Search

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]

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]

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]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

In recent years, cyber‐security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi‐homomorphic encryption to ensure cyber‐security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption‐decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed‐loop MPC of nonlinear systems. Thus, the closed‐loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade‐off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design. [ABSTRACT FROM AUTHOR]

• The effect of synchronisation on the master-slave NNs with time delay is examined. • The NN's chaotic attractor is reconstructed using the fractal interpolation. • Reconstructed chaotic sequence is applied in image encryption. • Image encryption is carried out using RSA algorithm. • Various statistical measures are used to verify the efficacy. This paper examines synchronization of delayed chaotic neural networks with impulsive control, event-triggered impulsive control, and event-triggered delayed impulsive control. Lyapunov-based event-triggered mechanism is constructed to derive few sufficient conditions in terms of Linear Matrix Inequalities (LMIs). The feedback and event-triggered gain matrices are evaluated with the help of numerical packages. The fractal interpolation functions are employed to reconstruct the chaotic sequence of the neural networks since the chaotic attractor has self-similar properties and coincides with the fractal functions. In this study, a linear fractal interpolation is used to reconstruct both the master-slave chaotic attractor and the encrypted chaotic attractor, with optimized scaling factors. Finally, an application of the image encryption algorithm is given in terms of RSA public-key cryptosystems, permutation, and finite field diffusion for the chaotic sequence generated by fractal interpolation functions. [ABSTRACT FROM AUTHOR]

Advances in quantum computing have urged the need for cryptographic algorithms that are low-power, lowenergy, and secure against attacks that can be potentially enabled. For this post-quantum age, different solutions have been studied. Code-based cryptography is one feasible solutionwhose hardware architectures have become the focus of research in the NIST standardization process and has been advanced to the final round (to be concluded by 2022-2024). Nevertheless, although these constructions, e.g., McEliece and Niederreiter public key cryptography, have strong error correction properties, previous studies have proved the vulnerability of their hardware implementations against faults product of the environment and intentional faults, i.e., differential fault analysis. It is previously shown that depending on the codes used, i.e., classical or reduced (using either quasi-dyadic Goppa codes or quasi-cyclic alternant codes), flaws in error detection could be observed. In this work, efficient fault detection constructions are proposed for the first time to account for such shortcomings. Such schemes are based on regular parity, interleaved parity, and two different cyclic redundancy checks (CRC), i.e., CRC-2 and CRC-8. Without losing the generality, we experiment on the McEliece variant, noting that the presented schemes can be used for other code-based cryptosystems. We perform error detection capability assessments and implementations on field-programmable gate array Kintex-7 device xc7k70tfbv676-1 to verify the practicality of the presented approaches. To demonstrate the appropriateness for constrained embedded systems, the performance degradation and overheads of the presented schemes are assessed. [ABSTRACT FROM AUTHOR]

Chaos-based cryptosystems have been an active area of research in recent years. Although these algorithms are not standardized like AES, DES, RSA, etc., chaos-based cryptosystems like Chebyshev polynomials can provide additional security when used with standard public key cryptosystems like RSA and El-gamal. Standard encryption algorithms such as AES have always been the primary choice, but when it comes to image or video encryption, many researchers recommend chaos-based encryption techniques due to their computational efficiency. This paper presents a survey on the most up-to-date chaos-based image encryption techniques and classifies them into spatial, temporal and spatiotemporal domains for better understanding. The significant improvements in the field of image encryption are discussed. In addition, comparative analysis is performed to validate the evaluation matrices for quantifying the encryption algorithms' security and performance in recent papers. [ABSTRACT FROM AUTHOR]

In this study, we construct a new public key cryptosystem both like El-Gamal and RSA cryptosystem based on Bass cyclic units in integral group rings. Naturally, the underlying hard problems for this system are both decisional Diffie-Hellman assumption and factorization of integers. Since the system is related to RSA scheme indirectly, key generation process is very efficient. This cryptosystem actually supports and strengthens the current public key cryptosystems in [6], [8] and [20]. Encryption algorithm in the system is constructed via non-commutative operations in integral group rings of dihedral groups. Finally, we briefly discuss the security of our cryptosystem against some known attacks. [ABSTRACT FROM AUTHOR]

In the modern world, the need for secure communication is of utmost importance and in that cryptography plays a significant role. The RSA algorithm is one of the most widely used public key cryptosystems and mathematicians throughout the world are proposing new variants for RSA in order to overcome its drawbacks. In our system, we introduce a new variant for the textbook RSA algorithm using continued fractions. We have developed the key generation using continued fractions and further improved the encryption using a technique similar to that of padding. We have also proved that our system is secure against the meet-in-the-middle-attack in contrast to the textbook RSA algorithm. [ABSTRACT FROM AUTHOR]

