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We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: — There are NP search problems solvable by quantum polynomial-time (QPT) machines but not classical probabilistic polynomial-time (PPT) machines. — There exist functions that are one-way, and even collision resistant, against classical adversaries but are easily inverted quantumly. Similar counterexamples exist for digital signatures and CPA-secure public key encryption (the latter requiring the assumption of a classically CPA-secure encryption scheme). Interestingly, the counterexample does not necessarily extend to the case of other cryptographic objects such as PRGs. — There are unconditional publicly verifiable proofs of quantumness with the minimal rounds of interaction: for uniform adversaries, the proofs are non-interactive, whereas for non-uniform adversaries the proofs are two message public coin. — Our results do not appear to contradict the Aaronson-Ambanis conjecture. Assuming this conjecture, there exist publicly verifiable certifiable randomness, again with the minimal rounds of interaction. By replacing the random oracle with a concrete cryptographic hash function such as SHA2, we obtain plausible Minicrypt instantiations of the above results. Previous analogous results all required substantial structure, either in terms of highly structured oracles and/or algebraic assumptions in Cryptomania and beyond. [ABSTRACT FROM AUTHOR]

The field of cryptography has grown significantly with the advent of information and communication technologies due to the increasing complexity of cyber threats and rising security requirements. This evolution has come with the creation of new cryptosystems and improvements to current ones. This study is the first to explore the RSA approach in the framework of t-intuitionistic fuzzy subgroups. This technique makes group-based cryptographic operations safer when there are unclear relationships and hesitations. This supports the complex and uncertain nature of subgroup membership, allowing for much more significant representations of the degrees of belonging, non-belonging, and hesitancy for the group elements along parameter 't'. The t-intuitionistic fuzzy RSA technique employs a t-intuitionistic fuzzy subgroup to address cryptosystem ambiguity, fuzziness, and imprecision. Consequently, inaccurate cryptographic data is more effectively represented, manipulated, and protected. Furthermore, this technique enhances the current level of fuzzy cryptography. The t-intuitionistic fuzzy RSA algorithms are of theoretical and practical value, as they significantly contribute towards developing fuzzy cryptography, fuzzy algebraic structures, and decision support systems. In this paper, the notions of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers are introduced. A new RSA cryptosystem based on a t-intuitionistic fuzzy subgroup is proposed in which the plaintext and the ciphertext are obtained in terms of t-intuitionistic fuzzy numbers and triangular t-intuitionistic fuzzy numbers. In addition, the significance of the concept of the t-intuitionistic fuzzy subgroup is highlighted as a suitable alternative tool to secure the data under consideration. In addition, the practical effect of the proposed methods is also investigated in this study. A mathematical mechanism is presented to implement the t-intuitionistic fuzzy RSA algorithm. Finally, a comparative analysis of the developed technique is presented with some existing methods to showcase the applicability and superiority of the recently developed method. [ABSTRACT FROM AUTHOR]

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- k i ) introduces the selective coefficient k i 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. [ABSTRACT FROM AUTHOR]

Shor's factorization algorithm (SFA) aims at finding the non-trivial factor of a given composite number, but the algorithm does not always work. In some cases, it has to call back to the beginning of the algorithm to make recalculation. After the analysis of the principle of SFA and the characteristics of RSA public-key cryptography with a series of data calculations, it can be concluded that the random value selected by the algorithm is closely related to whether the obtained period is effective. Therefore, a new optimized scheme is proposed to tackle with this defect from two perspectives: (a) When the a value is a perfect square, the algorithm can be completed with an odd cycle r. (b) When the period r obtained by the randomly selected a value is a multiple of 3 , the algorithm can be completed by modifying the decomposition method to relax the requirements for the period without affecting the complexity of the algorithm. Due to the limitations of hardware in applying the quantum algorithms, the classical algorithm is applied to simulate quantum algorithms to test the success rate of decomposition of some composite numbers. The result indicates the effectiveness of the improved algorithm, which significantly reduces the probability of repeated operations to save the quantum circuit resources. [ABSTRACT FROM AUTHOR]

