Public Key Cryptography Research Articles

Prime factorization via localized tile assembly in a DNA origami framework

Modern cybersecurity built on public-key cryptosystems like Rivest-Shamir-Adleman is compromised upon finding solutions to the prime factorization. Nevertheless, solving the prime factorization problem, given a large N, remains computationally challenging. Here, we design DNA origami frameworks (DOFs) to direct localized assembly of double-crossover (DX) tiles for solving prime factorization with a model consisting of the computing, decision-making, and reporting motifs. The model implementation is based on the sequential assembly of different DX tiles in the DOF cavity that carries overhangs encoding the prime and composite integers. The primes are multiplied and then verified with the composite, and the result is visualized under atomic force microscopy via the presence (success) or absence (failure) of biotin-streptavidin labels on the reporting DX tile. The factorization of semiprimes 6 and 15 is realized with this DOF-based demonstration. Given the potential of massively parallel processing ability of DNA, this strategy opens an avenue to solve complex mathematical puzzles like prime factoring with molecular computing.

블록체인을 위한 양자 내성의 격자 기반 블라인드 서명 기법

In the 4th industrial revolution, the blockchain that distributes and manages data through a P2P network is used as a new decentralized networking paradigm in various fields such as manufacturing, culture, and public service. However, with the advent of quantum computers, quantum algorithms that are able to break existing cryptosystems such as hash function, symmetric key, and public key cryptography have been introduced. Currently, because most major blockchain systems use an elliptic curve cryptography to generate signatures for transactions, they are insecure against the quantum adversary. For this reason, the research on the quantum-resistant blockchain that utilizes lattice-based cryptography for transaction signatures is needed. Therefore, in this paper, we propose a blind signature scheme for the blockchain in which the contents of the signature can be verified later, as well as signing by hiding the contents to be signed using lattice-based cryptography with the property of quantum resistance. In addition, we prove the security of the proposed scheme using a random oracle model.

Blockchain-based secret key extraction for efficient and secure authentication in VANETs

Intelligent transportation systems are an emerging technology that facilitates real-time vehicle-to-everything communication. Hence, securing and authenticating data packets for intra- and inter-vehicle communication are fundamental security services in vehicular ad-hoc networks (VANETs). However, public-key cryptography (PKC) is commonly used in signature-based authentication, which consumes significant computation resources and communication bandwidth for signatures generation and verification, and key distribution. Therefore, physical layer-based secret key extraction has emerged as an effective candidate for key agreement, exploiting the randomness and reciprocity features of wireless channels. However, the imperfect channel reciprocity generates discrepancies in the extracted key, and existing reconciliation algorithms suffer from significant communication costs and security issues. In this paper, PKC-based authentication is used for initial legitimacy detection and exchanging authenticated probing packets. Accordingly, we propose a blockchain-based reconciliation technique that allows the trusted third party (TTP) to publish the correction sequence of the mismatched bits through a transaction using a smart contract. The smart contract functions enable the TTP to map the transaction address to vehicle-related information and allow vehicles to obtain the transaction contents securely. The obtained shared key is then used for symmetric key cryptography (SKC)-based authentication for subsequent transmissions, saving significant computation and communication costs. The correctness and security robustness of the scheme are proved using Burrows–Abadi–Needham (BAN)-logic and Automated Validation of Internet Security Protocols and Applications (AVISPA) simulator. We also discussed the scheme’s resistance to typical attacks. The scheme’s performance in terms of packet delay and loss ratio is evaluated using the network simulator (OMNeT++). Finally, the computation analysis shows that the scheme saves ∼99% of the time required to verify 1000 messages compared to existing PKC-based schemes.