In 2018, N. Murru and F. M. Saettone proposed a novel RSA-like cryptosystem with modulus N = pq and ed ≡ 1(mod (p²+p+1)(q²+q+1)) based on a generalization of the Rffedei Rational functions. In this paper, we give some bounds on the deciphering exponent d = Nδ, in which this RSA-like cryptosystem is insecure. For the enciphering exponent e = Nα and p + q + 1 = Nα, the attack bound on d is ... in the case of α < 1 and ... when α > 1. Furthermore, we describe the magnitude of the bounds in all cases of α and β. [ABSTRACT FROM AUTHOR]

This paper investigates a novel RSA-like cryptosystem proposed by Murru-Saettone. This cryptosystem is constructed from a cubic field connected to the cubic Pell equation and Redei rational functions. The scheme is claimed to be secure against the Wiener-type attack. However, in this paper, we show a Wiener-type attack that can recover the secret key from the continued fraction constructed from public information. [ABSTRACT FROM AUTHOR]

Cryptography is a science that studies methods so that data or messages remain safe when sent, from the sender to the recipient without experiencing interference from unauthorized parties. The cryptographic system used is a combination of symmetrical cryptographic algorithms, and asymmetric cryptographic algorithms also called hybrid cryptosystems. This research work tries to explore the need of integration of different encryption algorithms and enhance the strength of encryption and complexity. This work observes that integrity check algorithm can also be used to generate key of asymmetric key cryptography and they can help to enhance power of confidentiality. In this paper, we present a new hybrid by using Blowfish, RC6 and RSA algorithms. Within this, the data is encrypted through symmetric algorithm using RC6 and blowfish algorithm and key is encrypted using an asymmetric algorithm called RSA. The complete solution was implemented using Java technology and it was evaluated based on computation time. [ABSTRACT FROM AUTHOR]

Information and communication technology are spreading very rapidly in terms of information exchange over the Internet, and this information is vulnerable to threats by hackers. Information security is mainly achieved by using encryption techniques to protect it when it is transmitted over an unsecured channel. In this paper, a modified encryption system for the RSA algorithm is presented using a fixed encryption key size and divide that key into specific sections, to encrypt and decrypt blocks using multiple public and private keys. The encryption process can be done for each block by choosing different keys according to the random generator key (seed key) and encrypt each block with these different keys. Through the random arrangement of blocks and the properties of a modified cipher block in the RSA algorithm within the proposed model, to increase security at the expense of time, the use of large keys in the RSA algorithm is very slow since small RSA keys are vulnerable to factorization attacks. To overcome that problem, we increase complexity and use larger block sizes without sacrificing speed, and compare them with the original RSA algorithm. As a result, this method is more efficient, secured, and not easily breakable. [ABSTRACT FROM AUTHOR]

We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an improved variant of the Faure–Loidreau (FL) system, which was broken in a structural attack by Gaborit, Otmani, and Talé Kalachi (GOT, 2018). We keep the FL encryption and decryption algorithms, but modify the insecure key generation algorithm. Our crucial observation is that the GOT attack is equivalent to decoding an interleaved Gabidulin code. The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail—hence LIGA resists the GOT attack. We also prove that the public-key encryption version of LIGA is IND-CPA secure in the standard model and the key encapsulation mechanisms version is IND-CCA2 secure in the random oracle model, both under hardness assumptions of formally defined problems related to list decoding and interleaved decoding of Gabidulin codes. We propose and analyze various exponential-time attacks on these problems, calculate their work factors, and compare the resulting parameters to NIST proposals. The strengths of LIGA are short ciphertext sizes and (relatively) small key sizes. Further, LIGA guarantees correct decryption and has no decryption failure rate. It is not based on hiding the structure of a code. Since there are efficient and constant-time algorithms for encoding and decoding Gabidulin codes, timing attacks on the encryption and decryption algorithms can be easily prevented. [ABSTRACT FROM AUTHOR]

Series of public key encryption (PKE) schemes have been proposed for remote sensing image encryption; however, most of these schemes are not secure against quantum attacks in the new era of quantum computing. In this paper, we present an improved anti-quantum MST3 PKE scheme for remote sensing images. Using the MST3 cryptosystem, the proposed scheme can effectively resist the current quantum attacks. Moreover, with the help of a collision-resistant hash function, the proposed method achieves a nonmalleable property with respect to possible malleable attacks. Compared with the previous MST series encryption schemes, our scheme has a slightly higher efficiency. [ABSTRACT FROM AUTHOR]

The novel cryptosystem was designed to be fast and secure for cloud. Circle was used for encryption. A 3D hyperbola was used for decryption. Mathematical properties were used to ensure that an eavesdropper could not perform side-channel attacks. The number of equations which an eavesdropper had was lesser than the number of unknowns for every block. The cryptosystem could work anywhere from smartwatches to supercomputer. It was designed to be flexible. 3D hyperboloid cryptosystem could work as both stream and block cipher. There was no restriction on key size and block size. Confusion and diffusion were measured as parameters for security. It is a complete encryption type cryptosystem. Performance and security analysis was performed both in terms of hardware and software implementations. Problem of key management, handling and key distribution was solved. Experimental results indicate that the proposed cryptosystem was faster than both symmetric and asymmetric key cryptosystems. [ABSTRACT FROM AUTHOR]