Steganography is a technique for hiding secret messages while sending and receiving communications through a cover item. From ancient times to the present, the security of secret or vital information has always been a significant problem. The development of secure communication methods that keep recipient-only data transmissions secret has always been an area of interest. Therefore, several approaches, including steganography, have been developed by researchers over time to enable safe data transit. In this review, we have discussed image steganography based on Discrete Cosine Transform (DCT) algorithm, etc. We have also discussed image steganography based on multiple hashing algorithms like the Rivest–Shamir–Adleman (RSA) method, the Blowfish technique, and the hash-least significant bit (LSB) approach. In this review, a novel method of hiding information in images has been developed with minimal variance in image bits, making our method secure and effective. A cryptography mechanism was also used in this strategy. Before encoding the data and embedding it into a carry image, this review verifies that it has been encrypted. Usually, embedded text in photos conveys crucial signals about the content. This review employs hash table encryption on the message before hiding it within the picture to provide a more secure method of data transport. If the message is ever intercepted by a third party, there are several ways to stop this operation. A second level of security process implementation involves encrypting and decrypting steganography images using different hashing algorithms. [ABSTRACT FROM AUTHOR]

Social media blockchain is emerging as a promising solution to deal with privacy issues, by putting user privacy in edge nodes rather than centralized nodes. Under the protection of information encryption, only those who have cryptographic keys can get access to key information. This work aims at multimedia information in social media blockchain and utilizes the RSA encryption mechanism to construct the information encryption system. Due to the resilience of biometric features, the biometric cryptographic keys are not easy to be fabricated. Thus, this paper proposes a biometric keys-enhanced multimedia encryption algorithm for social media blockchain. First of all, the wiener filter is adopted to make some preprocessing operations to images, such as noise reduction. On this basis, the discrete wavelet transform is adopted to extract feature representation from images, and nonlinear approximation of contourlet transform is adopted to make feature fusion. Next, cryptographic keys can be generated from the fused biometric feature vectors to encrypt biometric data. Finally, some simulation experiments are conducted to evaluate performance of the proposal from three aspects: key generation time, security level and encryption-decryption time complexity. For key generation time, processing speed of the proposal is approximately 1–2 ms per sample. For security level, the proposal can reach an index value beyond 95% which is higher than comparison methods. For encryption-decryption time complexity, the proposal is about 30% lower than comparison methods. [ABSTRACT FROM AUTHOR]

The modified RSA provides high efficiency against attacks and, as a result, it is considered the ideal choice for many applications. In this paper, we introduce an alternative to the modified RSA key encryption system called TPRSA, based on Tri-Cartesian algebra and polynomials, by modifying the mathematical structure of text encryption and decryption keys to obtain a high level of security. [ABSTRACT FROM AUTHOR]

Summary: The present scenario witnesses "the second quantum revolution," which has enabled the development of revolutionary novel quantum tools. Quantum computing endeavors to establish higher computing standards that can potentially solve complex structures. Post‐quantum cryptography (PQC) has emerged as one of the new domains of cryptography, which is resilient to quantum attacks owing to the revolution in quantum computing. To ensure quantum security, the lattice‐based cryptosystem (LB‐cryptosystem) is one of the promising tools of PQC to address quantum‐based threats. The traditional security algorithms, such as RSA and Diffie–Hellman (DH), are strong enough to resist present security threats. However, it has been predicted that quantum technologies have the capability to break the security of most traditional algorithms whose security is based on prime factorization and DH‐type hard problems. Therefore, research is currently focused on addressing the security and privacy threats by using LB‐cryptosystems to secure various applications, organizations' data, and information infrastructure in the quantum era. The purpose of this article is to investigate recent advances in LB‐cryptosystems that may allow the design of secure models for smart‐grid networks (SGNs) against existing and future quantum attacks. SGNs have been explored as the bi‐directional assimilation of communication in terms of electricity generation, transmission, allocation, and utilization. This survey provides a comprehensive overview of LB‐cryptosystems, as well as their potential applications in securing SGNs. Lastly, the article summarizes the various PQC primitives, NIST selected algorithms, open‐source tools along with their packages, and various PQC industrial initiatives, and also compares traditional cryptographic schemes with other PQC. [ABSTRACT FROM AUTHOR]

Big data, cloud computing and other hot areas are the use of personal information, but in the process of using this data, a large number of improper behavior is used to steal personal information. Most of the encryption algorithms in common use nowadays are based on ones that are no longer absolutely secure, such as RSA attacked by factorization, elliptic curves attacked by Pollard's lambda algorithm, and symmetric encryption algorithms attacked by collisions. In this paper, an integrated encryption and compression algorithm is designed, firstly, the data is transformed into the form of matrix, and the Jordan decomposition is used for preliminary compression and encryption from the two-dimensional point of view, and then based on the sparsity of matrix vectors, the compression-aware technique is used for compressing the set of key vectors, and the ciphertext group J produced by Jordan decomposition (which is a string of numbers with matrix diagonal length base √2 N), as well as the set of key vectors Y and the intermediate value Θ produced by compression awareness are obtained in the end. This sidesteps the common algorithms that have already been breached and is able to combine better encryption performance with compression performance while being innovative. [ABSTRACT FROM AUTHOR]

