A New LWE-based Homomorphic Encryption Algorithm over Integer

With the development of modern communication technology, an increasing number of people are choosing to communicate end-to-end over the network. However, the risk of information leakage and data tampering has also increased, and the issue of information confidentiality has become an increasing concern. Among the existing encryption algorithms, symmetric encryption algorithms cannot securely manage the key and share the key between communication parties; ECC and other public key encryption algorithms have problems such as slow encryption and decryption speed, low encryption strength, etc. In addition, key management is still not guaranteed to be very secure; conventional hybrid encryption algorithms need to manage two different types of keys, and key management may be very complicated and prone to key leakage or theft. Based on the problems of the above algorithms, this paper proposes RSA-Co-CP-ABE Architecture, which uses socket communication, encrypts the RSA public key passed from Client to Server with CP-ABE, encrypts the confidential message with the public key passed from Client at Server, and finally sends the encrypted message to Client. This scheme has higher flexibility than the traditional symmetric encryption and public key encryption schemes, and by using CP-ABE encryption, it can realize attribute-based access control. And RSA encryption can make the scheme make a better balance between encryption and decryption efficiency and encryption strength. In addition, because the communication is transmitted in full cipher text during the communication, the scheme can effectively resist tampering or stealing by man-in-the-middle attacks.

This article critically examines the increasing reliance on cloud computing for data storage and processing, with a focus on the associated security and privacy challenges, especially when handling sensitive data. It explores homomorphic encryption (HE), particularly fully homomorphic encryption (FHE), as a promising solution for enabling computations on encrypted data without compromising confidentiality. Through a systematic literature review of studies published between 2017 and 2024, the article evaluates various homomorphic encryption algorithms, assessing their effectiveness in encryption and decryption, as well as performance metrics such as execution time, communication overhead, and energy consumption. The findings identify FHE as a widely researched technique, yet highlight significant challenges, including high computational overhead and complexity, which limit its suitability for real-time applications. The article underscores the need for continued research to enhance the efficiency of HE algorithms and calls for collaborative efforts among academia, industry, and regulators to establish robust frameworks for data privacy and security in cloud computing environments.

As huge data need to store on clouds for big data analytics and related features to analyze data computationally. Cloud computing serves many services to the client over their data such as data storage, analysis, and different resources. To avail such services over clouds, client needs to provide the access to cloud service providers (CSPs) over their data, which leaves data unprotected and confidentiality of their data is at stake. Different techniques are proposed to preserve the privacy and confidentiality of client’s data. One of the most common is, cryptography, which converts plaintext to unreadable form that is ciphertext. But almost all the existing cryptographic techniques are not up to mark and don’t have potential to perform the computation on the ciphertext. The recent trends in field of cryptography, the homomorphic encryption is emerged as a boom, which enhance the privacy of data to a large extent, without compromising the confidentiality of users’ data at cloud end. Homomorphic encryption provides the ability to perform computation on encrypted data, even when data is in use. Most of the existing homomorphic encryption algorithms are having high computational and time complexity. In this paper, an enhanced homomorphic encryption algorithm is proposed specifically for the cloud environments, having better performance. In this paper, an enhanced homomorphic encryption algorithm is proposed specifically for the cloud environments, may having better performance. The algorithm uses prime number-based matrix for encryption and decryption. The algorithm may give better performance in terms of encryption, decryption, and overall execution time.

Mobile computing works on the principle of broadcasting so that the information is radiated to everyone within the wave range which increases security threats and cyber attacks replicated quickly and easily. Thus, care must be taken in handling those types of attacks to provide information security while the user roams through different networks with heterogeneous security infrastructure. For that several cryptographic techniques are employed in mobile devices. Among them the public key cryptographic algorithms like RSA and ECC play a vital role in performing security. The basic building blocks of ECC is scalar point multiplication k[P] where k is a scalar and P is a point on elliptic curve. Similarly, in RSA the encryption and decryption is of the form xe mod n where encryption /decryption key. Normally exponentiation operation takes more time than multiplication which takes more time than addition and subtraction. To reduce the time, exponentiations and multiplications are performed by repeated multiplications and additions respectively. To reduce the time further addition chain is used. In order to generate the addition chain nature inspired based algorithms like PSO and SSO are considered in this paper. Using them, the addition chains for exponent of RSA and K[P] of ECC are generated. The encryption/decryption time and energy required for encryption/decryption are also computed and the performance of the cryptographic algorithms in mobile devices are analyzed with and without the incorporation of addition chain.

Data protection is the most important consideration when storing data in the cloud. We use hybrid cryptography to provide data protection in the cloud, while most current approaches use a single cryptography algorithm. As a result, we need a method that is both efficient and safe. In this paper, we employ hybrid cryptography, which makes use of existing cryptographic algorithms. We use cloud platform to promote the tremendous benefits of distributed computing in a variety of ways, from reducing enterprise sizes to lowering development costs. Organizations are most concerned about the security of their data. A single algorithm is used for data encryption and decryption in current systems, which may not be sufficient to achieve high security. A problem of stable key transmission and storage arises when using a public key cryptography algorithm. We use hybrid cryptography and file splitting for data protection. To data less accessible to attackers, components of the files are sorted on separate data.

