Private Key Research Articles

Mixed Chaotic Keys to Protect Digital Color Image

A high speed and highly secure method of image cryptography will be introduced. The introduced method will decrease the encryption time and increase the throughput of image cryptography, and it will have a significant speed up comparing with other existing methods of data cryptography. The introduced method will use a complicated private key, which will provide a huge key space to resist hacking attacks, and the generated images will be very sensitive to the selected values of the private key. The private key will use two chaotic logistic map models and one chaotic tent map model to generate three 2D chaotic keys, these keys will be converted to integers and resized to match the size of the image. The quality of the proposed method will be tested to insure that the introduced method will always produce an encrypted image with low quality and a decrypted image with high quality, the quality parameters calculated between the source images and the encrypted and decrypted images will be calculated to prove that the method will satisfy the quality requirements of good cryptography.

High-Performance Encryption Algorithms for Dynamic Images Transmission

With the proliferation of the internet, the issue of image tampering has escalated, necessitating robust image encryption schemes. Despite the multitude of proposed image encryption algorithms, challenges such as slow computational speed, weak security, and suboptimal visibility persist. This study addresses these challenges by introducing a high-performance encryption algorithm tailored for dynamic images—QEDI (Quick Encryption Algorithm for Dynamic Images). QEDI leverages elliptic curve-based asymmetric encryption algorithms and hash algorithms. The process involves using a hash algorithm to calculate the hash of the dynamic image slated for encryption, employing the elliptic curve algorithm to generate public and private keys, and utilizing the asymmetric encryption algorithm to process the image hash, resulting in a signature ciphertext. This ciphertext is embedded into the dynamic image, completing the encryption process. To enhance the execution speed without compromising the image quality and visibility, the bit depth of the dynamic image is reduced before hash calculation, and custom information fields are encapsulated to embed the signature ciphertext into the dynamic image. Experimental evaluations, conducted within a dynamic image generation system, encompassed assessments of security, encryption algorithm execution time, and image quality. The results indicate that utilizing QEDI for dynamic image encryption yields better security compared to EDI (Encryption Algorithm for Dynamic Images). QEDI exhibits minimal impact on image quality, with a noteworthy 69.77% reduction in execution time compared to EDI. Furthermore, when compared to existing algorithms employing image conversion for encryption, QEDI-encrypted images demonstrate enhanced visibility, better image quality, and expedited encryption speed.

TWO-FACTOR AUTHENTICATION PROTOCOL IN ACCESS CONTROL SYSTEMS

Background. To ensure the protection of the biometric access control system used in unsecured communication channels, it is necessary to exclude the storage and transfer, transfer of biometric data as well as sequences generated on their basis. The paper proposes a cryptographic protocol of two-factor authentication with the zero-knowledge over the extended field GF(2m) on elliptic curves using biometric data and the private key of the user.
 Objective. The aim of the article is to develop a cryptographic protocol for zero-knowledge two-factor authentication based on elliptic curves using biometric data and the user’s private key, which allows increasing cryptographic strength and reducing the duration of the authentication process.
 Methods. The process of implementing zero-knowledge proof protocols is as follows: one user (proofer) can convince another user (verifier) that he has some secret without disclosing the secret itself.
 Results. A cryptographic protocol for two-factor authentication with zero-knowledge over the extended field GF(2m) of elliptic curves using user biometric data is proposed, which significantly reduces the size of the protocol parameters and increases cryptographic strength (computational complexity of the breaking). There is no leakage of private key information and biometric data of the user during the execution of the zero-knowledge proof protocol.
 Conclusions. The implementation of a cryptographic protocol with zero-knowledge proof two-factor authentication based on elliptic curves allows significantly reducing the size of protocol parameters and increasing the cryptographic strength (computational complexity of the breaking).

