Public Key Cryptographic Algorithms Research Articles

An optical image compression and encryption scheme based on compressive sensing and RSA algorithm

Most of the image encryption algorithms are the private-key cryptosystem, in which the encryption process and the decryption process employ the same keys. To enhance the security of image encryption system, an optical image compression and encryption scheme based on compressive sensing and RSA public-key cryptographic algorithm is proposed, where the optical compressive imaging system is utilized to sample the original image. In the encryption process, the Walsh-Hadamard transform and a measurement matrix are adopted to simulate the optical compressive imaging system to measure the original image, which can effectively reduce the redundant information in the original image. Then the pixel positions of the resulting image are scrambled with pseudorandom sequence generated by one-dimensional (1D) cascade chaotic system. Furthermore, deoxyribonucleic acid (DNA) sequence operations are exploited to change the pixel values. The keys used in the scheme are generated based on the original image and are protected by the RSA algorithm. Experimental results demonstrate the effectiveness and reliability of the proposed optical image compression and encryption scheme with considerable compression and security performance.

Efficient and Secure ECDSA Algorithm and its Applications: A Survey

Public-key cryptography algorithms, especially elliptic curve cryptography (ECC)and elliptic curve digital signature algorithm (ECDSA) have been attracting attention frommany researchers in different institutions because these algorithms provide security andhigh performance when being used in many areas such as electronic-healthcare, electronicbanking,electronic-commerce, electronic-vehicular, and electronic-governance. These algorithmsheighten security against various attacks and the same time improve performanceto obtain efficiencies (time, memory, reduced computation complexity, and energy saving)in an environment of constrained source and large systems. This paper presents detailedand a comprehensive survey of an update of the ECDSA algorithm in terms of performance,security, and applications.

Lightweight Implementations of NIST P-256 and SM2 ECC on 8-bit Resource-Constraint Embedded Device

Elliptic Curve Cryptography (ECC) now is one of the most important approach to instantiate asymmetric encryption and signature schemes, which has been extensively exploited to protect the security of cyber-physical systems. With the advent of the Internet of Things (IoT), a great deal of constrained devices may require software implementations of ECC operations. Under this circumstances, the SM2, a set of public key cryptographic algorithms based on elliptic curves published by Chinese Commercial Cryptography Administration Office, was standardized at ISO in 2017 to enhance the cyber-security. However, few research works on the implementation of SM2 for constrained devices have been conducted. In this work, we fill this gap and propose our efficient, secure, and compact implementation of scalar multiplication on a 256-bit elliptic curve recommended by the SM2, as well as a comparison implementation of scalar multiplication on the same bit-length elliptic curve recommended by NIST. We re-design some existent techniques to fit the low-end IoT platform, namely 8-bit AVR processors, and our implementations evaluated on the desired platform show that the SM2 algorithms have competitive efficiency and security with NIST, which would work well to secure the IoT world.

Implementation of Digital Signature Algorithm by using Elliptical Curve p-192

The public key cryptographic algorithms considered unsuitable for Internet of Things due to use of longer keys, stressful calculations and consumption of battery resources for 16bit processers. This paper presents a novel algorithm based on elliptical curve for securing communication between internet of things by use of single coordinate system of Elliptical curve cryptography. Though lengdre symbol or single coordinate system exist in mathematics literature, it’s use for securing IoT devices is fairly new. In the proposed system IoT device transfer one coordinate of public key with extra bit allowing to save 50 % of bandwidth and storage for IoT devices.