This paper falls within the framework of the security of satellite images, in particular interferograms from an Interferometric Synthetic Aperture Radar (inSAR) system. The innovation of this work consists in the application of a cryptosystem based on two algorithms Advanced Encryption Standard (AES) and the Rivest, Shamir and Adleman (RSA) encryption algorithm for securing interferograms of inSAR systems. AES employs five encryption modes Electronic Code Book (ECB), Cipher Bloc Chaining (CBC), Cipher FeedBack (CFB), Output FeedBack (OFB), and counter-mode encryption (CTR). The use of the AES algorithm alone can only ensure the confidentiality function. In the proposed cryptosystem confidentiality is ensured by the AES algorithm, authenticity is guaranteed by the RSA algorithm, and integrity is ensured by two parameters; the correlation function between the adjacent pixels and the SSIM parameters (structural similarity index SSIM). For evaluation and analysis of security performance for interferogram encryption, several test metrics are employed. These metrics are: Analysis of histograms of the encrypted interferograms, correlation between the adjacent pixels, between the original interferogram and the encrypted interferogram, SSIM between the original interferogram and the decrypted one. Moreover, we exploit the analysis of resistance to error propagation for the five modes. The obtained results show a superiority of the OFB and CTR modes for the encryption of in- SAR interferograms compared to ECB, CFB, and CBC modes. It is noteworthy, that the main criteria that can be used to choose between OFB and CTR for encryption of satellite images are propagation of errors and the complexity material for their locations on the edges of the satellites propagation of errors and the complexity material for their locations on the edges of the satellites. OFB mode is employed in satellites to minimize the number of on-board circuits, which is decisive for satellites. CTR mode is recommended by the CCSDS (Consultative Committee for Space Data Systems) for telemetry (TM) and remote control (TC) encryption. [ABSTRACT FROM AUTHOR]

Big data require cloud that provides dynamically expanding data storage accessed through the Internet. The outsourcing data in the cloud for storing makes the user data management easier and reduces the cost of maintaining data. Still organizations are not confident to store their data in the cloud, because of security and privacy concerns. However, existing encryption methods are able to protect data confidentiality, but it has some drawbacks of access patterns can also leak sensitive information. The proposed system uses an Elliptic curve with Diffie–Hellman (ECDH) algorithm for encryption and decryption of data to improve the data security in the cloud. This algorithm reduced the computational complexity and encrypted data efficiently. In experimental analysis, the performance of proposed ECDH is calculated using evaluation parameters such as encryption time, decryption time, computation overhead and key generation time. The proposed ECDH algorithm has approximately 70% better performance in terms of encryption time than existing methods such as RSA, MRSA and MRSAC. [ABSTRACT FROM AUTHOR]

In the secure multicast communication, data is transmitted in such a manner that only authorized group members are able to receive the data. The main challenging issue in dynamic and secure multicast communication is to design a centralized group key distribution protocol with minimum computation and storages complexity. This paper, proposes a more efficient centralized group key distribution (CGKD) protocol that minimizes the computation cost of key server (KS) during key updating. The computation cost of members is balanced during key recovery. This reduction in computation cost of KS is achieved by performing one addition, one multiplication and one encryption during single member join and one subtraction, one division and one encryption during a single member leave operation. Moreover, the storage complexity of KS is also minimized. Further, this paper also proposes an extended CGKD protocol based on clustered tree which is very scalable and efficient to deal with enormous membership changes. By comparing with existing similar protocols, the proposed protocol has significantly reduced computation and storage complexity of KS while maintaining less and balanced communication overhead of KS and storage load of each group member. The proposed protocol is implemented and tested on key-star and cluster tree based structure. The experimental results show that the proposed protocol is efficient in terms of computational overhead of KS and group members. [ABSTRACT FROM AUTHOR]

Public key cryptosystems such as RSA, rebalanced RSA and ElGamal have the disadvantage of serious asymmetry between encryption and decryption speed. We reduced the CRT (Chinese Remainder Theorem) exponents maintaining full sized private exponent in ElGamal with composite modulus (CRT–ElGamal) for the fast decryption as in rebalanced RSA. In this case, unlike rebalanced RSA, decryption speed up can be obtained without losing of the fast encryption speed which is comparable to RSA with small public exponent. As a result, it is possible to propose the fast public key cryptosystem in which both encryption and decryption are fast, by reducing the asymmetry (i.e., fast encryption/slow decryption) in CRT–ElGamal encryption. [ABSTRACT FROM AUTHOR]