In the face of advancing quantum computing capabilities posing significant threats to current cryptographic protocols, the need for post-quantum cryptography has become increasingly urgent. This paper presents a comprehensive analysis of the performance of various post-quantum cryptographic algorithms specifically applied to digital signatures. It focuses on the implementation and performance analysis of selected algorithms, including CRYSTALS-Dilithium, Falcon, and SPHINCS+, using the liboqs library. Performance tests reveal insights into key pair generation, file signing, and signature verification processes. Comparative tests with the well-known and popular RSA algorithm highlight the trade-offs between security and time efficiency. The results can help to select secure and efficient ciphers for specific 5G/6G services. [ABSTRACT FROM AUTHOR]

Advances in quantum computers may pose a significant threat to existing public-key encryption methods, which are crucial to the current infrastructure of cyber security. Both RSA and ECDSA, the two most widely used security algorithms today, may be (in principle) solved by the Shor algorithm in polynomial time due to its ability to efficiently solve the discrete logarithm problem, potentially making present infrastructures insecure against a quantum attack. The National Institute of Standards and Technology (NIST) reacted with the post-quantum cryptography (PQC) standardization process to develop and optimize a series of post-quantum algorithms (PQAs) based on difficult mathematical problems that are not susceptible to being solved by Shor's algorithm. Whilst high-powered computers can run these PQAs efficiently, further work is needed to investigate and benchmark the performance of these algorithms on lower-powered (constrained) devices and the ease with which they may be integrated into existing protocols such as TLS. This paper provides quantitative benchmark and handshake performance data for the most recently selected PQAs from NIST, tested on a Raspberry Pi 4 device to simulate today's IoT (Internet of Things) devices, and provides quantitative comparisons with previous benchmarking data on a range of constrained systems. CRYSTALS-Kyber and CRYSTALS-Dilithium are shown to be the most efficient PQAs in the key encapsulation and signature algorithms, respectively, with Falcon providing the optimal TLS handshake size. [ABSTRACT FROM AUTHOR]

In recent times, blockchain-based data auditing protocols have emerged as a cutting-edge area of study. Nevertheless, a conspicuous dearth of a generic framework upon which to ground such protocols is evident. This study introduces a pioneering and all-encompassing framework, designated as "Blockchain-assisted On-chain Auditing for Off-chain Storage" (BA2OC). The BA2OC framework operates without the reliance on a predefined auditor for the auditing process or a centralized verifier for the verification of on-chain auditing. It is conceivable that BA2OC forms the cornerstone of public data auditing protocols underpinned by blockchain technology. This framework bestows evidence of data ownership, ensures data integrity, facilitates public verification, supports batch verification, and bolsters the security against cyber threats through the utilization of cryptographic tools. The analysis underscores the comprehensive nature of the BA2OC framework, which positions it as the linchpin of blockchain-based public auditing protocols. Following a parametric evaluation of the BA2OC framework, this study takes into account real-world considerations, such as the utilization of the RSA cryptosystem and Android-based smartphones, to proffer a concrete protocol. The investigation further demonstrates that the BA2OC framework minimizes communication overhead while maintaining operational efficiency. [ABSTRACT FROM AUTHOR]

Fog computing provides a suitable development for real-time processing in the Internet of Things (IoT). Attribute-based encryption (ABE) is the main method to control data access in fog computing. A residue number system (RNS) can speed up multiplication and exponential operations by converting very large integers to small integers. This paper proposes a fine-grained lightweight access control scheme using ABE modified with RNS properties (RNS-ABE) with fog computing. Decryption is implemented with the Chinese remainder theorem (CRT), and a new access structure based on the CRT secret sharing scheme is also introduced. Security of the proposed scheme proved based on RNS properties and the complicated problem of factoring a very large integer into its large prime factors, like RSA encryption. The time cost comparison shows that the total encryption and decryption time of our scheme is more efficient than the lightweight schemes with the underlying operation of bilinear pairing. [ABSTRACT FROM AUTHOR]