The primary operation performed by cloud computing is to provide dynamic storage capacity and security to its users. The main benefit from using the cloud computing is the reduction in the economic expenditure and ease in the accessibility of data. This whole mechanism involves various security algorithms; still there are some security issues which needs to be solved. In this paper, various security algorithms have been discussed in order to analyze the performance of the algorithms and to find out that which encryption algorithm is better for the data protection in the cloud computing platform. The mainly concerned algorithms in this paper are RSA Algorithm and Modification in RSA Encryption Algorithm (MREA). One of the modifications in RSA encryption algorithm is named as Homomorphic Encryption Algorithm.

Introduction. Widespread use of unmanned aerial vehicles in the civilian and military spheres requires the development of new algorithms for identification friend or foe of targets, as used in the Armed Forces of Ukraine (AFU) devices of the "Parol" system are designed to service approximately 110 objects military equipment. AFU automation systems allow the use of additional sources of information about various objects from civil or special data transmission networks, which can be the basis for building a networked multi-level system of state recognition. Predictions of the development of quantum computers foresee the possibility of breaking modern algorithms for information security in polynomial time in the next 5-10 years, which requires the development and implementation of new encryption algorithms and revision of modern parameters. The purpose of the article is to develop a new algorithm for state recognition of objects, which can be scaled to process the required number of manned and unmanned aerial vehicles. Potential threats to classical cryptographic protection algorithms for data networks, which will result in the execution of algorithms such as Grover and Shore on quantum computers, were also discussed. Results. The article proposes a new multilevel algorithm of state recognition based on modern cryptographic methods of information protection, which allows to perform reliable automated identification of objects, scale systems using data on potential targets from other sources through secure special networks. Grover's search algorithm does not give a strong increase in key search performance for symmetric encryption algorithms, so there is no need to increase the key lengths for this type of information security algorithms. Post-quantum asymmetric encryption algorithms require additional study and comprehensive testing of information security or increasing the key lengths of cryptographic algorithms, which corresponds to the number of qubits, i.e. more than twice. The most promising is the family of asymmetric post-quantum cryptographic algorithms based on supersingular isogenic elliptic curves. Conclusions. The developed algorithm of identification friend or foe of objects is more secure compared to existing algorithms and is focused on the use of modern on-board computers and programmable radio modems. Shore's algorithm and the like will be a significant threat to modern asymmetric cryptography algorithms when the number of qubits of quantum computers exceeds the number of bits in public keys more than twice. Keywords: identification friend or foe, symmetric encryption, asymmetric cryptography, quantum computer, post-quantum cryptography.

Voting refers to the submission of an election or an opinion on a specific matter by expressing an intention on the ballot to a certain place. The existing voting method has the burden of counting time and cost. For this reason, research has been conducted to introduce an e-voting system. However, despite the advantages of e-voting, it is not widely used due to the risk of manipulation of voting results and various requirements. Recently, in order to reduce the risk of data manipulation, research is being conducted to apply the blockchain, a technology that guarantees data integrity, to e-voting. Blockchain guarantees the integrity of data, but has a weakness in secrecy. This paper applies the critical encryption technique to the blockchain and satisfies the requirements for voting such as verifiability, anonymity, fairness, non-reusability, competence, safety, transparency, and non-ticketing. We propose a system design and implementation method. The proposed blockchain-based e-voting system provides voter anonymity by issuing a voter certificate based on a blockchain address. The e-voting election monitoring committee generates a threshold group encryption key, and the proposed blockchain-based e-voting system guarantees confidentiality by a threshold group encryption algorithm during the voting process. The voting result is encrypted through a homomorphic encryption algorithm and stored in the blockchain. Thus, the released voting results ensure safety, confidentiality, transparency, and non-vote ticketing. In addition, the proposed blockchain-based e-voting system guarantees the unity and competence of voting through the blockchain’s smart contract.

In recent years, with the development of new energy industry and digital transformation, a large amount of business data is stored and transmitted, which contains important business secrets and user privacy information, so data security has become an important task. New energy business data security is a comprehensive task that requires a comprehensive consideration of factors such as technology, management and personnel training. By adopting appropriate security measures, the confidentiality, integrity and availability of new energy business data can be protected. With the rapid development of the Internet of Things, cloud computing and sensor technology, a large number of data characterized by a large number of types and strong timeliness has emerged, and the concept of big data has emerged. Big data is usually unable to be stored and calculated with conventional software within a certain time frame, and the adoption of new technical architectures can make big data play a greater value. In order to realize the secure storage of static big data and ensure the high storage efficiency, a scheme of secure storage of static big data based on lightweight encryption and homomorphic encryption algorithm is proposed. For unstructured data, a parallel encryption scheme based on elliptic curve lightweight encryption algorithm is designed. With the proposed dual-channel storage model, the data to be stored can be encrypted and stored from two storage channels at the same time. The dual-channel storage mode can increase the data storage speed and make up for the time consumption caused by the data encryption process. The reliability of the algorithm is verified by experiments.

