Public Key Cryptographic Algorithms Research Articles

Digital signature based on ISRSAC

Digital signature has recently played an increasingly important role in cyberspace security. Most of them are based on the public key cryptography. Public key cryptography is a mainstream cryptographic algorithm system that has been widely used in cyberspace security in recent years. The most classic public key cryptography algorithm is RSA and its difficulty is based on the large integer decomposition problem. In 2017, ISRSAC was proposed by M.Thangaval. ISRSAC has made security improvements to the RSA algorithm by increasing the complexity in factoring the value of modulus ‘n’. A digital signature algorithm based on ISRSAC algorithm was completed in this paper, and furthermore, a proxy signature algorithm based on ISRSAC and two kinds of multi-signature algorithms were presented, which include sequential multi-signature and broadcasting multi-signature.

An Experimental Study of Building Blocks of Lattice-Based NIST Post-Quantum Cryptographic Algorithms

Security of currently deployed public-key cryptography algorithms is foreseen to be vulnerable against quantum computer attacks. Hence, a community effort exists to develop post-quantum cryptography (PQC) algorithms, most notably the NIST PQC standardization competition. In this work, we have investigated how lattice-based candidate algorithms fare when implemented in hardware. To achieve this, we have assessed 12 lattice-based algorithms in order to identify their basic building blocks. We assume the algorithms will be implemented in an application-specific integrated circuit (ASIC) platform and the targeted technology is 65 nm. To estimate the characteristics of each algorithm, we have assessed the following characteristics: memory requirements, use of multipliers, and use of hashing functions. Furthermore, for these building blocks, we have collected area and power figures for all studied algorithms by making use of commercial memory compilers and standard cells. Our results reveal interesting insights about the relative importance of each building block for the overall cryptosystem, which can be used for guiding ASIC designers when selecting an algorithm or when deciding where to focus optimization efforts such that the final design respects requirements and design constraints.

Safeguarding unmanned aerial systems: an approach for identifying malicious aerial nodes

The coordination between aerial and ground nodes has enhanced the versatility and quality of the traditional networks. The application of aerial systems in mission-critical operations, as well as civilian applications, brings in the context of safeguarding unmanned aerial systems (UAS) from malicious attackers. This study discusses the threats and attacks mounted on UAS, alongside the challenges introduced by the unmanned aerial vehicle (UAV) network structure itself. A framework for safeguarding UAS against malicious attackers and recovering the rogue UAVs is proposed in the study. The proposed framework enforces a dynamic conceptual grid-based layout over the actual geographical deployment. The dynamically shuffling grid ascertains the security of transmission channels, as every time the grid is shuffled periodically or based on abnormal behaviour, the safety paradigm is reinitiated. Public key cryptographic algorithms are deployed for securing the communication links. Neural networks-based predictions are used for detecting abnormality in behavioural, statistical, and mobility patterns. Principal component analysis based on multivariate statistical analysis is used for detecting outliers in the aerial network environment. The behaviour prediction and outlier detection algorithms significantly improve the overall performance of the network and provide immunity against the intruders with reduced false positives, high accuracy, and better detection rate.

RSA Encryption and Decryption System

For communication in the wireless networking, transmission of data over network sometimes is not safe. In such case security of network is one of the essential aspect in computer networking. Cryptography is antechnique of transforming an plaindata into encrypted one, and then retransform that encrypted data back to its plain (original) form. In this we authenticate the sender to whom you want to send that data file. There are two different techniques of cryptography, symmetric key cryptography (called public-key cryptography) algorithms and asymmetric key cryptography (called public-key cryptography) algorithms. There are also various algorithms for encrypted data using either public or private key or both. This paper describes RSA algorithm which first convert our data into other form and then encrypt it using RSA public key encryption at sender side & at receiver side, first it authenticate the receiver then decrypt the data/ file and convert into original form.