RSA is a well-known public-key cryptosystem. It is the most commonly used and currently most important public-key algorithm which can be used for both encryption and signing. RSA cryptosystem involves exponentiation modulo an integer number n that is the product of two large primes p and q. The security of the system is based on the difficulty of factoring large integers in terms of its key size and the length of the modulus n in bits which is said to be the key size. In this paper, we present a method that increases the speed of RSA cryptosystem. Also, an efficient implementation of arithmetic and modular operations are used to increase its speed. The security is also enhanced by using a variable key size space. There exist numerous implementations (hardware or software) of RSA cryptosystem, but most of them are restricted in key size. An important improvement achieved in this paper is that the system is designed flexible in terms of key size according to user security. [ABSTRACT FROM AUTHOR]

In threshold cryptography, private keys are divided into n shares, each one of which is given to a different server in order to avoid single points of failure. In the case of threshold public-key encryption, at least t ≤ n servers need to contribute to the decryption process. A threshold primitive is said robust if no coalition of t malicious servers can prevent remaining honest servers from successfully completing private key operations. Non-interactive schemes, considered the most practical ones, allow servers to contribute to decryption without interactions. So far, most non-interactive threshold cryptosystems were only proved secure against static corruptions. In the adaptive corruption scenario (where the adversary can corrupt servers at any time, based on its complete view), all existing robust threshold encryption schemes that also resist chosen-ciphertext attacks till recently require interaction in the decryption phase. A very specific method (in composite order groups) for getting rid of interaction was recently suggested, leaving the question of more generic frameworks and constructions with better security and, in particular, better flexibility (i.e., compatibility with distributed key generation). This paper advances the state of the art and describes a general construction of adaptively secure robust non-interactive threshold cryptosystems with chosen-ciphertext security. We define the novel notion of all-but-one perfectly sound threshold hash proof systems that can be seen as (threshold) hash proof systems with publicly verifiable and simulation-sound proofs. We show that this notion generically implies threshold cryptosystems combining the aforementioned properties. Then, we provide efficient instantiations under well-studied assumptions in bilinear groups (e.g., in such groups of prime order). These instantiations have a tighter security proof in the single-challenge setting and are indeed compatible with distributed key generation protocols. [ABSTRACT FROM AUTHOR]

RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Ø(n), can be rewritten as Ø(n) = ad + b, where d is the private key and a,b, if a divides both of Ø(n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = ha is higher than modulus. [ABSTRACT FROM AUTHOR]

RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, (n), can be rewritten as (n) = ad + b, where d is the private key and a,b, if a divides both of (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = ha is higher than modulus. [ABSTRACT FROM AUTHOR]

Summary: To ensure secure communication over the insecure public network, this work presents a privacy‐preserving biometrics‐based authenticated key agreement scheme using elliptic curve cryptography, making full use of the advantages that the biometrics can be used to uniquely identify a particular human, and the elliptic curve cryptography can provide the same level security with far less key size compared with other public key cryptography. The proposed scheme realizes the mutual authentication of participants, session key agreement, and various security properties and also can resist kinds of known attacks. Moreover, the proposed scheme has perfect user experience in the aspect of changing password by not interacting with the server. In addition, the security features of our new designed scheme are formally proved under the widely used BPR adversary model. Therefore, from the viewpoint of the authors, the proposed scheme can be considered as the authenticated key agreement scheme for mobile users. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Private-key functional encryption enables fine-grained access to symmetrically encrypted data. Although private-key functional encryption (supporting an unbounded number of keys and ciphertexts) seems significantly weaker than its public-key variant, its known realizations all rely on public-key functional encryption. At the same time, however, up until recently it was not known to imply any public-key primitive, demonstrating our poor understanding of this primitive. Bitansky et al. (Theory of cryptography—14th international conference, TCC 2016-B, 2016) showed that sub-exponentially secure private-key function encryption bridges from nearly exponential security in Minicrypt to slightly super-polynomial security in Cryptomania, and from sub-exponential security in Cryptomania to Obfustopia. Specifically, given any sub-exponentially secure private-key functional encryption scheme and a nearly exponentially secure one-way function, they constructed a public-key encryption scheme with slightly super-polynomial security. Assuming, in addition, a sub-exponentially secure public-key encryption scheme, they then constructed an indistinguishability obfuscator (or a public-key functional encryption scheme if the given building blocks are polynomially secure). We show that quasi-polynomially secure private-key functional encryption bridges from sub-exponential security in Minicrypt all the way to Cryptomania. First, given any quasi-polynomially secure private-key functional encryption scheme, we construct an indistinguishability obfuscator for circuits with inputs of poly-logarithmic length. Then, we observe that such an obfuscator can be used to instantiate many natural applications of indistinguishability obfuscation. Specifically, relying on sub-exponentially secure one-way functions, we show that quasi-polynomially secure private-key functional encryption implies not just public-key encryption but leads all the way to public-key functional encryption for circuits with inputs of poly-logarithmic length. Moreover, relying on sub-exponentially secure injective one-way functions, we show that quasi-polynomially secure private-key functional encryption implies a hard-on-average distribution over instances of a PPAD-complete problem. Underlying our constructions is a new transformation from single-input functional encryption to multi-input functional encryption in the private-key setting. The previously known such transformation (Brakerski et al. J Cryptol 31(2):434–520, 2018) required a sub-exponentially secure single-input scheme, and obtained a scheme supporting only a slightly super-constant number of inputs. Our transformation both relaxes the underlying assumption and supports more inputs: Given any quasi-polynomially secure single-input scheme, we obtain a scheme supporting a poly-logarithmic number of inputs. [ABSTRACT FROM AUTHOR]