Analysis of Cryptography in Information Technology

Cryptography is the practice of securing information through the use of codes, ciphers, and other methods of encryption. It is an essential aspect of modern communication, enabling the secure transmission of data over networks and protecting sensitive information from unauthorized access. Cryptography has been used throughout history to protect messages from interception and decipherment. In ancient times, cryptography was used by military leaders and diplomats to communicate confidential information. Over time, cryptographic techniques have become more sophisticated, and modern cryptography now employs complex algorithms and mathematical principles.Today, cryptography is used in various applications, including online banking, e-commerce, secure messaging, and government communication. Cryptography also plays a critical role in securing sensitive information such as medical records, personal data, and intellectual property.As technology continues to evolve, the importance of cryptography will only increase. Cryptography ensures the confidentiality, integrity, and authenticity of data, and it is an essential tool for protecting digital assets and maintaining trust in the online world. Literature Review: Cryptography has been a subject of interest in computer science and mathematics for decades. The literature on cryptography is vast and covers a wide range of topics, including encryption algorithms, key management, and protocols for secure communication. One of the earliest and most well-known encryption algorithms is the Caesar cipher, which was used by Julius Caesar to encode his messages. Since then, numerous encryption techniques have been developed, including symmetric-key cryptography and public-key cryptography.Symmetric-key cryptography involves the use of a single key for both encryption and decryption, while public-key cryptography uses two keys, one for encryption and one for decryption.In recent years, research on post-quantum cryptography has gained significant attention due to the potential threat quantum computers pose to current encryption methods. Post- quantum cryptography aims to develop algorithms that are resistant to quantum attacks.

On the security of multivariate-based ring signature and other related primitives

The multivariate public-key cryptography (MPKC) provides a promising class of post-quantum signature schemes. Its theoretical security comes from the intractability of the multivariate quadratic problem (MQ problem), which is an NP-hard problem [1]. Nevertheless, not every instance of MQ-problem is hard [2–6] while the problem itself is NP-hard. Thus, it is important to understand and analyze the nature of the quadratic systems used in existing MPKC so that the security of the multivariate schemes can be properly assessed. Herein, we present a detailed cryptanalysis of the multivariate based ‘ring’ signature scheme presented by Wang et al. [7]. We utilize the attacks on the underdetermined system of multivariate quadratic equations. We prove both theoretically and experimentally that the scheme (Wang et al. [7]) can be broken in polynomial time even for rings of small size. Additionally, we observed that the attack strategy we proposed in this work is not only limited to [7], but can also be applied to break the unforgeability of other multivariate based schemes such as verifiable ring signature scheme [8], multivariate group signature scheme [9], and Gui and GeMSS based ring signature scheme [10,11].

Lightweight Cloud Computing-Based RFID Authentication Protocols Using PUF for e-Healthcare Systems

In the present of convenience, cloud computing services have increasingly become used to resolve low-latency and high-efficiency issues. In particular, they can help medical staff remotely obtain patients’ data. The RFID system is popularly used to collect the physiological signals of patients in e-Healthcare, which include their heartbeat, blood pressure, pulse, brain activity, and others. Although cloud computing services and RFID systems are used in many environments, they have some problems that are associated with security and efficiency. For example, the RFID system cannot be used to perform time-consuming and burdensome computations. Therefore, the public key cryptosystem is difficult to be used. Additionally, due to the overload of cloud servers when a large number of devices join, the use of traditional cryptosystems is not feasible. Recently, many protocols have been proposed to resolve the above issues. However, most of them consider only the authentication of communicating entities rather than authenticated key agreement for secure data transmission. Some protocols are not secure against possible attacks. Thus, this study proposes authentication key agreement protocols for e-Healthcare systems to solve problems of efficiency using lightweight operations and to enhance security by adopting the Physical Unclonable Function (PUF). Since PUFs use the uniqueness and randomness of their circuits to perform computation, they have message fingerprints that act as authentication keys. A PUF is lightweight and suitable for use in e-Healthcare systems with limited resources. The proposed protocols satisfy more security requirements than related authentication protocols, require fewer computational resources and are more efficient.