Key Generation Using Generalized Pell’s Equation in Public Key Cryptography Based on the Prime Fake Modulus Principle to Image Encryption and Its Security Analysis

Abstract RSA is one among the most popular public key cryptographic algorithm for security systems. It is explored in the results that RSA is prone to factorization problem, since it is sharing common modulus and public key exponent. In this paper the concept of fake modulus and generalized Pell’s equation is used for enhancing the security of RSA. Using generalized Pell’s equation it is explored that public key exponent depends on several parameters, hence obtaining private key parameter itself is a big challenge. Fake modulus concept eliminates the distribution of common modulus, by replacing it with a prime integer, which will reduce the problem of factorization. It also emphasizes the algebraic cryptanalysis methods by exploring Fermat’s factorization, Wiener’s attack, and Trial and division attacks.

A Hybrid Cryptosystem Using Vigenère Cipher and Rabin-p Algorithm in Securing BMP Files

Vigenère cipher is a classical cryptography algorithm and similar to other classical algorithms, it produces smaller but less secure ciphertexts than a public key cryptography algorithm. Meanwhile, Rabin-p is a public key cryptography algorithm with a stronger encryption than Vigenère cipher. Nevertheless, as a public key algorithm, Rabin-p is inefficient to encrypt vast amounts of messages such as BMP image files, since the size of the cipherimages will increase manyfold and this would lead to a problem in storing and sending the cipherimages. To overcome these problems, in this study, we combined the Vigenère cipher and the Rabin-p algorithm in a hybrid cryptosystem scheme. In the experiment, the Vigenère cipher was used to encrypt the BMP files and the Rabin-p algorithm was used to encrypt the Vigenère keys. The result showed that the size of the cipherimages did not increase and the decryption procedure could recover the original BMP files while maintaining their integrity.

Hybrid cryptosystem based on plaintext related computational ghost imaging encryption and elliptic curve algorithm

A hybrid cryptosystem based on plaintext-related ghost imaging and elliptic curve public-key cryptographic algorithm (ECC) is proposed in this paper. Thereinto, the ECC algorithm is used to protect and distribute session keys and the optical encryption system with session keys is used to encrypt and decrypt images. Thousands of phase-only mask keys can be replaced by parameter keys in this method, which successfully reduces the pressure of key storage. With dynamic updating session keys, the attacks are effectively prevented and the security resilience is enhanced. In addition, the utilization of an ECC cryptosystem solves the inevitable problem of key management and dispatch in conventional ghost imaging encryption system. The feasibility, security and robustness of the method are further analyzed through computer simulations.

Alternative signature generation procedures in the digital signature schemes based on the hidden discrete logarithm problem

Public-key cryptographic algorithms and protocols based on computational difficulty of the factorization problem and on the discrete logarithm problem are widely used in information-telecommunication systems. Currently the problem of construction of the post-quantum algorithms and protocols, i.e. cryptoschemes that are secure to potential attacks using quantum computers, represents a challenge in the area of applied and theoretic cryptography. In the literature the postquantum signature schemes based on the hidden discrete logarithm problem that is formulated in the finite non-commutativeassociative algebras were proposed. A disadvantage of such signature schemes is comparatively large size of the private key. The goal of the study is to develop an alternative signature generation procedures that will allow to reduce significantly the size of the private key. To achieve the goal, it is using the elements of the public key to compute the fixation vector at the first step of the signature formation procedure. As a result, there are designed alternative signature generation procedures in two known signature schemes based on the computational difficulty of the hidden discrete logarithm problem. Application of the proposed procedures gives possibility to reduce the size of the private key. The practical significance of the study is reduction the size of the protected memory in the electronic devices used for computation of the digital signatures.

An Efficient MQ-Signature Scheme Based on Sparse Polynomials

Multivariate quadratic (MQ) equations-based cryptography is one of the most promising alternatives for currently used public-key cryptographic algorithms in the post-quantum era. It is important to design practical public-key signature schemes on embedded processors and resource-constrained devices for emerging applications in Internet of Things. The MQ-signature schemes are suitable for low-cost constrained devices since they require only modest computational resources. In this paper, we propose an efficient MQ-signature scheme, SOV, using sparse polynomials with a shorter secret key and give its security analysis against known algebraic attacks. Compared to Rainbow, the secret key of SOV has reduced by a factor of 90% without increasing the public key size. In particular, SOV requires signatures of 52 bytes, while ECDSA-256 requires signatures of 64 bytes.