Maximizing proof-of-work decentralization

Introduction: Blockchain technology is one of the emerging technologies that implements the concept of decentralization. The first application of this technology was with Bitcoin, which is a decentralized application. However, the decentralization of Bitcoin has become problematic due to the formation of mining pools. In this work, decentralization is intended to be maximized. Problem: Decentralization is the main concept of blockchain technologies. However, decentralization suffers mainly from mining pools in the Bitcoin network. Objective: In this work, the proposed solution to maximize upon the decentralized nature of Bitcoin is to revise the consensus protocol of Bitcoin. The proposed novel consensus protocol called Signature Proof-of-Work uses signatures instead of hashes. The proposed method aims to minimize the number of mining pools and maximize the number of solo miners by arguing that no one can share their private keys with others, which would ensure greater decentralization of the network. Methodology: The consensus algorithm in Bitcoin is Proof-of-Work. Proof-of-Work allows for the formation of mining pools. Mining pools control the Bitcoin network and reduce decentralization. Therefore, a novel Proof-of-Work consensus algorithm is proposed to empower decentralization. Results: The proposed consensus algorithm called Signature Proof-of-Work uses signatures instead of hashes. The proposed method aims to minimize the number of mining pools and maximize the number of solo miners by arguing that no one can share their private keys with others, which would ensure greater decentralization of the network. Conclusion: The proposed consensus algorithm minimizes mining pools by enforcing non-shareable private keys. Originality: The proposed consensus algorithm is an enhancement of the default Proof-of-Work algorithm of Bitcoin. The proposed algorithm uses signatures instead of hashes, which differentiates it from the default algorithm. Limitations: In the proposed algorithm, the main argument is that no one shares their private keys. In other words, miners cannot share their private keys with others. If they share their private keys, others can control their own money. Therefore, each miner does not want to collaborate with other miners to mine new blocks. As a result, the mining pools will not be formed.

Kth min Threshold Encryption for Privacy-preserving Data Evaluation

Abstract The $k$th min threshold is to judge whether the $k$th smallest element of an attribute set along with a confidential file is greater than a predefined threshold, which is a fundamental, primitive operation in data evaluation, such as risk evaluation in business investment. However, it will compromise the privacy of the confidential files when proceeding with such a data evaluation because there is often a large amount of sensitive information involved in them, which the organizations/individuals are reluctant to expose due to the risk of losing a competitive advantage. Motivated by the issue how to preserve the privacy of the confidential files during data evaluation, in this research, we first present a new encryption notion called $k$th min threshold encryption (KTE) for serving privacy-preserving data evaluation. In this notion, the confidential file will be encrypted under an attribute set for its privacy protection prior to being sent to a receiver, and a decryption key is generated from a threshold $d$ and a rank $k$ of element, both selected by the receiver. The decryption will be successful if and only if the $k$th smallest element of the attribute set is greater than $d$. We then describe a concrete construction of KTE in the public-key setting. In particular, our construction features optimally short private keys, which only consists of one group element. By virtue of this advantage, it is quite practical because of only two pairing operations for decryption computation.

Quantum Key Distribution for Critical Infrastructures: Towards Cyber-Physical Security for Hydropower and Dams.

Hydropower facilities are often remotely monitored or controlled from a centralized remote control room. Additionally, major component manufacturers monitor the performance of installed components, increasingly via public communication infrastructures. While these communications enable efficiencies and increased reliability, they also expand the cyber-attack surface. Communications may use the internet to remote control a facility's control systems, or it may involve sending control commands over a network from a control room to a machine. The content could be encrypted and decrypted using a public key to protect the communicated information. These cryptographic encoding and decoding schemes become vulnerable as more advances are made in computer technologies, such as quantum computing. In contrast, quantum key distribution (QKD) and other quantum cryptographic protocols are not based upon a computational problem, and offer an alternative to symmetric cryptography in some scenarios. Although the underlying mechanism of quantum cryptogrpahic protocols such as QKD ensure that any attempt by an adversary to observe the quantum part of the protocol will result in a detectable signature as an increased error rate, potentially even preventing key generation, it serves as a warning for further investigation. In QKD, when the error rate is low enough and enough photons have been detected, a shared private key can be generated known only to the sender and receiver. We describe how this novel technology and its several modalities could benefit the critical infrastructures of dams or hydropower facilities. The presented discussions may be viewed as a precursor to a quantum cybersecurity roadmap for the identification of relevant threats and mitigation.