Efficient lattice-based revocable attribute-based encryption against decryption key exposure for cloud file sharing

Cloud file sharing (CFS) has become one of the important tools for enterprises to reduce technology operating costs and improve their competitiveness. Due to the untrustworthy cloud service provider, access control and security issues for sensitive data have been key problems to be addressed. Current solutions to these issues are largely related to the traditional public key cryptography, access control encryption or attribute-based encryption based on the bilinear mapping. The rapid technological advances in quantum algorithms and quantum computers make us consider the transition from the tradtional cryptographic primitives to the post-quantum counterparts. In response to these problems, we propose a lattice-based Ciphertext-Policy Attribute-Based Encryption(CP-ABE) scheme, which is designed based on the ring learing with error problem, so it is more efficient than that designed based on the learing with error problem. In our scheme, the indirect revocation and binary tree-based data structure are introduced to achieve efficient user revocation and dynamic management of user groups. At the same time, in order to further improve the efficiency of the scheme and realize file sharing across enterprises, the scheme also allows multiple authorities to jointly set up system parameters and manage distribute keys. Furthermore, by re-randomizing the user’s private key and update key, we achieve decryption key exposure resistance(DKER) in the scheme. We provide a formal security model and a series of security experiments, which show that our scheme is secure under chosen-plaintext attacks. Experimental simulations and evaluation analyses demonstrate the high efficiency and practicality of our scheme.

Privacy-preserving distributed deep learning via LWE-based Certificateless Additively Homomorphic Encryption (CAHE)

Current privacy-preserving schemes proposed for distributed deep learning (DDL) are based on public key infrastructure (PKI) which has management of keys problem and also key escrow problem for those that may use identity-based public key cryptography (ID-PKC). This presents the possibility for the privacy guarantee of the distributed/collaborative deep learning system to be flawed due to the presence of a Trusted Third Party (TTP) (i.e. a certificate authority (CA) for public key cryptography (PKC) and a key generation center (KGC) for an ID-PKC), that must be trusted. Additionally, the presence of high communication cost associated with the transmission of homomorphically encrypted gradients from participants to the cloud server in distributed deep learning needs more attention. Furthermore, few schemes have been proposed for DDL that have post-quantum robustness. We, therefore, propose and design a new privacy-preserving distributed deep learning solution. First, a new LWE-based certificateless additively homomorphic encryption scheme called CAHE is proposed and designed. Secondly, partial sharing algorithms based on random selection and selection of the largest (or topmost) gradients in terms of magnitude are proposed. Thirdly, we put forward a new privacy-preserving distributed deep learning framework that combines the certificateless additively homomorphic encryption and partial sharing in the DDL. Our approach provides better privacy (i.e. not relying solely on the TTP) and also reduces communication cost for distributed deep learning. We note emphatically that this is the first time certificateless HE is being proposed, designed, and implemented in DDL. Results from our work indicate that the accuracy of the CAHE-based deep learning does not deteriorate (97.20%) while greatly preserving the privacy of participant’s dataset. With partial sharing, our solution records 97.17% and 97.12% accuracy for the selection of topmost gradients and random selection of gradients scenarios respectively, and with a great reduction in communication cost for transmitting encrypted gradients.

Some New Methods to Generate Short Addition Chains

Modular exponentiation and scalar multiplication are important operations in most public-key cryptosystems, and their efficient computation is essential to cryptosystems. The shortest addition chain is one of the most important mathematical concepts to realize the optimization of computation. However, finding a shortest addition chain of length r is generally regarded as an NP-hard problem, whose time complexity is comparable to O(r!). This paper proposes some novel methods to generate short addition chains. We firstly present a Simplified Power-tree method by deeply deleting the power-tree whose time complexity is reduced to O(r2). In this paper, a Cross Window method and its variant are introduced by improving the Window method. The Cross Window method uses the cross correlation to deal with the windows and its pre-computation is optimized by a new Addition Sequence Algorithm. The theoretical analysis is conducted to show the correctness and effectiveness. Meanwhile, our experiments show that the new methods can obtain shorter addition chains compared to the existing methods. The Cross Window method with the Addition Sequence algorithm can attain 44.74% and 9.51% reduction of the addition chain length, in the best case, compared to the Binary method and the Window method respectively.