Partially known information attack on SM2 key exchange protocol

SM2 key exchange protocol is a part of the SM2 public key cryptographic algorithm based on elliptic curves which has been issued by Chinese State Cryptography Administration since 2010. Under the guide of Chinese government, SM2 has been widely used in Chinese commercial applications. This paper gives the first partially known information attack on SM2 key exchange protocol. Our attack is based on a technique modified from the hidden number problem (HNP) which was introduced originally to study the bit security of Diffie-Hellman and related schemes. We present a polynomial-time algorithm which could recover the users secret key when given about half least significant bits of the two unknown intermediate values in each congruence over about 30 to 40 instances. Compared with the standard HNP, our approach deals with congruence involved two independent unknown variables and each of them possesses the same size as the secret key. Moreover, our results almost coincide with the previous best result among the same field considering the extreme case in which one variant is completely revealed.

Interoperable identity management protocol for multi-cloud platform

Multi-cloud adaptive application provisioning promises to solve data storage problem and leads to interoperability of data within multi-cloud environment. This also raises concern about interoperability of user among these computing domains. Although various standards and techniques have been developed to secure the identity of cloud consumer, but neither of them provides facility to interoperate and to secure the identity of cloud consumer. Thus, there is a need to develop an efficient authentication protocol that maintains single unique identity of cloud consumer and make it interoperable among various cloud service providers. Elliptic curve cryptography (ECC) based algorithms are the best choice among Public Key Cryptography (PKC) algorithms due to their small key sizes and efficient computation. In this paper, a secure ECC based mutual authentication protocol for cloud service provider servers using smart device and one time token has been proposed. The proposed scheme achieves mutual authentication and provides interoperability among multiple cloud service providers. The security analysis of the proposed protocol proves that the protocol is robust against all the security attacks. The formal verification of the proposed protocol is performed using AVISPA tool, which proves its security in the presence of intruder.

Correlated Extra Reductions Defeat Fixed Window Exponentiation

The security of modular power algorithm is a very important research topic, which is the core operation of public key cryptography algorithm. Since the first timing attack was public in 1996, the attacker can exploit time differences between specific events to recover a secret key. In 2016, Dugardin took advantage of extra reductions to attack a regular exponentiation algorithm, which did not entirely adapt the fixed window method with Montgomery’s algorithm. The central thesis of this paper is that there exists a positive correlation between extra reductions of pre-computation and post-computation when the calculation has the same multiplier factor. In this article, basing on this dependency we present an attack method, and confirm the feasibility and effectiveness of it by conducting simulation experiments. Experimental results verify that the method can effectively attack modular power algorithm.

Analysis Review on Public Key Cryptography Algorithms

This paper presents several Public Key Cryptography (PKC) algorithms based on the perspective of researchers’ effort since it was invented in the last four decades. The categories of the algorithms had been analyzed which are Discrete Logarithm, Integer Factorization, Coding Theory, Elliptic Curve, Lattices, Digital Signature and Hybrid algorithms. This paper reviewed the previous schemes in different PKC algorithms. The aim of this paper is to present the comparative trends of PKC algorithms based on number of research for each algorithm in last four decades, the roadmap of PKC algorithms since they were invented and the most chosen algorithms among previous researchers. Finally, the strength and drawback of proposed schemes and algorithms also presented in this paper.

To construct high level secure communication system: CTMI is not enough

Public key cryptographic (PKC) algorithms, such as the RSA, elliptic curve digital signature algorithm (ECDSA) etc., are widely used in the secure communication systems, such as OpenSSL, and a variety of information security systems. If designer do not securely implement them, the secret key will be easily extracted by side-channel attacks (SCAs) or combinational SCA thus mitigating the security of the entire communication system. Previous countermeasures of PKC implementations focused on the core part of the algorithms and ignored the modular inversion which is widely used in various PKC schemes. Many researchers believe that instead of straightforward implementation, constant time modular inversion (CTMI) is enough to resist the attack of simple power analysis combined with lattice analysis. However, we find that the CTMI security can be reduced to a hidden t-bit multiplier problem. Based on this feature, we firstly obtain Hamming weight of intermediate data through side-channel leakage. Then, we propose a heuristic algorithm to solve the problem by revealing the secret (partial and full) base of CTMI. Comparing previous necessary input message for masking filtering, our procedure need not any information about the secret base of the inversion. To our knowledge, this is the first time for evaluating the practical security of CTMI and experimental results show the fact that CTMI is not enough for high-level secure communication systems.

