enable fast and secure authentication among the objects participating in the IoT environment. The first scheme is an authentication and key agreement scheme with limited resource devices that can use the elliptic curve Qu–Vanstone (ECQV) implicit certificate to quickly agree on the session key. The second scheme is also an authentication and key agreement scheme that can be used more securely, but slower than first scheme using certificateless public key cryptography (CL-PKC). In addition, we compare and analyze existing schemes and propose new schemes to improve security requirements that were not satisfactory.

RM- RSA algorithm

The RSA public key cryptographic strength (either security of encryption and decryption schemes or efficiency of algorithms) depends upon the complexity in factorizing the largest integer into odd primes. For every chosen integer, the RSA’s strength varies. RSA key generation space is the group of non-negative integers relatively prime to φ(n) and encryption, decryption spaces are both equal to the group of integers relatively prime to n. Operational time and data storage are two of its efficiency aspects. To reduce the operational time along with reduction data storage is a difficult task in RSA public key cryptography. In addition that the Security of RSA public key cryptography for an adversary with polynomial bounds computations is another biggest task. In this paper, we are going to propose a new kind of public key cryptographic system, nearly four times more efficient in data storage and operational time to that of RSA and probably one fourth of security complexity of RSA. This new crypto system is possible only based on one of the strong pseudo prime test :Rabin-Miller test. So, name it as RM-RSA. In this way,we are going to compare the efficiency of that RM-RSA and previously our proposed S-RSA in “Solovay-Strassen test in a RSA Pubic key Cryptosystem”.

Certain sequence of arithmetic progressions and a new key sharing method

We consider a special type of sequence of arithmetic progressions, in which consecutive progressions are related by the property: ithterms ofjth, (j + 1)thprogressions of the sequence are multiplicative inverses of each other modulo(i + 1)thterm ofjthprogression. Such a sequence is uniquely defined for any pair of co-prime numbers. A computational problem, defined in the context of such a sequence and its generalization, is shown to be equivalent to the integer factoring problem. The proof is probabilistic. As an application of the equivalence result, we propose a method for how users securely agree upon secret keys, which are ensured to be random. We compare our method with factoring based public key cryptographic systems: RSA (Rivest et al., ACM 21, 120–126, 1978) and Rabin systems (Rabin 1978). We discuss the advantages of the method, and its potential use-case in the post quantum scenario.

A Secure Electronic Messaging System in Client Server Cryptography-RSA Algorithm

The potency and effectiveness of the knowledge systems, in some ways, rely upon its design and the way knowledge area unit transmitted among totally different parties. Similarly, a really crucial side within the computer code development is that the security of knowledge that flows through open communication channels. one in all the foremost widespread design is client/server design that creates the centralization of knowledge storage and process modify, and supply flexibility for applying authentication strategies and coding algorithms inside info systems. whereas the amount of shoppers increase, its need increasing the authentication and coding level as high as potential. Client/server could be a technology that enables to open associate degree interactive session between the user's browser and also the server. during this study, we tend to used client/server design to accomplish secure messaging/chat between shoppers while not the server having the ability to decode the message by applying 2 layer security: one layer of coding between the shoppers and also the server, and also the second layer of coding between the shoppers within the chat space. during this manner, a shopper / Server Cryptography- based mostly Secure electronic messaging System mistreatment RSA (Rivest- Shamir-Adelman), that could be a wide used public-key cryptography and authentication system for encryption of digital electronic messaging transactions like email over the computer network, extranet and net, to write in code and decipher messages in an exceedingly terminal window is developed.

A Primitive Proposal of an Algorithm for IP and Mac Based Data Aggregation and message authentication in Wireless Sensor Networks

In wireless sensor networks(WSN) ,authentication of messages is the highly important function in preventing threats from un wanted , un authorized and corrupt messages from being sent. There are various message verification and authentication methods have been proposed as well as developed based on cryptography technology such as symmetric key cryptographic systems or public-key cryptographic systems. Also there are many different techniques available based on polynomial-based schemes, elliptic curve cryptography (ECC) and so on. All the above said methods have its own merits and demerits. In this research work a new method of authenticating the message by its IP and MAC address (together encrypting) and analysing the encrypted message to find the authenticity of the message and the node which has sent the message at collecting node will be carried out.