Nowadays, technology is increasingly being adopted in different kinds of businesses to process, store, and share sensitive information in digital environments that include enormous numbers of users. However, this has also increased the likelihood of cyberattacks and misuse of information, potentially causing severe damage. One promising technology, which can provide the required security services with an improved level of efficiency, is blockchain. This research explores the use of Ethereum blockchain and smart contracts to create a secure and efficient quality assurance system (QAS) for academic programs. By utilizing blockchain and smart contracts, the proposed approach improves the integrity and reliability of sensitive information processed by the QAS, promotes transparency and governance, and reduces the time and effort required for quality operations. The current approach uses an additional access control layer to further enhance user privacy. Smart contracts automate various quality transactions and saves time and resources, and hence increases the efficiency of the QAS. The interplanetary file system (IPFS) is used to address the challenge of size limitations in blockchain. Additionally, this research investigates the use of various cryptographic schemes to provide robust security services at the application layer. The experimental results showed that the use of a hybrid cryptosystem relying on an Elliptic curve digital signature and AES encryption (AES_ECCDSA) outperforms other counterparts' cryptosystems using an RSA digital signature and AES encryption (AES_RSADSA) and Elliptic Curve Integrated Encryption Scheme (ECIES) in terms of speed. The performance results showed that AES_ECCDSA consumes 188 ms to perform the required cryptographic operations for a standard-quality document with a size of 8088 KB, compared to the 231 ms and 739 ms consumed by the AES_RSADSA and ECIES schemes, respectively. This study presents a prototype implementation of the blockchain-based QAS, which outlines the processing model and system requirements for key QAS processes. It has been found that the cost and time required for blockchain operations vary depending on the size of the input data—a larger data size requires more time and costs more to process. The results of the current study showed that the time delay for blockchain transactions ranges from 15 to 120 s, while the cost ranges from USD 50 to USD 400. This research provides evidence that blockchain and smart contract technologies have the potential to create a secure, efficient, and trustworthy QAS environment for academic programs. [ABSTRACT FROM AUTHOR]

In wireless sensor networks, ensuring data confidentiality and integrity is paramount, particularly in sensitive environments. However, existing encryption methods encounter challenges, including key maintenance in symmetric encryption and lower security levels in asymmetric encryption. To address these issues, this paper proposes a novel security protocol employing a hybrid encryption approach, combining both symmetric (AES) and asymmetric (RSA) cryptographic techniques. The protocol introduces a two-phase cryptographic technique utilizing AES for robust encryption in Phase 1 and RSA for efficient key management in Phase 2. Experimental results demonstrate enhanced efficiency in encryption, decryption, and total execution time compared to existing algorithms, marking a significant advancement in cryptographic protocols for improved security in data transmission and management. Key contributions include the division of plaintext for simplified cryptographic processing, AES encryption for Phase 1, RSA encryption for Phase 2, and a seamless decryption process ensuring data integrity and security against attacks. [ABSTRACT FROM AUTHOR]

A blockchain is a decentralized digital network system consisting of multiple blocks connected in a chain. Each block comprises multiple transactions and is linked to the previous block through its hash value. The hash values are calculated using the active transactions within each block and the hash value of the preceding block. A positive impact can be made by combining blockchain technology with the healthcare sector. The consensus mechanism is the key protocol for implementing agreements in the blockchain. This paper proposes a combined RSA (Rivest–Shamir–Adleman) cryptography algorithm with a novel consensus protocol IPBFT (Improved Practical Byzantine Fault Tolerance) in the Hyperledger Fabric platform, for a patient-centered approach using blockchain technology in the healthcare sector. It ensures the reliability and integrity of transactions and prevents malicious nodes from disrupting the network. The Hyperledger Fabric platform is used to provide transparency, security, and trust in the blockchain. Performance metrics such as latency, throughput, scalability, and comparative analysis for the proposed algorithm Improved Practical Byzantine Fault Tolerance (IPBFT) and existing Practical Byzantine Fault Tolerance (PBFT) algorithms have been evaluated to achieve enhanced results. The proposed algorithm solves many problems associated with existing Practical Byzantine Fault Tolerance solutions and improves efficiency and security in the healthcare sector. [ABSTRACT FROM AUTHOR]