Improved Hybrid Approach for Side-Channel Analysis Using Efficient Convolutional Neural Network and Dimensionality Reduction

Deep learning-based side channel attacks are burgeoning due to their better efficiency and performance, suppressing the traditional side-channel analysis. To launch the successful attack on a particular public key cryptographic (PKC) algorithm, a large number of samples per trace might need to be acquired to capture all the minor useful details from the leakage information, which increases the number of features per instance. The decreased instance-feature ratio increases the computational complexity of the deep learning-based attacks, limiting the attack efficiency. Moreover, data class imbalance can be a hindrance in accurate model training, leading to an accuracy paradox. We propose an efficient Convolutional Neural Network (CNN) based approach in which the dimensionality of the large leakage dataset is reduced, and then the data is processed using the proposed CNN based model. In the proposed model, the optimal number of convolutional blocks is used to build powerful features extractors within the cost limit. We have also analyzed and presented the impact of using the Synthetic Minority Over-sampling Technique (SMOTE) on the proposed model performance. We propose that a data-balancing step should be mandatory for analysis in the side channel attack scenario. We have also provided a performance-based comparative analysis between proposed and existing deep learning models for unprotected and protected Elliptic curve (ECC) Montgomery Power ladder implementations. The reduced network complexity, together with an improved attack efficiency, promote the proposed approach to be effectively used for side-channel attacks.

Algebraic Fault Analysis of UOV and Rainbow With the Leakage of Random Vinegar Values

A public-key cryptographic algorithm based on multivariate quadratic equations is one of promising post-quantum alternatives for current public-key cryptography. The security of multivariate quadratic schemes has been sufficiently analyzed mathematically, but few works have been devoted to implementation attacks. In this paper, we present algebraic fault analysis of two well-known multivariate quadratic schemes, UOV and Rainbow, which combines fault attacks with key recovery attacks using good keys. We focus on fault attacks which cause faults on random Vinegar values used in signing. Our fault models are divided into three cases according to the leakage types of the Vinegar values: reused, revealed and set to zero. We show that the equivalent key of UOV is completely recovered in polynomial time from $(m+1)$ , $n$ and $m$ signatures generated by the entire faulty Vinegar values in the three cases, respectively. Specifically, the equivalent key of UOV is completely recovered from 45, 103 and 44 signatures generated by 59 bytes of faulty Vinegar values in the three cases, respectively, at a 128-bit security level. The equivalent key of Rainbow is also recovered from 44, 79 and 43 signatures with 36 bytes of faulty Vinegar values in the three cases, respectively. This is the first result that leads to the full secret key recovery of UOV and Rainbow from the leakage of the Vinegar values. In the other cases, we show that complexities of the key recovery attacks on Rainbow and UOV are significantly weakened in terms of the number of faulty Vinegar values. Our attacks can be applied to Rainbow and LUOV selected to NIST Post-Quantum Cryptography Standardization Round 2. Countermeasures against our attacks are investigated.

Advances in Discrete Mathematics: From Combinatorics to Cryptography

Discrete mathematics forms the foundation for various fields, including computer science and cryptography, by providing essential tools for problem-solving in discrete structures. This paper explores the advancements in discrete mathematics, focusing on combinatorics and cryptography. It discusses the basic concepts of combinatorics, such as permutations, combinations, and graph theory, along with their applications in modern cryptography. The paper also examines symmetric and public key cryptography algorithms, including DES, AES, RSA, and ECC, highlighting their key features and security mechanisms. Furthermore, it explores the role of discrete structures, such as sets, relations, functions, and lattices, in cryptography, emphasizing their importance in designing secure cryptographic systems. Overall, this paper provides a comprehensive overview of the advancements in discrete mathematics and their applications in modern cryptography.