Research on double camouflage encryption mechanism of QR code based on UAV landing scenario

Usually, the landing area of the drone is presented with QR code images, so it is crucial to ensure the information security of the landing area and prevent it from being occupied by other users. This paper proposes a double camouflage encryption method of QR code based on UAV landing scenario. For the QR code image required for UAV landing, the private key and carrier image are used to complete double camouflage encryption, and then the public key is modulated according to the principle of ghost imaging to obtain the ciphertext. After receiving the ciphertext, the receiver first decrypts the camouflage image according to the public key, and then decrypts the QR code image using the private key. The UAV receives ciphertext information through the detector, for non-users, the correct QR code image cannot be decrypted through the wrong key. Even if the eavesdropper obtains the public key information, they can only decrypt the camouflage image and cannot land. For our users, the public key and the double private key can decrypt the correct QR code image for landing. This encryption method can effectively decrypt the image at non-full sampling rate, while also resisting the external noise attack, and has high security.

Digital Signature Based on Cryptography Implementing in Java

The digital signature in Java utilizes cryptographic techniques to create a unique hash of a message, which is then encrypted using a private key. This encrypted hash, along with the original message, forms the digital signature. Verification involves decrypting the signature with the corresponding public key, confirming the integrity and origin of the message

ICRB: An improved consensus‐based redactable blockchain considering contextual consistency

AbstractBlockchain is a distributed ledger proposed by Satoshi Nakamoto. It has become one of the most important networks for humans in the world. With the rapid development of blockchain technology, an increasing number of criminals are engaging in fraudulent activities, extortion and other financial crimes on the blockchain. Due to the immutability of blockchain, it is difficult for users to recover their losses. Some scholars have proposed the concept of the redactable blockchain. However, most redactable blockchain schemes fail to consider the impact of modification on the contextual economic relationships of the blockchain. We propose an improved redactable blockchain considering contextual consistency. Additionally, we utilize a security deposit mechanism to guarantee financial contextual consistency for the modified blockchain. We distribute users' security deposit account private keys to random users on the blockchain using Verifiable Secret Sharing, Verifiable Random Functions and other cryptographic primitives to achieve decentralized key management and modification. Experiments show that the performance of our scheme is acceptable in realistic situations.

Tensor-Enabled Communication-Efficient and Trustworthy Federated Learning for Heterogeneous Intelligent Space–Air–Ground-Integrated IoT

Federated Learning (FL) could provide a promising privacy-preserving intelligent learning paradigm for Space-Air-Ground Integrated Internet of Things (SAGI-IoT) by breaking down data islands and solving the dilemma between data privacy and data sharing. Currently, adaptivity, communication efficiency and model security are the three main challenges faced by FL, and they are rarely considered by existing works simultaneously. Concretely, most existing FL works assume that local models share the same architecture with global model, which is less adaptive and cannot meet the heterogeneous requirements of SAGI-IoT. Exchanging numerous model parameters not only generates massive communication overhead but also poses the risk of privacy leakage. The security of FL based on homomorphic encryption with single private key is weak as well. Given this, this paper proposes a tensor-empowered communication-efficient and trustworthy heterogeneous FL, where various participants could choose suitable heterogeneous local models according to their actual computing and communication environment, so that clients with different capabilities could do what they are good at. Additionally, tensor train decomposition is leveraged to reduce communication parameters while maintaining model performance. The storage requirements and communication overhead for heterogeneous clients are reduced further. Finally, the homomorphic encryption with double trapdoor property is utilized to provide a robust and trustworthy environment, which can defend against the inference attacks from malicious external attackers, honest-but-curious server and internal participating clients. Extensive experimental results show that the proposed approach is more adaptive and can improve communication efficiency as well as protect model security compared with the state-of-the-art.