Large number factorization is not only the most critical entry point for Rivest–Shamir–Adleman (RSA) security analysis, but also the most direct means of attacking the asymmetric encryption algorithm RSA. In this paper, the factorization methods of large numbers are summarized and analysed: classical integer factoring algorithms, Shor's circuit model algorithm, quantum adiabatic methods (integer factorization based on a quantum nuclear magnetic resonance (NMR) platform and D-Wave quantum annealing), and hybrid quantum-classical computing. Finally, the feasibility of integer factorization based on quantum adiabatics is discussed. In this paper, quantum annealing is regarded as a quantum attack method that is completely different from the famous Shor algorithm, and the potential of D-Wave factorization of large numbers to crack RSA cryptography is verified, which provides a new idea for a quantum attack on RSA public key cryptography. [ABSTRACT FROM AUTHOR]

We introduce a novel image encryption and decryption algorithm for multiple images incorporating multiple parameter fractional discrete cosine transform (MPFrDCT), 3D Arnold transform and RSA cryptosystem. Before encryption, the images are changed into their indexed formats by removing their color maps. The indexed formats of the images are taken as the red, green and blue channel of an RGB image. Firstly, the RGB image is taken as the input of 3D Arnold transform. The 3D Arnold transform not only dislocates the pixel positions, but also changes the pixel values. Mathematically, the 3D map performs both permutation as well as substitution. The distorted image is now encrypted using RSA cryptosystem which is a public key cryptosystem. The RSA cryptosystem makes the image secure in public domain as the hard problem is the factorization of large primes which is unbreakable. Lastly, the domain of the encrypted image is changed to frequency domain using MPFrDCT. If the secret keys are known to an unauthorized person, the encryption algorithm is still secure as the security of the presented cryptosystem depends upon the secret keys and the arrangements of the secret keys. The proposed image encryption algorithm is storage efficient. The statistical and simulation analysis are conducted to evaluate the robustness of the presented encryption and decryption processes. [ABSTRACT FROM AUTHOR]

Summary: Communicating large amounts of data requires an encryption solution that ensures fast and secure data transfer. Unfortunately, it faced privacy and security issues, resulting in higher power consumption, data scarcity, energy, diversity, data reliability, low security, and packet loss in the communication process. The goal of this research is to ensure data transfer while conserving energy and protecting data transmission in WSNs. Therefore, this paper proposes a multipath routing protocol using the HGSPSO algorithm, which is a combination of hybrid gravitational search algorithm (HGSA) and particle swarm optimization (PSO), to securely transmit data from one node to another node under public and private key cryptography. The PSO approach is utilized to resolve the energy hole problem by selecting the cluster head in the sink coverage area. The RSA can be employed for data encryption, data decryption, key generation, and sharing. The metrics like acceleration constants and inertial weights are used for the HGSPSO algorithm. The result of this implementation demonstrated that the scheme had a low energy consumption of 36%, a maximum packet delivery ratio (PDR) of 96%, a higher throughput rate of 88%, and a low packet loss of 39%. [ABSTRACT FROM AUTHOR]

The connected digital environment generates massive amounts of data that must be protected from unauthorized disclosure. Technological advancements and the creative techniques attackers use can exacerbate data security breaches. Security protocols and cryptographic algorithms are the two components of information security, the last being information security's basis and fundamental technology. The cryptographic conception will improve and assure security while also protecting network resources that are exchanged. The goal of this study is to demonstrate the few encryption algorithms that are used to encrypt data on an unsecured network. This research presents a new hybrid encryption strategy for encrypting data. MRDAES encrypts data using Rivest, Shamir, Adleman (RSA), Diffie Hellman (DH), and the Advanced Encryption System. The data will be encoded in two stages: the first by producing the encoded data using the XOR function, and the second by using AES to encode data and obtain the final result to be shared with intended reception with high-security complexity compared to other methods in terms of performance and avalanche effect. The proposed study examines the three most widely used cryptographic symmetric and asymmetric algorithms, RSA, Diffie-Hellman, and AES, and how they operate and impact security and complexity when integrated into a unified hybrid (MRDAES) computation with the proper adjustments. The study also presents an approach for increasing data security while minimizing the number of mathematical equations and obtaining high-security complexity while slightly increasing execution time with chosen large random prime numbers. The results indicate that the new hybrid technique (MRDAES) has more efficient performance and avalanche effect inputs with a minor increase in execution time. The proposed approach MRDAES produced more advanced complexity than classical RSA existing methods and others. According to avalanche effect data, the proposed technique provides better results with a higher percentage than existing algorithms on modified RSA Random Bit Insertion Algorithm (RBMRSA) and classical Rivest, Shamir, and Adleman (RSA). The proposed approach enhances the avalanche effect by 88% compared to 48% achieved by an RBMRSA, with a 40% increase and 87.80% compared to RSA. [ABSTRACT FROM AUTHOR]