Post-quantum signature algorithms on noncommutative algebras, using difficulty of solving systems of quadratic equations

A recently proposed new concept for constructing algebraic signature schemes with a hidden group is used to develop two new post-quantum signature algorithms on four-dimensional and six-dimensional finite noncommutative associative algebras. As in the case of the post-quantum signature schemes of multivariate cryptography, the security of the introduced algorithms is based on the computational difficulty of solving systems of many quadratic equations (44 and 42) with many unknowns (40 and 36). The signature represents a pair of a natural number e and a vector S. The latter enters three times in the verification equation used, providing resistance to the forging signature attacks by using the value S as a fitting parameter. A public key is generated in the form of a set of vectors, each of which is calculated as the product of triples of secret vectors. With a special choice of these triples, a signer has the possibility of calculating a signature that satisfies the verification equation. The developed post-quantum signature algorithms are practical, having sufficiently small signatures (97 and 109 bytes), public keys (387 and 291 bytes), and secret keys (315 and 451 bytes). A significant difference from the public-key algorithms of multivariate cryptography is that in the developed signature schemes, the system of quadratic equations is derived from the formulas for generating the public-key elements in the form of a set of vectors of m-dimensional finite noncommutative algebra with an associative vector multiplication operation. The formulas define the system of n quadratic vector equations, which reduces to the system of m quadratic equations over a finite field.

PCAS: Cryptanalysis and improvement of pairing-free certificateless aggregate signature scheme with conditional privacy-preserving for VANETs

Certificateless aggregate signature (CLAS) is an effective approach for the multiple authentications in multi-users and multi-information environments like the vehicular ad hoc networks (VANETs), which can address the certificate management issue in the traditional public key cryptography (PKC) and solve the key escrow problem in identity-based cryptography (IBC). In recent years, a new CLAS mechanism (LICLAS) is presented for the authentication of sensors in healthcare wireless medical sensor networks (HWMSNs). In this paper, we make an analysis and prove that LICLAS is not able to against forgery attacks. Thus, we present an improved CLAS scheme (PCAS) for vehicle authentication in VANETs, which satisfies the privacy and security requirements. PCAS constructs the signature algorithm based on Elliptic Curve Cryptography (ECC) to avoid bilinear pairing and Map-to-Hash function operations. In order to further improve security and efficiency of PCAS, the vehicle key generation and signature algorithm is revised. The pseudonym mechanism is also adopted to achieve conditional privacy preservation. Besides, PCAS allows to execute a batch verification of messages, where RSUs may verify the aggregated signatures from vehicles to reduce time overhead. Under the assumption that the elliptic curve discrete logarithm problem (ECDLP) is hard, PCAS is proved to be existentially unforgeable against adaptive chosen message attacks in the random oracle model. Through the performance analysis, under the same time complexity, PCAS is shown to more effective. Compared with LICLAS, for a single message and 2000 messages, the transmission overhead of PCAS is reduced by 25% and 25% respectively, and the computation overhead is reduced by 16.56% and 25.34% respectively.

Identity-Based Proxy Signature with Message Recovery over NTRU Lattice

Proxy signature is one of the important primitives of public-key cryptography and plays an essential role in delivering security services in modern communications. However, existing post quantum proxy signature schemes with larger signature sizes might not be fully practical for some resource-constrained devices (e.g., Internet of Things devices). A signature scheme with message recovery has the characteristic that part or all of the message is embedded in the signature, which can reduce the size of the signature. In this paper, we present a new identity-based proxy signature scheme over an NTRU lattice with message recovery (IB-PSSMR), which is more efficient than the other existing identity-based proxy signature schemes in terms of the size of the signature and the cost of energy. We prove that our scheme is secure under a Short Integer Solution (SIS) assumption that is as hard as approximating several worst-case lattice problems in the random oracle model. We also discussed some application scenarios of IB-PSSMR in blockchain and Internet of Things (IOT). This paper provides a new idea for the design of lattice signature schemes in low resource constrained environments.