Portable Implementation of Postquantum Encryption Schemes and Key Exchange Protocols on JavaScript-Enabled Platforms

Quantum computers have the potential to solve some difficult mathematical problems efficiently and thus will inevitably exert a more significant impact on the traditional asymmetric cryptography. The National Institute of Standards and Technology (NIST) has opened a formal call for the submission of proposals of quantum-resistant public-key cryptographic algorithms to set the next-generation cryptography standards. Compared to powerful machines with ample amount of hardware resources such as racks of servers and IoT devices, including the massive number of microcontrollers, smart terminals, and sensor nodes with limited computing capacity, should also have some postquantum cryptography features for security and privacy. To ensure the correct execution of encryption algorithms on any platforms, the portability of implementation becomes more important. As distinguished from C/C++, JavaScript is a popular cross-platform language that can be used for the web applications and some hardware platforms directly, and it could be one of the solutions of portability. Therefore, we investigate and implement several recent lattice-based encryption schemes and public-key exchange protocols including Lizard, ring-Lizard, Kyber, Frodo, and NewHope in JavaScript, which are the active candidates of postquantum cryptography due to their applicabilities and efficiencies. We show and compare the performance of our JavaScript implementation on web browsers, embedded device Tessel2, Android phone, and several JavaScript-enabled platforms on PC and Mac. Our work shows that implementing lattice-based cryptography on JavaScript-enabled platforms is achievable and results in desirable portability.

Authentication and Encryption Using Modified Elliptic Curve Cryptography with Particle Swarm Optimization and Cuckoo Search Algorithm

Elliptic Curve Cryptography (ECC) uses two keys private key and public key and is considered as a public key cryptographic algorithm that is used for both authentication of a person and confidentiality of data. Either one of the keys is used in encryption and other in decryption depending on usage. Private key is used in encryption by the user and public key is used to identify user in the case of authentication. Similarly, the sender encrypts with the private key and the public key is used to decrypt the message in case of confidentiality. Choosing the private key is always an issue in all public key Cryptographic Algorithms such as RSA, ECC. If tiny values are chosen in random the security of the complete algorithm becomes an issue. Since the Public key is computed based on the Private Key, if they are not chosen optimally they generate infinity values. The proposed Modified Elliptic Curve Cryptography uses selection in either of the choices; the first option is by using Particle Swarm Optimization and the second option is by using Cuckoo Search Algorithm for randomly choosing the values. The proposed algorithms are developed and tested using sample database and both are found to be secured and reliable. The test results prove that the private key is chosen optimally not repetitive or tiny and the computations in public key will not reach infinity.

An Anonymous Handover Authentication Scheme Based on LTE‐A for Vehicular Networks

Vehicular networks play an important role in the intelligent transportation systems which have gained technical supports from car industry. Due to the mobility and the broadcast nature of wireless communication, security of the vehicular networks is a critical issue for the academia and industry. Many solutions have been proposed to target the security provisioning. However, most of them have various shortcomings. Based on the elliptic curve public key cryptography algorithm, in this paper, we propose a new anonymous roaming authentication protocol for the Long Term Evolution‐Advanced (LTE‐A) supported vehicular networks. For a vehicular LTE‐A network, an authentication protocol should be able to fulfill a variety of security requirements, which can be met by our proposal and proved by using Burrows–Abadi–Needham (BAN) logic. Compared with some existing solutions, our scheme has lower communication costs with stronger security functionality. The analyses on the security functions and the performance of the proposed solution show that our scheme is secure and efficient with ability against various types of malicious attacks.