Evaluating RSA encryption: Primality testing, pollards algorithms, and security challenges

In the dynamic realm of cryptography, Rivest, Shamir, and Adleman (RSA) encryption stands as a pivotal element in ensuring secure communications. This analysis offers a detailed exploration of RSA encryption, emphasizing critical aspects such as primality testing, the intricacies of Pollards factorization algorithms, and the overarching security challenges intrinsic to this prevalent encryption paradigm. Delving deep into the heart of RSA, the research underscores the paramount role of primality testing in the RSA key generation process and critically evaluates the efficiency and reliability of diverse primality test methodologies. Moreover, it navigates the potential pitfalls introduced by Pollards algorithms and ponders their consequential implications for RSAs security matrix. Beyond these technicalities, the analysis brings to the forefront a spectrum of security challenges besieging RSA. This encompasses nuances like vulnerabilities arising from diminutive private keys, pitfalls linked to common modulus attacks, and susceptibilities stemming from cache timing discrepancies. By illuminating both the robust facets and inherent vulnerabilities of RSA encryption, this scholarly work elevates the current narrative on cryptographic security. It accentuates the perpetual necessity for meticulous scrutiny and agile adaptability in the quest to shield sensitive digital information in our progressively interconnected world.

Anonymity preserving lightweight authentication protocol for resource-limited wireless sensor networks

Wireless sensor networks have been deployed in areas such as healthcare, military, transportation and home automation to collect data and forward it to remote users for further processing. Since open wireless communication channels are utilized for data transmissions, the exchanged messages are vulnerable to various threats such as eavesdropping and message falsifications. Therefore, many security solutions have been introduced to address these challenges. However, the resource-constrained nature of the sensor nodes makes it inefficient to deploy the conventional security schemes which require long keys for improved security. Therefore, lightweight authentication protocols have been presented. Unfortunately, majority of these schemes are still insecure while others incur relatively higher energy, computation, communication and storage complexities. In this paper, a protocol that deploys only lightweight one-way hashing and exclusive OR operations is presented. Its formal security analysis using Real-or Random (ROR) model demonstrates its capability to uphold the security of the derived session keys. In addition, its semantic security evaluation shows that it offers user privacy, anonymity, untraceability, authentication, session key agreement and key secrecy. Moreover, it is shown to resist attacks such as side-channeling, physical capture, eavesdropping, offline guessing, spoofing, password loss, session key disclosure, forgery and impersonations. In terms of performance, it has relatively lower communication overheads and improves the computation costs and supported security characteristics by 31.56% and 33.33% respectively.

Various matching keys for asymmetric topology encryption

With the fast development of quantum computer technology, one has to focus on the security of information running in real networks. Topological coding is a technology of basic topological structure, number theory and algebra has potential application value in asymmetric encryption system. The public key and private key of topological graph encryption system designed by topological coding may be able to resist attacks equipped with artificial intelligence technology and quantum computer. In order to further investigate topology encoding, we propose new techniques for designing public and private keys using graph coloring and labeling.

Implementation of Elliptic Curve Cryptosystem with Bitcoin Curves on SECP256k1, NIST256p, NIST521p, and LLL

Very recent attacks like ladder leaks demonstrated the feasibility of recovering private keys with side-channel attacks using just one bit of secret nonce. ECDSA nonce bias can be exploited in many ways. Some attacks on ECDSA involve complicated Fourier analysis and lattice mathematics. This paper will enable cryptographers to identify efficient ways in which ECDSA can be cracked on curves NIST256p, SECP256k1, NIST521p, and weak nonce, kind of attacks that can crack ECDSA and how to protect yourself. Initially, we begin with an ECDSA signature to sign a message using the private key and validate the generated signature using the shared public key. Then we use a nonce or a random value to randomize the generated signature. Every time we sign, a new verifiable random nonce value is created, and a way in which the intruder can discover the private key if the signer leaks any one of the nonce values. Then we use Lenstra–Lenstra–Lovasz (LLL) method as a black box, we will try to attack signatures generated from bad nonce or bad random number generator (RAG) on NIST256p, SECP256k1 curves. The combination of nonce generation, post-message signing, and validation in ECDSA helps achieve Uniqueness, Authentication, Integrity, and Non-Repudiation. The analysis is performed by considering all three curves for the implementation of the Elliptic Curve Digital Signature Algorithm (ECDSA). The comparative analysis for each of the selected curves in terms of computational time is done with the leak of nonce and with the Lenstra–Lenstra–Lovasz method to crack ECDSA. The average computational costs to break ECDSA with curves NIST256p, NIST521p, and SECP256k1 are 0.016, 0.34,0.46 respectively which is almost zero depicting the strength of the algorithm. The average computational costs to break ECDSA with curves SECP256K1 and NIST256p using LLL are 2.9 and 3.4 respectively

Advancing Federated Learning through Verifiable Computations and Homomorphic Encryption.