In recent years, there has been significant growth in location-based services (LBSs) and applications. These services empower users to transmit their location data to location service providers, thereby facilitating the provisioning of pertinent resources and services. However, in order to prevent malicious users from sending fake location data, users must attest to their location for service providers, namely, through a proof of location (PoL). Such a proof should additionally prevent attackers from being able to obtain users' identity and location information through it. In this paper, we propose an efficient privacy-preserving proof of location (PPPoL) scheme. The scheme is based on the standard cryptographic primitives, including Group Time-based One-Time Password (GTOTP) and public key encryption, which achieves entity privacy, location privacy, and traceability. Unlike the previous GTOTP-based PPPoL scheme, our scheme enables instant location verification with additional hash operations. To encourage the active participation of witnesses in location proofs, we propose an incentive mechanism based on smart contracts. Additionally, we implement a proof of concept of our PPPoL scheme on an Android device. Our experimental results show that proof generation and verification time are on the order of milliseconds. Meanwhile, the total overhead for the incentive mechanism amounts to 0.0011 ETH. This result is practical for mobile device-based LBSs. [ABSTRACT FROM AUTHOR]

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., C R P K C − K i . This algorithm introduces alternative multiplication coefficients K i , the selection of which is determined by the size of T r T d x m o d   N = T d T r x m o d   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. [ABSTRACT FROM AUTHOR]

The article informs about the deep-rooted cybersecurity issues and the potential catastrophic consequences if not addressed, highlighting concerns in cryptocurrency, artificial intelligence, and ransomware. Topic include It proposes the recreation of a conceptual machine based on cybernetics principles to tackle these challenges, emphasizing the need for a new Turing machine and presenting five hypotheses as the foundation of this endeavor.

This work addresses the pressing issue of ensuring reliable information protection amidst increasing data volumes and rising numbers of cyber threats. Traditional cryptographic systems, while generally reliable, may prove vulnerable to new types of attacks, especially quantum ones. This highlights the need for exploring and researching more resilient encryption methods. The work proposes a hybrid cryptosystem that combines the McEliece system with the RSA encryption algorithm. This approach leverages the advantages of both methods: the high security level of RSA, based on the difficulty of factoring large numbers, and the resilience of McEliece to quantum attacks due to the complexity of decoding arbitrary linear codes. A distinctive feature of the proposed hybrid system is the use of Galois fields GF(p) for all operations, which provides an additional layer of protection and flexibility compared to traditional systems based on binary numeral systems. The integration of two asymmetric cryptographic algorithms, whose resilience is based on solving different mathematical problems, enhances the reliability and security of the proposed system. The use of a common parameter n for key generation also simplifies key management and expands the key space by a factor of n. This solution combines error protection with cryptographic security, making it a powerful tool for data protection in environments with potentially unreliable communication channels. The research conducted as part of this work focuses on analyzing the effectiveness and security of the proposed hybrid cryptosystem. Special attention is given to characteristics such as relative information transmission speed, ciphertext length, key size, and resistance to cryptanalysis. The results demonstrate the advantages of the hybrid system compared to using each algorithm individually. The findings could form the basis for further development of cryptographic methods for information protection in the face of modern threats. [ABSTRACT FROM AUTHOR]

With technological development, hackers are possible to access the transmitted data, so we need to constantly develop encryption methods to increase security. In this paper, we have introduced a new cryptosystem hexadecnion polynomial RSA (PH-RSA) by mixing NTRU and polynomial RSA based on a hexadecnion polynomial instead of polynomial RSA with a high level of security. [ABSTRACT FROM AUTHOR]

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Encryption methods had been widely used for secure data transmission and communication in both public and private organizations against intruders. Rivest-shamir-adleman (RSA) encryption algorithm is one of the most popular and efficient encryption schemes that has been in used for decades. Due to technological advancement and innovation, there is a threat to this algorithm. It is believed that introduction of quantum computer will break RSA algorithm easily. In view of this, it is pertinent to research into how RSA algorithm could be strengthened against all adversaries. This research aim at protecting client/server communication and file sharing by generating dynamic public and private keys. The proposed method was implemented in visual basic.net 2008. The result shows that dynamic keys do not affect the performance of the system and it is capable of protecting communication and file sharing between client/server. As the key generated keeps changing at an interval, it will difficult for most advance computer to factor any of the keys before another key is generated. This is the basis of the security of the proposed system. [ABSTRACT FROM AUTHOR]