Smart cards are widely used in high security applications due to their self-contained nature. At the same time, the security of smart card has become an urgent problem in the field of intelligent environment. Public-key Cryptography is the main means to solve the security problems based on smart card password authentication and identity authentication protocol. This paper reviews the security issues of public key cryptography used in smart cards from the perspective of information theory. By constructing a attackers channel, we model the Public-key Cryptography process in the way of an adversary to capture the attack ability in the Public-key Cryptography setting. Then, we convert the secure problems of Public-key Cryptography into the attack channels capacity of adversaries that the maximum value of the average mutual information is the secure limitations of a Public-key Cryptography scheme, which is a reachable theoretic limitation of secure communication parties. Finally, we give the bounds of insecure for public-key encryption and signature in different secure levels, and analyze and discuss the secure limitation. [ABSTRACT FROM AUTHOR]

In the following article, a proprietary method of anonymisation of identifiable statistical data using context-free probabilistic grammar is proposed. The advantage of this method is that it is simple and thanks to this, the identifier is easy to retrieve after masking the identifiable data, e.g. when it is necessary to modify or update the micro-data. This can be done using public-key cryptography, i.e. encrypting some probabilistic context-free grammar with this method. In the case of public statistics, there is often a need to use an anonymised source value, for example when economic operators' reports are verified by statistical officers. With appropriate information generated by context-free grammar, the verifier can easily identify an economic operator or a natural person. The idea of the anonymising algorithm used in the proposed method is presented by means of an example. According to the authors, the combination of the proposed method with asymmetric encryption of the definition of context-free grammar using public key infrastructure, makes it probable that its resistance to attacks will be quite high. This is because statistical methods that are used in the analysis of natural languages are not susceptible to attacks. [ABSTRACT FROM AUTHOR]

Let (n = p q , e = n β) be an RSA public key with private exponent d = n δ , where p and q are large primes of the same bit size. At Eurocrypt 96, Coppersmith presented a polynomial-time algorithm for finding small roots of univariate modular equations based on lattice reduction and then succussed to factorize the RSA modulus. Since then, a series of attacks on the key equation e d − k ϕ (n) = 1 of RSA have been presented. In this paper, we show that many of such attacks can be unified in a single attack using a new notion called Coppersmith's interval. We determine a Coppersmith's interval for a given RSA public key (n , e). The interval is valid for any variant of RSA, such as Multi-Prime RSA, that uses the key equation. Then we show that RSA is insecure if δ < β + 1 3 α − 1 3 1 2 α β + 4 α 2 provided that we have approximation p 0 ≥ n of p with p − p 0 ≤ 1 2 n α , α ≤ 1 2. The attack is an extension of Coppersmith's result. [ABSTRACT FROM AUTHOR]

Alwen et al. in Eurocrypt 2010, showed that an identity-based hash proof system (IB-HPS), where IB-HPS generalizes the notion of hash proof system (HPS) to the identity-based setting, almost immediately yields an identity-based encryption (IBE) scheme which is secure against partial leakage of the target identity's decryption key. That is, an IBE scheme with bounded leakage resilience can be naturally created from an IB-HPS. However, in the real world, the leakage is unbounded, and any adversary can break the security of cryptography shceme by performing continuous leakage attacks. To further increase the practicability, a cryptography scheme must hold the claimed security in the continuous leakage setting. Dodis et al. in FOCS 2010, showed a generic method how to create a cryptography shceme with continuous leakage resilience from the bounded leakage-resilient cryptosystem by performing an additional key update algorithm while the public parameters keep unchanged. To construct a continuous leakage-resilient cryptography scheme, a new primitive, called it updatable identity-based hash proof system (U-IB-HPS), is proposed, which is an improved IB-HPS. In particular, the improved system has an additional key update algorithm, which can push some new randomness into the private key of user (or the master secret key), the updated results are random in the adversary's view, and the leakage of previous private key of user (or the master secret key) does not work for the updated results. However, the previous instantiations of U-IB-HPS cannot achieve the claimed security. To solve the above problems, in this paper, two instantiations of U-IB-HPS with better performance are created, and the security of proposed system is proved, in the standard model, based on the classic decisional bilinear Diffie-Hellman assumption. The corresponding IBE scheme created with our U-IB-HPS allows continuous leakage of multiple keys, i.e., continuous leakage of the master secret key and the private key of user. Additionally, our U-IB-HPS can also be employed as an underlying basic tool to build the generic construction of continuous leakage-amplified public-key encryption scheme, continuous leakage-resilient identity-based authenticated key exchange protocol, and continuous leakage-resilient public-key encryption scheme with keyword search, etc. [ABSTRACT FROM AUTHOR]