Federated learning, as one of the three main technical routes for privacy computing, has been widely studied and applied in both academia and industry. However, malicious nodes may tamper with the algorithm execution process or submit false learning results, which directly affects the performance of federated learning. In addition, learning nodes can easily obtain the global model. In practical applications, we would like to obtain the federated learning results only by the demand side. Unfortunately, no discussion on protecting the privacy of the global model is found in the existing research. As emerging cryptographic tools, the zero-knowledge virtual machine (ZKVM) and homomorphic encryption provide new ideas for the design of federated learning frameworks. We have introduced ZKVM for the first time, creating learning nodes as local computing provers. This provides execution integrity proofs for multi-class machine learning algorithms. Meanwhile, we discuss how to generate verifiable proofs for large-scale machine learning tasks under resource constraints. In addition, we implement the fully homomorphic encryption (FHE) scheme in ZKVM. We encrypt the model weights so that the federated learning nodes always collaborate in the ciphertext space. The real results can be obtained only after the demand side decrypts them using the private key. The innovativeness of this paper is demonstrated in the following aspects: 1. We introduce the ZKVM for the first time, which achieves zero-knowledge proofs (ZKP) for machine learning tasks with multiple classes and arbitrary scales. 2. We encrypt the global model, which protects the model privacy during local computation and transmission. 3. We propose and implement a new federated learning framework. We measure the verification costs under different federated learning rounds on the IRIS dataset. Despite the impact of homomorphic encryption on computational accuracy, the framework proposed in this paper achieves a satisfactory 90% model accuracy. Our framework is highly secure and is expected to further improve the overall efficiency as cryptographic tools continue to evolve.

A Blockchain-Based Privacy-Preserving and Fair Data Transaction Model in IoT

The rapid development of the Internet of Things (IoT) has resulted in vast amounts of widely distributed data. Sharing these data can spur innovative advancements and enhance service quality. However, conventional data-sharing methods often involve third-party intermediaries, posing risks of single-point failures and privacy leaks. Moreover, these traditional sharing methods lack a secure transaction model to compensate for data sharing, which makes ensuring fair payment between data consumers and providers challenging. Blockchain, as a decentralized, secure, and trustworthy distributed ledger, offers a novel solution for data sharing. Nevertheless, since all nodes on the blockchain can access on-chain data, data privacy is inadequately protected, and traditional privacy-preserving methods like anonymization and generalization are ineffective against attackers with background knowledge. To address these issues, this paper proposes a decentralized, privacy-preserving, and fair data transaction model based on blockchain technology. We designed an adaptive local differential privacy algorithm, MDLDP, to protect the privacy of transaction data. Concurrently, verifiable encrypted signatures are employed to address the issue of fair payment during the data transaction process. This model proposes a committee structure to replace the individual arbitrator commonly seen in traditional verifiable encrypted signatures, thereby reducing potential collusion between dishonest traders and the arbitrator. The arbitration committee leverages threshold signature techniques to manage arbitration private keys. A full arbitration private key can only be collaboratively constructed by any arbitrary t members, ensuring the key’s security. Theoretical analyses and experimental results reveal that, in comparison to existing approaches, our model delivers enhanced transactional security. Moreover, while guaranteeing data availability, MDLDP affords elevated privacy protection.