In cryptography, we use different methods to hide information and make sure it's safe when shared. This keeps hackers from getting at it. The RSA cryptosystem is a way to protect messages that uses two different keys. In this paper, a new method is suggested. It includes changing messages into hexadecimal values and then turning them into decimals. Public and private keys are generated based on the input of message's length, adding an increase of complexity to enhance the security of the cryptosystem. The proposed algorithm uses two different keys to encrypt and decrypt each character, this makes the cryptosystem increasing the difficultly for attackers trying to hack it. A comparison is made between the proposed algorithm and the original RSA, using NIST tests and measuring the running time of key generation, encoding, and decoding operations. The results show that the new algorithm provides a secure transmitting of data. The proposed algorithm enhances security over the standard RSA algorithm by using hexadecimal conversion, multiple keys, dual key encryption per one-character, increased randomness, and a more advanced cryptography method, offering improved resistance against attacks and protecting data. [ABSTRACT FROM AUTHOR]

We consider a new class of square Fibonacci (q+1)x(q+1)-matrices in public key cryptography. This extends previous cryptography using generalized Fibonacci matrices. For a given integer q, a (q+1)x(q+1) binary matrix Mq is a matrix which nonzero entries are located either on the super diagonal or on the last row of the matrix. In this article, we have proposed a modified public key cryptography using such matrices as key in Hill cipher and key agreement for encryption-decryption of terms of Mq-matrix. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers needed to be exchanged, which reduces the time complexity as well as the space complexity of the transmission and has a large key space. [ABSTRACT FROM AUTHOR]

As a typical representative of the public key cryptosystem, RSA has attracted a great deal of cryptanalysis since its invention, among which a famous attack is the small private exponent attack. It is well-known that the best theoretical upper bound for the private exponent d that can be attacked is d ≤ N 0.292 , where N is a RSA modulus. However, this bound may not be achieved in practical attacks since the lattice constructed by Coppersmith method may have a large enough dimension and the lattice-based reduction algorithms cannot work so well in both efficiency and quality. In this paper, we propose a new practical attack based on the binary search for the most significant bits (MSBs) of prime divisors of N and the Herrmann-May's attack in 2010. The idea of binary search is inspired by the discovery of phenomena called "multivalued-continuous phenomena", which can significantly accelerate our attack. Together with several carefully selected parameters according to our exact and effective numerical estimations, we can improve the upper bound of d that can be practically achieved. More specifically, without the binary search method, we successfully attack RSA with a 1024-bit-modulus N when d ≤ N 0.285 . Moreover, by our new method, we can implement a successful attack for a 1024-bit-modulus RSA when d ≤ N 0.292 and for a 2048-bit-modulus RSA when d ≤ N 0.287 in about a month. We believe our method can provide some inspiration to practical attacks on RSA with mainstream-size moduli. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cyberphysical systems connect physical devices and large private network environments in modern communication systems. A fundamental worry in the establishment of large private networks is mitigating the danger of transactional data privacy breaches caused by adversaries using a variety of exploitation techniques. This study presents a privacy-preserving architecture for ensuring the privacy and security of transaction data in large private networks. The proposed model employs digital certificates, RSA-based public key infrastructure, and the blockchain to address user transactional data privacy concerns. The model also guarantees that data in transit remains secure and unaltered and that its provenance remains authentic and secure during node-to-node interactions within a large private network. The proposed model has increased the encryption speed by about 17 times, while the decryption process is expedited by 4 times. Therefore, the average overall acceleration obtained was 16.5. Both the findings of the security analysis and the performance analysis demonstrate that the proposed model can safeguard transactional data during communications on large private networks more effectively and securely than the existing solutions. [ABSTRACT FROM AUTHOR]

RSA is a well-known cryptosystem in Modern Cryptography and its efficiency is based on the hardness of the Integer Factorization problem. The algorithm is shown to be vulnerable to several attacks in a number of special scenarios with assumptions. In this paper, the strength of RSA is investigated if the primes in the modulus are close and the same modulus is used for two instances. The attack is highly efficient compared to other known attacks which are only concentrated on either closeness of the primes or the same modulus used for two or more instances. This attack examines the closeness of the primes chosen whenever the RSA system is used for two instances with the same modulus. The LLL algorithm is used to obtain the bound, and the bound is highly efficient compared to other known attacks. [ABSTRACT FROM AUTHOR]