On factoring RSA modulus using random-restart hill-climbing algorithm and Pollard’s rho algorithm

The security of the widely-used RSA public key cryptography algorithm depends on the difficulty of factoring a big integer into two large prime numbers. For many years, the integer factorization problem has been intensively and extensively studied in the field of number theory. As a result, a lot of deterministic algorithms such as Euler’s algorithm, Kraitchik’s, and variants of Pollard’s algorithms have been researched comprehensively. Our study takes a rather uncommon approach: rather than making use of intensive number theories, we attempt to factorize RSA modulus n by using random-restart hill-climbing algorithm, which belongs the class of metaheuristic algorithms. The factorization time of RSA moduli with different lengths is recorded and compared with the factorization time of Pollard’s rho algorithm, which is a deterministic algorithm. Our experimental results indicates that while random-restart hill-climbing algorithm is an acceptable candidate to factorize smaller RSA moduli, the factorization speed is much slower than that of Pollard’s rho algorithm.

Low Cost RFID Security Protocol Based on Rabin Symmetric Encryption Algorithm

Research shows that heavy-weighted RFID authentication protocol is weak to adapt to low-cost RFID tags because of the usage of public key Encryption Algorithm. The lightweight authentication protocol is suitable for low-cost RFID security authentication protocol because it adopts only the operation of AND, OR, XOR and shift, etc., but is hard to resist complex attacks. In this article, we use the features of the Rabin public key cryptography algorithm, which verifies that the signature process requires only low-cost square multiplication and modulo operations. Based on this, an RFID security authentication protocol with Rabin encryption algorithm is designed. The protocol improves the security of low-cost RFID tags to the height of the public key cryptosystem, and greatly increasing the security of low-cost RFID.

Energy efficient modular exponentiation for public-key cryptography based on bit forwarding techniques

Modular exponentiation and modular multiplications are two fundamental operations in various cryptographic applications, and hence the performance of public-key cryptographic algorithms is strongly influenced by the efficient implementation of these operations. Reducing the frequency of modular multiplications and the time requirements for modular multiplication will help in developing efficient modular exponential algorithms. This work proposes an energy efficient modular exponential algorithm based on bit forwarding techniques. In particular, two algorithms, Bit Forwarding 1-bit (BFW1) and Bit Forwarding 2-bits (BFW2), which are modifications of the existing binary exponential algorithm, have been developed. Hardware realizations of the proposed algorithms have been evaluated in terms of throughput, power and energy. Results show increased throughput of the order of 11.02% and 15.13%, reduction in power to 1.93% and 6.35% and energy saving of the order of 1.9% and 6.35% for BFW1 and BFW2 algorithms respectively. Xilinx ISE-14.2 on Virtex-5 evaluation board and ICARUS verilog simulation and synthesis tool are used for hardware realization for FPGA and synthesized using Cadence for ASIC.

Parallel GNFS algorithm integrated with parallel block Wiedemann algorithm for RSA security in cloud computing

RSA algorithm is one of the most popular and secure public key cryptographic algorithms. To guarantee data security in cloud computing, RSA algorithm has been widely used in cloud. The security of RSA algorithm lies in the difficulty of factoring large integers efficiently. The General Number Field Sieve (GNFS) algorithm is the most efficient algorithm for factoring integers greater than 110 digits at present, and cloud computing is able to provide powerful ability for carrying out GNFS algorithm. Focusing on the research regarding security of RSA, in this paper, we study the GNFS algorithm in cloud. More specifically, we discuss the current research about solving large and sparse linear systems over GF(2), which is one of the most time-consuming steps of the GNFS algorithm. Then, we propose a novel parallel block Wiedemann algorithm in cloud to reduce the communication cost of solving large and sparse linear systems over GF(2). The proposed parallel block Wiedemann algorithm includes strip partitioning, cyclic partitioning, and improved strip partitioning which accelerate different steps in the block Wiedemann algorithm in a parallel way. Theoretical and experimental results show that the parallel block Wiedemann algorithm can greatly enhance the performance of GNFS compared with other existing algorithm, in terms of both execution time and speedup.