Optical single-channel cryptosystem based on the non-negative matrix factorization and face biometric in cyan–magenta–yellow–black color space

In this paper, an optical color single-channel asymmetric cryptosystem based on the non-negative matrix factorization (NMF) and a face biometric in cyan–magenta–yellow–black (CMYK) space is proposed. To the best of our knowledge, this is the first time that NMF has been introduced into optical color image encryption. In the proposed cryptosystem, the color image in CMYK space is first decomposed into four color channels: C, M, Y, and K. By performing NMF operations on the four color channels, the four basic and sparse matrices can be obtained, respectively, which achieves asymmetry and saves computational resources. The four basis matrices can be used as private keys, and the four coefficient matrices are synthesized by the inverse discrete wavelet transform for subsequent encryption. Finally, the synthesized image is encoded with double random phase encoding based on phase truncation (PT). Compared with the existing PT-based cryptosystems, our cryptosystem can improve security against a special attack. In addition, the chaotic random phase mask is generated by a face biometric, which is noncontact and unique. Numerical simulation results are shown to verify the feasibility and robustness of our cryptosystem. Further, the proposed cryptosystem can be extended to encrypt multiple images conveniently.

Tag-Based PHY-Layer Authentication for RIS-Assisted Communication Systems

This paper proposes a tag-based approach for physical (PHY)-layer authentication in a reconfigurable intelligent surface (RIS) communication system. We first extract the intrinsic PHY-layer features of RIS communication systems in terms of channel gain and background noise, and then apply these PHY-layer features, a random signal as well as the private key of the transmitter to construct a robust cover tag signal against the impersonation attack. We adopt an asymmetric cryptography technique to encrypt tagged signals and to resist against unauthorized detection and tampering attacks during the transmission process. The receiver then applies the maximum a-posteriori (MAP) ratio test to conduct authentication based on the received tag signal, a reference tag signal transmitted in training phase and the knowledge of distributions of the channel gain, background noise and the random signal. We also provide security analysis to demonstrate how the proposed scheme can resist unauthorized detection, tampering attacks, etc. With the help of tools of the MAP ratio test, maximum likelihood estimation, we further analyze the distribution of the test statistics and derive analytical models for the false alarm and detection probabilities. Finally, extensive simulations are conducted to verify the theoretical results and to illustrate the performance of the proposed scheme.

Enhanced Efficiency and Security in LSB2 Steganography: Burst Embedding and Private Key Integration

Enhanced Efficiency and Security in LSB2 Steganography: Burst Embedding and Private Key Integration

Torus Ring Signcrypted Kademlia Hash Storage-Based Cryptography For Secured Data Storage In Fog Computing

Fog computing is decentralized computing infrastructure which used to present various services. Generally, fog network includes numerous data, computation, storage and application processes among data in the server. The fog node toward large-scale end-users offers a variety of interacted IoT services. Security is main concern for preserving data from unauthorized user access as carry outing secure data storage from fog user as well as server. Thus, secure data storage in fog is a demanding and rising concern for Fog-IoT security paradigms. Several research works have developed for secured fog data storage. But, data security level was minimum because performance of signcryption was not effectual. To overcome such problems, Torus Ring Signcrypted Kademlia Hash Storage (TRSKHS) method is proposed in fog computing. The designed TRSKHS method contains key generation, encryption as well as decryption for enhancing fog data storage by lesser computational cost. At first, registration process is carried to register fog users detail to the fog server. After registering, fog server generates pair of keys namely public key and public key for every registered user using Torus Ring Signcryption. Then, the fog user carry outs encryption as well as signature generation process. Initially, fog user data is encrypted in ciphertext as well as signature is generated for each data to provide secured data storage. Before storing encrypted data in server, hash value of each data is generated by using Kademlia Hash function. Then, encrypted user data through their hash value is stored in database. Finally, the decryption and signature verification is performed by the user to decrypt data. After that authorized users attain original data and enhance secure data storage. Through data accessing process, fog data is decrypted by their generated private key. This assists for TRSKHS method to enhance secure data storage by lesser amount of encryption time. Experimental assessment of TRSKHS method and conventional methods are performed with number of fog users as well as data. Proposed TRSKHS method carries the experimental evaluation using encryption time, storage complexity, data confidentiality rate as well as data integrity rate.