We introduce a new family of rank metric codes: Low Rank Parity Check codes (LRPC), for which we propose an efficient probabilistic decoding algorithm. This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We then use these codes to design cryptosystems à la McEliece: more precisely we propose two schemes for key encapsulation mechanism (KEM) and public key encryption (PKE). Unlike rank metric codes used in previous encryption algorithms -notably Gabidulin codes - LRPC codes have a very weak algebraic structure. Our cryptosystems can be seen as an equivalent of the NTRU cryptosystem (and also to the more recent MDPC code-based cryptosystem) in a rank metric context, due to the similar form of the public keys. The present paper is an extended version of the article introducing LRPC codes, with important new contributions. We have improved the decoder thanks to a new approach which allows for decoding of errors of higher rank weight, namely up to $\frac {2}{3}(n-k)$ when the previous decoding algorithm only decodes up to $\frac {n-k}{2}$ errors. Our codes therefore outperform the classical Gabidulin code decoder which deals with weights up to $\frac {n-k}{2}$. This comes at the expense of probabilistic decoding, but the decoding error probability can be made arbitrarily small. The new approach can also be used to decrease the decoding error probability of previous schemes, which is especially useful for cryptography. Finally, we introduce ideal rank codes, which generalize double-circulant rank codes and allow us to avoid known structural attacks based on folding. To conclude, we propose different parameter sizes for our schemes and we obtain a public key of 3337 bits for key exchange and 5893 bits for public key encryption, both for 128 bits of security. [ABSTRACT FROM AUTHOR]

Several ways to perform data encryption have been found, and one of the functions involved in standard algorithms such as RSA is the modular exponentiation. Basically, the RSA algorithm uses some properties of modular arithmetic to cipher and decipher plain text, with a certain performance dependence on text lengths. The growth in computing capacity has created the need to use robust systems that can perform calculations with significantly large numbers and the formulation of procedures focused on improving the speed to achieve it. One of these is the M-ary algorithm for the execution of the modular exponential function. This paper describes an implementation of this algorithm in reprogrammable hardware (FPGA) to evaluate its performance. The first section of this work introduces the M-ary algorithm. The second section uses block description for implementation understanding. The third section shows the results in time diagrams, and finally, the last section conclusions.

In the situation where there are one sender and multiple receivers and the sender transmits ciphertexts of correlated plaintexts, a receiver selective opening (RSO) attack for a public key encryption (PKE) scheme considers adversaries that can corrupt some of the receivers and get their secret keys and plaintexts. Security against RSO attacks for a PKE scheme ensures confidentiality of ciphertexts of uncorrupted receivers. Simulation-based RSO security against chosen ciphertext attacks (SIM-RSO-CCA) is the strongest security notion in all RSO attack scenarios. Jia, Lu, and Li (2016) [19] proposed the first SIM-RSO-CCA secure PKE scheme. However, their scheme used indistinguishability obfuscation, which is not known to be constructed from any standard computational assumption. In this paper, we give two contributions for constructing SIM-RSO-CCA secure PKE from standard computational assumptions. Firstly, we propose a generic construction of SIM-RSO-CCA secure PKE using an IND-CPA secure PKE scheme and a non-interactive zero-knowledge proof system satisfying one-time simulation soundness. Secondly, we propose an efficient and concrete construction of SIM-RSO-CCA secure PKE based on the decisional Diffie-Hellman (DDH) assumption. Moreover, we give a method for efficiently expanding the plaintext space of the DDH-based construction. By applying this method to the construction, we obtain the first DDH-based SIM-RSO-CCA secure PKE scheme supporting a super-polynomially large plaintext space with compact ciphertexts. [ABSTRACT FROM AUTHOR]

In this work, we first design a function encryption scheme by using key encapsulation. We combine public key encryption with symmetric encryption to implement the idea of key encapsulation. In the key encapsulation, we use a key to turn a message (plaintext) into a ciphertext by symmetric encryption, and then we use public key encryption to turn this key into another ciphertext. In the design of function encryption scheme, we use the public key encryption system, symmetric encryption system, noninteractive proof system, indistinguishable obfuscator, and commitment scheme. Finally, we prove the indistinguishable security of our function encryption scheme. [ABSTRACT FROM AUTHOR]