An improved parallel block Lanczos algorithm over GF(2) for integer factorization

RSA algorithm is one of the most popular and secure public key cryptographic algorithms and has been widely used in many real-life applications. The security of the RSA algorithm lies in the difficulty of factoring large integers efficiently and the General Number Field Sieve (GNFS) algorithm is the most efficient algorithm for factoring integers greater than 110 digits at present. In this paper, targeted to speed up the factorization process of RSA, we discuss the current research about solving large and sparse linear systems over GF(2), which is one of the most time-consuming steps of the GNFS algorithm. With that, we propose an improved parallel block Lanczos (IBL) algorithm to reduce the communication cost of solving large and sparse linear systems over GF(2). More specifically, we firstly re-implement the parallel block Lanczos algorithm from the BSP paradigm to Open MPI. To further improve the performance, we then reorganize and redesign the algorithm to reduce the synchronization and communication costs during the outer product step. After this, we integrate the improved parallel block Lanczos algorithm with the GNFS algorithm. Finally, theoretical and experimental results demonstrate that the IBL algorithm greatly enhances the performance of GNFS compared with previous parallel block Lanczos (PBL) algorithm, in terms of both execution time and speedup.

STUDY ON IMPROVEMENT IN RSA ALGORITHM AND ITS IMPLEMENTATION

The Network Security means to protect data during their transmission over channel of networks similarly Internet Security also to protect data during their transmission over a collection of interconnected networks in all over the world. Cryptography is the way of hiding information during transmission over a cannel. There are lots of cryptographic algorithms available to protect our data from intruders.RSA also one of effective the public key cryptographic algorithm which needs time and memory. Many research papers submitted on this cryptographic algorithm. Each paper has different perspective.

Selective Plane Replacement Watermarking and Cryptography (SPRWC)

Background/Objectives: Telemedicine is an innovative system of healthcare provision from long distance. Though the technology adds to facilitating in reducing the patients’ visit, but requires innovative techniques to prevent illegal intruders during the transaction of medical images. Methods/Statistical Analysis: This paper introduces Selective Plane Replacement Watermarking with RSA Cryptography (SPRWRC) that combines bit plane slicing technique with a standard public key cryptographic algorithm by embedding the hospital logo as invisible watermark. The medical image that is to be shared over the public network is subjected to bit plane slicing. The hospital logo is encrypted by the standard public key cryptographic algorithm namely Rivest Shamir Adleman (RSA). The encrypted hospital logo is embedded into the MSB plane of the medical image. The LSB plane of the medical image is replaced with the embedded MSB plane. The image is reconstructed and transmitted over the public network. Findings: The hybrid algorithm explores a watermarking approach in spatial domain with hospital logo as the watermark. The maximum Entropy, NPCR and UACI values are 7.988, 0.998 and 0.46 respectively which are closer to the upper limit of theoretical values. The effectiveness of the proposed algorithm is verified against various attacks. The proposed method with encryption gives better result than without encryption due to scrambling of the watermark and embedding into the cover image does not show perceptible change on watermarked image. Application/Improvements: Protection of the integrity and confidentiality of medical images transactioned over public networks.

Enhanced a TCP security protocol by using optional fields in TCP header

The Transfer Control Protocol (TCP) itself does not guarantee the security of data that it transmits. However, under some circumstances, the security of TCP communication is required, e.g. the client-server communication in banking systems. Nowadays, the source socket layer (SSL) protocol is widely used; however, SSL is based on RSA (a public-key cryptographic algorithm) algorithm, which would require more computational resource. Therefore, an alternative faster solution utilizing symmetrical algorithm (AES) are proposed to achieve these goals: bidirectional authentication, encrypted data transmission and Integrity check. Moreover, use the optional fields in TCP header for carrying related information and introduced a new device SAM (Secure access module) which provides security-related functionalities: encryption, decryption, key-diversification etc