Hyper Elliptical Curve Cryptography (Hecc) For Cloud

This system provides an insight into developing a distributed system which is secure, robust and user friendly. This thesis suggests a design and implementation of a digital envelope that combines the hashing algorithm of MD5, the symmetric key algorithm of AES and the asymmetric key algorithm of Hyper Elliptic Curve. A hybrid algorithm is designed, combining the best of both AES and ECC over GF(p) cryptography. The MD5 hash algorithm is adopted to ensure integrity of the data. Cryptography (HECC). This paper discusses securing the data in clouds through implementing the key for encryption and decryption using hyper elliptical curve cryptography. The focus is on Advanced Encryption Standard (AES), the most commonly used secret key cryptographic algorithm, and Hyper Elliptic Curve Cryptography (HECC), public key cryptographic algorithms which have gained popularity in the recent years and are replacing traditional public key cryptosystems, such as RSA and ECC. Such techniques are necessary in order to use high security cryptographic algorithms in real world applications.

Systematic construction of high dimensional fractional-order hyperchaotic systems

Abstract The problem of designing fractional-order hyperchaotic systems (FOHSs) by a consistent and systematic procedure is still an open one at large. The tedious hit and trial design procedures adopted in literature to generate hyperchaos pose as a hindrance; especially when the dimension of the system is high. The paper thus presents a solution to the above problem and further discusses the application of FOHSs by putting forward three proposals. First is the design of the simplest possible single state nonlinear feedback controller based on fractional-order stability theorems for creating hyperchaos from a nominal system. The design is organised and even higher dimensional FOHSs can be easily constructed. Secondly, a hybrid synchronisation controller is designed so that the FOHSs obtained using the proposed systematic methodology, are both completely synchronised and antisynchronised simultaneously. Thirdly, a public key cryptographic algorithm is presented using the higher unpredictable nature and complexity of FOHSs to encrypt and decrypt private messages. Two representative examples presented in this work distinctly confirm the effectiveness of the proposed techniques.

Development of Public Key Cryptographic Algorithm Using Matrix Pattern for Tele-Ultrasound Applications

A novel public key cryptographic algorithm using a matrix pattern is developed to improve encrypting strength. Compared to the Rivest–Sharmir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) algorithms, our proposed algorithm has superior encrypting strength due to several unknown quantities and one additional sub-equation during the encrypting process. Our proposed algorithm also provides a faster encoding/decoding speed when the patient’s images for tele-ultrasound applications are transmitted/received, compared to the RSA and ECC encrypting algorithms, because it encodes/decodes the plain memory block by simple addition and multiplication operations of n terms. However, the RSA and ECC algorithms encode/decode each memory block using complex mathematical exponentiation and congruence. To implement encrypting algorithms for tele-ultrasound applications, a streaming server was constructed to transmit the images to the systems using ultrasound machines. Using the obtained ultrasound images from a breast phantom, we compared our developed algorithm, utilizing a matrix pattern, with the RSA and ECC algorithms. The elapsed average time for our proposed algorithm is much faster than that for the RSA and ECC algorithms.

Multiple-Image Encryption Mechanism Based on Ghost Imaging and Public Key Cryptography

On the basis of ghost imaging, this paper proposes a multiple-image encryption scheme combining public key cryptography and Hadamard basis pattern. In the encryption system, a plurality of light paths are set, and the Hadamard basis patterns are used for illumination, so that each light path is concentrated in a bucket detector to obtain intensity values of all images. Then, all the detected intensity values are encrypted by using public key cryptography algorithm to obtain the final ciphertext. The use of basis patterns allows for high-quality reconstruction. In addition, randomness in the permutation operation and public key cryptography provide a strong security feature for the encryption system. The multiple-image encryption scheme solves the crosstalk problem among images. The basic principle of the encryption scheme is theoretically analyzed, and the feasibility and security of the proposed method are verified by numerical simulation.