Progress in Multivariate Cryptography: Systematic Review, Challenges, and Research Directions

Multivariate Public Key Cryptosystem (MPKC) seem to be promising toward future digital security even in the presence of quantum adversaries. MPKCs derive their security from the difficulty of solving a random system of multivariate polynomial equations over a finite field, which is known to be an NP-hard problem. This article aims at presenting a comprehensive survey that covers multivariate public key encryption and signature schemes specifically targeting toward security, efficiency, and parameter choice. The survey starts by giving an overview of the existing security challenges which include structural attacks such as MinRank attack, differential attack , and finding Gröbner basis for direct attack , and so on. Additionally, it discusses the necessary algorithms for the implementation of the multivariate schemes. This study also compares the promising multivariate encryption and signature schemes. The critical open challenges that are reviewed in this survey will serve as a single comprehensive source of information on multivariate encryption and signature schemes and a ready reference for researchers working in this rising area of public key cryptography.

Data transmission using secure hybrid techniques for smart energy metering devices

Data transfer between components, continuous device monitoring, and other features are possible with an IoT-based energy management system. Due to its lightweight, compact, and expandable characteristics, the Message Queuing Telemetry Transport protocol (MQTT) has recently played an important role in IoT. Since the MQTT protocol cannot provide security between the publishing house and the subscription service, cryptographic techniques can be enforced. This work implements a public-key encryption system-based Elliptic Curve Cryptography (ECC) technique to secure data from Publisher's end to the Subscriber's end. The data from the Raspberry plane is sent to the MQTT publisher with elliptical curve encryption built-in feature. The message/text is converted into cipher text and conveyed through the topic within the MQTT protocol to the subscribed Broker. The subscriber decrypts the cipher text using the elliptical curve cryptography technique with the secret key. This protects data, personal privacy, and safety in a more efficient and convenient way. ECC and MQTT protocols implemented in this work proved to be worthy for both burst mode and continuous data transmissions when compared to the conventional cryptographic techniques.

Acceleration of Wheel Factoring Techniques

The efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems’ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a traditional computer, there is no polynomial time algorithm. We investigate how to enhance the wheel factoring technique in this paper. Current wheel factorization algorithms rely on a very restricted set of prime integers as a base. In this study, we intend to adapt this notion to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time. The experiments on composite numbers n reveal that the proposed algorithm improves on the existing wheel factoring algorithm by about 75%.

A Comprehensive Survey on Certificate-Less Authentication Schemes for Vehicular Ad hoc Networks in Intelligent Transportation Systems.

Data transmission in intelligent transportation systems is being challenged by a variety of factors, such as open wireless communication channels, that pose problems related to security, anonymity, and privacy. To achieve secure data transmission, several authentication schemes are proposed by various researchers. The most predominant schemes are based on identity-based and public-key cryptography techniques. Due to limitations such as key escrow in identity-based cryptography and certificate management in public-key cryptography, certificate-less authentication schemes arrived to counter these challenges. This paper presents a comprehensive survey on the classification of various types of certificate-less authentication schemes and their features. The schemes are classified based on their type of authentication, the techniques used, the attacks they address, and their security requirements. This survey highlights the performance comparison of various authentication schemes and presents the gaps in them, thereby providing insights for the realization of intelligent transportation systems.

Solving the Problem of Blockwise Isomorphism of Polynomials with Circulant Matrices

The problem of Isomorphism of Polynomials (IP problem) is known to be important to study the security of multivariate public key cryptosystems, one of the major candidates of post-quantum cryptography, against key recovery attacks. In these years, several schemes based on the IP problem itself or its generalization have been proposed. At PQCrypto 2020, Santoso introduced a generalization of the problem of Isomorphism of Polynomials, called the problem of Blockwise Isomorphism of Polynomials (BIP problem), and proposed a new Diffie-Hellman type encryption scheme based on this problem with Circulant matrices (BIPC problem). Quite recently, Ikematsu et al. proposed an attack called the linear stack attack to recover an equivalent key of Santoso's encryption scheme. While this attack reduced the security of the scheme, it does not contribute to solving the BIPC problem itself. In the present paper, we describe how to solve the BIPC problem directly by simplifying the BIPC problem due to the conjugation property of circulant matrices. In fact, we experimentally solved the BIPC problem with the parameter, which has 256 bit security by Santoso's security analysis and has 72.7bit security against the linear stack attack, by about 10 minutes.