• This paper proposes an encryption scheme based on an improved chaotic system that can hide key information. First, we use the RSA algorithm to calculate the parameters of the improved coupled map lattice (CML) system as well as the initial values and the control parameters of the logistics map and the Chebyshev polynomial, respectively. • Then, we obtain a pseudorandom sequence of CML as the key for a one-time pad. Second, we extract the key information from the original image and perform pixel-level diffusion and confusion using different parameters on key and nonkey information based on the pseudorandom sequence generated by the CML system and the sorting function. • In the diffusion step, different diffusion modes are used to ensure that the diffusion effect is not repeated. This paper proposes an encryption scheme based on an improved chaotic system that can hide key information. First, the CML chaotic map is improved, and the chaotic state can be entered from 0. The image of the person is divided into key information and non-key information and spread by different diffusion methods. The RSA algorithm is used to encrypt the size of the key information as part of the key to enhancing the resistance to the chosen plaintext attack. Scrambling is performed at the pixel level using a CML system with a sorting function. The experimental and security analysis results show that the new algorithm has a large key space, is sensitive to keys and plaintext images, has a good encryption effect, and can resist common attack methods. [ABSTRACT FROM AUTHOR]

In leakage resilient cryptography, there is a seemingly inherent restraint on the ability of the adversary that it cannot get access to the leakage oracle after the challenge. Recently, a series of works made a breakthrough to consider a postchallenge leakage. They presented achievable public key encryption (PKE) schemes which are semantically secure against after-the-fact leakage in the split-state model. This model puts a more acceptable constraint on adversary's ability that the adversary cannot query the leakage of secret states as a whole but the functions of several parts separately instead of prechallenge query only. To obtain security against chosen ciphertext attack (CCA) for PKE schemes against after-the-fact leakage attack (AFL), existing works followed the paradigm of "double encryption" which needs noninteractive zero knowledge (NIZK) proofs in the encryption algorithm. We present an alternative way to achieve AFL-CCA security via lossy trapdoor functions (LTFs) without NIZK proofs. First, we formalize the definition of LTFs secure against AFL (AFLR-LTFs) and all-but-one variants (ABO). Then, we show how to realize this primitive in the split-state model. This primitive can be used to construct AFLR-CCA secure PKE scheme in the same way as the method of "CCA from LTFs" in traditional sense. [ABSTRACT FROM AUTHOR]

Efficient hardware implementations of public-key cryptosystems have been gaining interest in the past few decades. To achieve the goal, a high frequency as well as low latency Rivest-Shamir-Adleman (RSA) cryptosystem is reported in this paper. To configure such cryptosystem shift-add multiplier have been re-constructed and binary digit based modular exponentiation circuitry is proposed. Such exponentiation circuitry has been implemented through binary bit distribution technique, where, most significant bit (MSB) has been discarded for the implementation, owing to increase the operating frequency. The functionality of the reported algorithms were justified and compared in Hardware Description Language (HDL), simulated in Modelsim and synthesized in Xilinx ISE 14.2 platform. The proposed hardware implementation of RSA algorithm has a maximum frequency of operation of 545 MHz and 298 MHz for the bit sizes of 8 and 64 respectively. The proposed method shows improvements in terms of speed as well as in number of Look-up-tables (LUTs). Moreover, application-specific integrated circuit (ASIC) implementation of such cryptosystem of RSA was carried out through Encounter® RTL Compiler v11.10-p005_1 of Cadence® tool. [ABSTRACT FROM AUTHOR]

A family of ring-based cryptosystems, including the multilinear maps of Garg, Gentry and Halevi [Candidate multilinear maps from ideal lattices, Advances in Cryptology—EUROCRYPT 2013, Lecture Notes in Comput. Sci. 7881, Springer, Heidelberg 2013, 1–17] and the fully homomorphic encryption scheme of Smart and Vercauteren [Fully homomorphic encryption with relatively small key and ciphertext sizes, Public Key Cryptography—PKC 2010, Lecture Notes in Comput. Sci. 6056, Springer, Berlin 2010, 420–443], are based on the hardness of finding a short generator of a principal ideal (short-PIP) in a number field typically in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. In this paper, we present a polynomial-time quantum algorithm for recovering a generator of a principal ideal in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} , and we recall how this can be used to attack the schemes relying on the short-PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} by using the work of Cramer et al. [R. Cramer, L. Ducas, C. Peikert and O. Regev, Recovering short generators of principal ideals in cyclotomic rings, IACR Cryptology ePrint Archive 2015, https://eprint.iacr.org/2015/313], which is derived from observations of Campbell, Groves and Shepherd [SOLILOQUY, a cautionary tale]. We put this attack into perspective by reviewing earlier attempts at providing an efficient quantum algorithm for solving the PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. The assumption that short-PIP is hard was challenged by Campbell, Groves and Shepherd. They proposed an approach for solving short-PIP that proceeds in two steps: first they sketched a quantum algorithm for finding an arbitrary generator (not necessarily short) of the input principal ideal. Then they suggested that it is feasible to compute a short generator efficiently from the generator in step 1. Cramer et al. validated step 2 of the approach by giving a detailed analysis. In this paper, we focus on step 1, and we show that step 1 can run in quantum polynomial time if we use an algorithm for the continuous hidden subgroup problem (HSP) due to Eisenträger et al. [K. Eisenträger, S. Hallgren, A. Kitaev and F. Song, A quantum algorithm for computing the unit group of an arbitrary degree number field, Proceedings of the 2014 ACM Symposium on Theory of Computing—STOC'14, ACM, New York 2014, 293–302]. [ABSTRACT FROM AUTHOR]