Encryption and Decryption using Hybrid Cryptography Techniques and Multi-level Steganography

Data Encryption, in the present time, is used to deter malicious parties from accessing sensitive data, allowing the access to only authorized parties as it uses the key to safeguard the sensitive information to be transferred. Various cryptography techniques are used to maintain confidentiality and integrity of the data, and this paper proposes the hybrid scheme of using four layers of encryption including steganography to safeguard the authenticity of the information to be transferred. In this paper, three conventional key cryptography algorithms, which are Fibonacci series, XOR cipher and PN sequence encryption, are used along with RSA cryptography which is a public key cryptography algorithm. In addition to it, steganography technique is also used in the last two layers of our proposed model. Firstly, the whole of the encrypted string, obtained after the above cryptography algorithms, is hidden inside the first image. Now this encrypted host image is further hidden inside another image by using one bit LSB algorithm. This model offers the double security of the data as here the data is not only encrypted but also hidden in an image which again is hidden inside another image making it very hard even to detect the data.

A new enhancement of elliptic curve digital signature algorithm

Elliptic Curve Digital Signature Algorithm (ECDSA) is a public key cryptographic algorithm based on the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP), it is used to ensure users’ authentication, data integrity and transactions non-repudiation. However, its weakness is to derive the signer’s private key in case he uses the same random number for to generate two signatures for two different messages. Firstly, in this paper we present the ECDSA and analyse its variants proposed in the literature.Also, we propose a new improvement technique for ECDSA of Liao and Shen and ECDSA of Chande and Lee. We intend to do so by introducing the unknown parameters which are used in the verification of the signature. Our aim is to overcome the problem which has not been explained in ECDSA schemes of both Liao and Shen and Chande and Lee.

Implementing RSA for Wireless Sensor Nodes.

As wireless sensor networks (WSNs) become more widespread, potential attacks against them also increase and applying cryptography becomes inevitable to make secure WSN nodes. WSN nodes typically contain only a constrained microcontroller, such as MSP430, Atmega, etc., and running public key cryptography on these constrained devices is considered a challenge. Since WSN nodes are spread around in the field, the distribution of the shared private key, which is used in a symmetric key cryptographic algorithm for securing communications, is a problem. Thus, it is necessary to use public key cryptography to effectively solve the key distribution problem. The RSA cryptosystem, which requires at least a 1024-bit key, is the most widely used public key cryptographic algorithm. However, its large key size is considered a drawback for resource constrained microcontrollers. On the other hand, RSA allows for extremely fast digital signature generation which may make it desirable in applications where messages transmitted by sensor nodes need to be authenticated. Furthermore, for compatibility with an existing communication infrastructure, it may be desirable to adopt RSA in a WSN setting. With this work, we show that, in spite of its long key size, RSA is applicable for wireless sensor networks when optimized arithmetic, low-level coding and some acceleration algorithms are used. We pick three versions of the MSP430 microcontroller, which is used widely on wireless sensor network nodes, and implement 1024-bit RSA on them. Our implementation achieves 1024-bit RSA encryption and decryption operations on MSP430 in only s and s, respectively. In order to achieve these timings, we utilize several acceleration techniques, such as the subtractive Karatsuba-Ofman, Montgomery multiplication, operand scanning, Chinese remainder theorem and sliding window method. To the best of our knowledge, our timings for 1024-bit RSA encryption and decryption operations are the fastest reported timings in the literature for the MSP430 microcontroller.

The cryptanalysis of the Rabin public key algorithm using the Fermat factorization method

As a public key cryptography algorithm, the Rabin algorithm has two keys, i.e., public key (n) and private key (p, q). The security of Rabin algorithm relies on the difficulty of factoring very large numbers, so the greater the private keys are used, the better the security becomes. In order to test how hard it is to cryptanalyze the Rabin public key n, we use the Fermat factorization method to obtain the values of p and q. After obtaining the factors, both of these factors are tested whether or not they are in accordance with the Rabin private key requirements. The first is to test whether or not the factors are prime numbers using Fermat Little Theorem. The second is to test whether or not the factors are congruent to 3 in modulo 4. If the results of the two tests turn out to be positive, then the factors are indeed p and q, the private keys of the Rabin algorithm. The result of our experiment indicates that the value of public key n does not have a directly proportional correlation to the factoring time. A factor which may affect the factoring time is the difference between the private keys (p - q): the larger the difference, the longer the factoring time.