Performance Comparison between RSA and El-Gamal Algorithms for Speech Data Encryption and Decryption

This article presents a performance comparison of two known public key cryptography techniques namely RSA (Rivest–Shamir–Adleman) and El-Gamal algorithms to encrypt/decrypt the speech signals during transferring over open networks. Specifically, this work is divided into two stages. The first stage is enciphering-deciphering the input speech file by employing the RSA method. The second stage is enciphering-deciphering the same input speech file by employing the El-Gamal method. Then, a comparative analysis is performed to test the performance of both cryptosystems using diverse experimental and statistical analyses for the ciphering and deciphering procedures like some known speech quality measures: histogram, spectrogram, correlation, differential, speed performance and noise effect analyses. The analyses outcomes reveal that the RSA and El-Gamal approaches are efficient and adequate for providing high degree of security, confidentiality and reliability. Additionally, the outcomes indicate that the RSA speech cryptosystem outperforms its counterpart the El-Gamal speech cryptosystem in most of ciphering/deciphering speech performance metrics.

Post Quantum Lattice-Based Secure Framework using Aggregate Signature for Ambient Intelligence Assisted Blockchain-Based IoT Applications

Many classical cryptographic techniques are breakable due to the quantum computing security threats, and it leads to design public key cryptography based on post-quantum cryptography primitives and security protocols. In recent years, Lattice-Based Cryptography (LBC) becomes a prominent post-quantum cryptographic primitive that can be applied in both traditional and emerging security domains, including encryption, key agreement, digital signature and homomorphic encryption. In this article, we first provide a LBC-based security framework using aggregate signature that can be applied in ambient intelligence-assisted blockchain-based Internet of Things (IoT) applications, called LAS-AIBIoT. In LAS-AIBIoT, the wearable/medical devices deployed in the patients' body securely send the sensing secret data (encrypted messages) with their respective lattice-based signatures to their nearby controller nodes (CN), where the CNs forward these secret messages to the attached aggregator node (Aggr). Each Aggr verifies the individual signature of the devices and constructs the aggregate signature on the received secret messages and signatures, and sends the aggregated secret messages with their aggregate signature to the cloud server(s) for block construction in the blockchain center. Through the consensus protocol, the block is then mined and added into the blokchain. We show the robustness of LAS-AIBIoT against various potential attacks including quantum computing security threats through the threat model discussed in this article. Finally, through the blockchain-based simulation study we show that LAS-AIBIoT can be applied for real-time ambient intelligence-assisted IoT applications.

MU-TEIR: Traceable Encrypted Image Retrieval in the Multi-User Setting

The encrypted image retrieval technique allows users to retrieve images in an encrypted manner without decrypting images. However, most of the existing schemes still are vulnerable to security threats and inefficiency, caused by malicious users and inefficient feature extraction methods, respectively. To this end, we propose a traceable encrypted image retrieval in the multi-user setting in this article, termed as MU-TEIR. First, MU-TEIR employs a convolutional neural network VGG16 to extract image feature vectors and calculate the mean and variance of the feature vectors to construct the index, then encrypts index with the distributed two trapdoors public-key cryptosystem. After that, MU-TEIR protects image content by encrypting each image pixel with a standard stream cipher. Furthermore, MU-TEIR utilizes a watermark-based mechanism to prevent malicious query users from maliciously distributing images. Detailed security analysis shows that MU-TEIR protects the outsourced images and indexes security as well as query privacy, and can track malicious users. Experimental results verify effectiveness of MU-TEIR.