Protecting digital data, especially digital images, from unauthorized access and malicious activities is crucial in today's digital era. This paper introduces a novel approach to enhance image encryption by combining the strengths of the RSA algorithm, homomorphic encryption, and chaotic maps, specifically the sine and logistic map, alongside the self-similar properties of the fractal Sierpinski triangle. The proposed fractal-based hybrid cryptosystem leverages Paillier encryption for maintaining security and privacy, while the chaotic maps introduce randomness, periodicity, and robustness. Simultaneously, the fractal Sierpinski triangle generates intricate shapes at different scales, resulting in a substantially expanded key space and heightened sensitivity through randomly selected initial points. The secret keys derived from the chaotic maps and Sierpinski triangle are employed for image encryption. The proposed scheme offers simplicity, efficiency, and robust security, effectively safeguarding against statistical, differential, and brute-force attacks. Through comprehensive experimental evaluations, we demonstrate the superior performance of the proposed scheme compared to existing methods in terms of both security and efficiency. This paper makes a significant contribution to the field of digital image encryption, paving the way for further exploration and optimization in the future. [ABSTRACT FROM AUTHOR]

Fog computing accredits by utilizing the network edge while still rendering the possibility to interact with the cloud. Nevertheless, the features of fog computing are encountering several security challenges. The security of end users and/or fog servers brings a significant dilemma in implementing fog computing. The computational power of the resources constrains Internet of Things (IoT) devices in the fog-computing environment. Therefore, an attacker can easily attack. The traditional methods like attribute-based encryption (ABE) techniques are inappropriate for resource-constraint devices with protracted computing and limited computational capabilities. In this regard, we investigate a multiauthority ciphertext policy-attribute-based encryption (MA-CP-ABE) method that enables multiauthority attribute revocation and computation outsourcing. Moreover, the encryption and decryption processes of resource-constraint IoT devices are outsourced to the fog nodes. In this way, it also reduces the computational burden of the resource-constraint IoT devices. Hence, we propose MA-CP-ABE for encryption and decryption, attribute revocation and outsourcing by reducing the computational burden and securing the system. We compare the computational offloading approach with the existing techniques to prove that the proposed approach outperforms the existing approaches. The proposed method reduces the operation time for the encryption and decryption process. We outsource cryptography operations to the fog node, reducing the end user's computational cost. Eventually, simulated outcomes are used to assess the algorithm's computational cost. [ABSTRACT FROM AUTHOR]

In public-key cryptography, the RSA algorithm is an inevitable part of hardware security because of the ease of implementation and security. RSA Cryptographic algorithm uses many modular arithmetic operations that decide the overall performance of the architecture. This paper proposes VLSI architecture to implement an RSA public-key cryptosystem driven by the Residue Number System (RNS). Modular exponentiation in the RSA algorithm is executed by dividing the entire process into modular squaring and multiplication operations. Based on the RNS employment in modulo-exponential operation, two RSA architectures are proposed. A Verilog HDL code is used to model the entire RSA architecture and ported in Zynq FPGA (XC7Z020CLG484-1) for Proof of Concept (PoC). The Cadence Genus Synthesizer tool characterizes a system's performance for TSMCs standard Cell library. Partial RNS (Proposed-I)- and Fully RNS (Proposed-II)-based RSA architectures increase the operation speed by 13% and 35%, respectively, compared with the existing RSA. Even though there is an increase in parameters like area, power and PDP for a smaller key size, the improvement in area utilization and encryption/ decryption speed of RSA for a larger key size is evident from the analysis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme based on ephemeral elliptic curves over a finite ring with an RSA modulus. The new scheme is a variant of both the RSA and the KMOV cryptosystems and can be used for both signature and encryption. We study the security of the new scheme and show that it is immune to factorization attacks, discrete-logarithm-problem attacks, sum-of-two-squares attacks, sum-of-four-squares attacks, isomorphism attacks, and homomorphism attacks. Moreover, we show that the private exponents can be much smaller than the ordinary exponents in RSA and KMOV, which makes the decryption phase in the new scheme more efficient. [ABSTRACT FROM AUTHOR]