A family of ring-based cryptosystems, including the multilinear maps of Garg, Gentry and Halevi [Candidate multilinear maps from ideal lattices, Advances in Cryptology—EUROCRYPT 2013, Lecture Notes in Comput. Sci. 7881, Springer, Heidelberg 2013, 1–17] and the fully homomorphic encryption scheme of Smart and Vercauteren [Fully homomorphic encryption with relatively small key and ciphertext sizes, Public Key Cryptography—PKC 2010, Lecture Notes in Comput. Sci. 6056, Springer, Berlin 2010, 420–443], are based on the hardness of finding a short generator of a principal ideal (short-PIP) in a number field typically in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. In this paper, we present a polynomial-time quantum algorithm for recovering a generator of a principal ideal in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} , and we recall how this can be used to attack the schemes relying on the short-PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} by using the work of Cramer et al. [R. Cramer, L. Ducas, C. Peikert and O. Regev, Recovering short generators of principal ideals in cyclotomic rings, IACR Cryptology ePrint Archive 2015, https://eprint.iacr.org/2015/313], which is derived from observations of Campbell, Groves and Shepherd [SOLILOQUY, a cautionary tale]. We put this attack into perspective by reviewing earlier attempts at providing an efficient quantum algorithm for solving the PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. The assumption that short-PIP is hard was challenged by Campbell, Groves and Shepherd. They proposed an approach for solving short-PIP that proceeds in two steps: first they sketched a quantum algorithm for finding an arbitrary generator (not necessarily short) of the input principal ideal. Then they suggested that it is feasible to compute a short generator efficiently from the generator in step 1. Cramer et al. validated step 2 of the approach by giving a detailed analysis. In this paper, we focus on step 1, and we show that step 1 can run in quantum polynomial time if we use an algorithm for the continuous hidden subgroup problem (HSP) due to Eisenträger et al. [K. Eisenträger, S. Hallgren, A. Kitaev and F. Song, A quantum algorithm for computing the unit group of an arbitrary degree number field, Proceedings of the 2014 ACM Symposium on Theory of Computing—STOC'14, ACM, New York 2014, 293–302]. [ABSTRACT FROM AUTHOR]

RSA cryptosystem has withstand a number of cryptanalysis over the years on its mathematical structures. The cryptanalysis provides the users of the cryptosystem some particular cases where the RSA private keys can be exposed hence diminishes its security elements. In this paper, we discusses a general case of our previous attack on RSA primes. Our attack corresponds to the special-structured RSA primes namely the primes are relatively close to their nearest squared numbers. We also count the number of primes that are vulnerable to our attack. Finally, we present the countermeasure that can be implemented in the RSA key generation algorithm to avoid our attack. [ABSTRACT FROM AUTHOR]

Security against selective opening attack (SOA) for receivers requires that in a multi-user setting, even if an adversary has access to all ciphertexts, and adaptively corrupts some fraction of the users to obtain the decryption keys corresponding to some of the ciphertexts, the remaining (potentially related) ciphertexts retain their privacy. In this paper, we study simulation-based selective opening security for receivers of public key encryption (PKE) schemes under chosen-ciphertext attacks (RSIM-SO-CCA). Concretely, we first show that some known PKE schemes meet RSIM-SO-CCA security. Then, we introduce the notion of master-key SOA security for identity-based encryption (IBE), and extend the Canetti–Halevi–Katz transformation to show generic PKE constructions achieving RSIM-SO-CCA security. Finally, we show how to construct an IBE scheme achieving master-key SOA security. [ABSTRACT FROM AUTHOR]

Let N = p q be an RSA modulus and e be a public exponent. Numerous attacks on RSA exploit the arithmetical properties of the key equation ed – k (p – 1)(q – 1) = 1. In this paper, we study the more general equation eu – (p – s)(p - r)v = w. We show that when the unknown integers u, v, w, r and s are suitably small and p - s or p - s is factorable using the Elliptic Curve Method for factorization ECM, then one can break the RSA system. As an application, we propose an attack on Demytko's elliptic curve cryptosystem. Our method is based on Coppersmith's technique for solving multivariate polynomial modular equations. [ABSTRACT FROM AUTHOR]