Cryptographic algorithms are crucial for secure communication in the Internet of Things (IoT). Quantum computers threaten public key cryptography algorithms like RSA (Rivest, Shamir, Adleman) and Diffie-Hellman (DH) key exchange schemes, which are widely in use today. As cryptographic algorithms are the foundation of secure internet communication, the development of Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) is essential to protect transactions over the internet. However, solutions like Quantum Key Distribution require heavy infrastructure. So, it is not feasible for the Internet of Things with fewer resources in computing power and form factor. Post-Quantum Cryptography is helpful on these devices. But, it needs further developments and improvements. This paper analyzes cryptography algorithms and protocols of IoT with different categories. Integrated PQC of National Institute of Standards and Technology (NIST) third level finalists on Raspberry Pi 4 (RPI4) board with Linux operating system. The performance of Post-Quantum Cryptography schemes for IoT has been evaluated. Finally, a Post-Quantum Cryptography scheme has been suggested for the Internet of Things based on the performance analysis.

The exponential growth of Internet of Things (IoT) deployments in resource-constrained environments has necessitated the development of secure and efficient cryptographic mechanisms tailored for limited computational, memory, and energy capacities. This book chapter provides a comprehensive exploration into the foundations of lightweight cryptography with a focus on its applicability to constrained IoT devices. It examines the design and evaluation of lightweight block ciphers, stream ciphers, hash functions, authenticated encryption with associated data (AEAD), and public key cryptographic algorithms, emphasizing their resilience against advanced cryptanalytic techniques including differential, linear, and algebraic attacks. Implementation challenges such as key size, energy footprint, computation time, and resistance to side-channel and replay attacks are critically analyzed to highlight the trade-offs between performance and security. The chapter addresses current research gaps, emerging standards, and future directions in the domain of low-power cryptographic systems, aiming to guide both theoretical advancements and practical implementations.

Modular multiplication is one of the most important operations in the public key cryptographic algorithms. In order to design a high-performance modular multiplier, we present a novel hybrid Montgomery modular multiplier over GF(p) on FPGAs, which employs Karatsuba and Knuth multiplication algorithms in different levels to implement large integer multiplication. A 9-stage pipeline full-word multiplier is proposed for the 256-bit multiplication with 4-level recursion. The performance of our modular multiplier is improved through optimizing the pipeline and reducing carry-chain latency of the modular adder. On average, our modular multiplier can perform one 256-bit modular multiplication in 3 cycles. We can integrate 13 modular multipliers on a Xilinx Virtex-6 V6VSX475T FPGA. The experimental results show that the throughput of 856.9 million modular multiplications per second can be achieved and the hybrid Montgomery modular multiplier has an outstanding performance in the situations which need continuous multiplications.

Chapter 5 - Multiplication and Squaring

Limited energy is the most critical constraint that limits the capabilities of wireless sensor networks (WSNs). Most sensors operate on batteries with limited power. Battery recharging or replacement may be impossible. Security mechanisms that are based on public key cryptographic algorithms such as RSA and digital signatures are prohibitively expensive in terms of energy consumption and storage requirements, and thus unsuitable for WSN applications. This paper proposes a new fragile watermarking technique to detect unauthorized alterations in WSN data streams. We propose the FWC-D scheme, which uses group delimiters to keep the sender and receivers synchronized and help them to avoid ambiguity in the event of data insertion or deletion. The watermark, which is computed using a hash function, is stored in the previous group in a linked-list fashion to ensure data freshness and mitigate replay attacks, FWC-D generates a serial number SN that is attached to each group to help the receiver determines how many group insertions or deletions occurred. Detailed security analysis that compares the proposed FWC-D scheme with SGW, one of the latest integrity schemes for WSNs, shows that FWC-D is more robust than SGW. Simulation results further show that the proposed scheme is much faster than SGW.

Security in embedded systems is of critical importance since most of our secure transactions are currently made via credit cards or mobile phones. Power analysis-based side channel attacks have been proved as the most successful attacks on embedded systems to retrieve secret keys, allowing impersonation and theft. State-of-the-art solutions for such attacks on public key cryptographic algorithms, such as elliptic curve cryptography, mostly in software, hinder performance and repeatedly attacked using improved techniques. To protect these public key ciphers from both simple power analysis and differential power analysis, as a hardware solution, we propose to take advantage of the inherent parallelisation capability in multi-modulo residue number systems (RNS) architectures to obfuscate the secure information. Random selection of moduli is proposed to randomly choose the moduli sets for each key bit operation. This solution allows us to prevent power analysis, although still providing all the benefits of RNS. In this study, the authors show that differential power analysis, cross correlation analysis and correlation power analysis for a simple binary double-and-add operation are thwarted using their solution.