Elliptic Curve Cryptosystem Research Articles

An efficient authentication and key agreement scheme with user anonymity for roaming service in smart city

Smart city improves quality of life for urban residents by using multiple information and communication technologies. As the network infrastructure of smart city, GLObal MObility NETwork (GLOMONET) can offer seamless network connection service for mobile subscribers. Whereas, because of the opening characteristics of wireless channel and various attacks, security becomes a vital issue in GLOMONET. Recently, Karuppiah and Saravanan proposed an enhanced user authentication for roaming service in GLOMONET. Unfortunately, their scheme lacks the features of session key update and perfect forward secrecy, and the session key can be revealed by home agent. Besides, their scheme faces clock synchronization problem and efficiency problem. In order to provide secure authentication service, a novel ECC (elliptic curve cryptosystem)- based user authentication scheme for roaming service in smart city is proposed in this manuscript. The security features of the proposed scheme are formally evaluated by using provable security method under random oracle model and also present informal analysis. In addition, comparative analysis is given among our scheme and relevant protocols. The results of comparative analysis illustrate that the proposed protocol provides robust and efficient for roaming service in smart city.

Low-computation certificateless hybrid signcryption scheme

Hybrid signcryption is an important technique signcrypting bulk data using symmetric encryption. In this paper, we apply the technique of certificateless hybrid signcryption to an elliptic-curve cryptosystem, and construct a low-computation certificateless hybrid signcryption scheme. In the random oracle model, this scheme is proven to have indistinguishability against adaptive chosen-ciphertext attacks (IND-CCA2) under the elliptic-curve computation Diffie-Hellman assumption. Also, it has a strong existential unforgeability against adaptive chosen-message attacks (sUF-CMA) under the elliptic-curve discrete logarithm assumption. Analysis shows that the cryptographic algorithm does not rely on pairing operations and is much more efficient than other algorithms. In addition, it suits well to applications in environments where resources are constrained, such as wireless sensor networks and ad hoc networks.

A new image encryption technique combining Elliptic Curve Cryptosystem with Hill Cipher

Image encryption is rapidly increased recently by the increasing use of the internet and communication media. Sharing important images over unsecured channels is liable for attacking and stealing. Encryption techniques are the suitable methods to protect images from attacks. Hill cipher algorithm is one of the symmetric techniques, it has a simple structure and fast computations, but weak security because sender and receiver need to use and share the same private key within a non-secure channels. A new image encryption technique that combines Elliptic Curve Cryptosystem with Hill Cipher (ECCHC) has been proposed in this paper to convert Hill cipher from symmetric technique to asymmetric one and increase its security and efficiency and resist the hackers. Self-invertible key matrix is used to generate encryption and decryption secret key. So, no need to find the inverse key matrix in the decryption process. A secret key matrix with dimensions 4×4 will be used as an example in this study. Entropy, Peak Signal to Noise Ratio (PSNR), and Unified Average Changing Intensity (UACI) will be used to assess the grayscale image encryption efficiency and compare the encrypted image with the original image to evaluate the performance of the proposed encryption technique.

Elliptic Curve Cryptosystem in securing Communication across Unsecure Channel

In the present day, exchanging information is the essential of successful business in our society. Securing the information from unauthorized individuals as well as unauthorized access is more essential. Cases of hacking bank accounts, stealing credit card numbers and decoding secret information are common occurrence. With the rapid grow of internet technology and increasing computational power of computer, securing privilege information against unauthorized access is a source of concern to the business managers. Different organisation use different methods to secure sensitive information. Most of these methods have not provided the desired result. This paper proposes the use of Elliptic Curve Cryptography (ECC) over finite fields to send and receive information in an unsecure channel without jeopardizing the security of the information. The basisof using ECC is because there is no known technique of finding solution of discrete logarithm problem, in a reasonable time, on a properly chosen elliptic curve. ECC has advantagesof smaller key sizes, faster computations, reductions in processing power, less storage space and low bandwidth rate consumption.In this paper, group theory, elliptic curves, finite fields and ECC encoding were explained.

A New Key Management Scheme for Wireless Sensor Networks using an Elliptic Curve

Objectives: Our objective is to design a new key management scheme for wireless sensor networks. Methods/Analysis: The paper describes an effective and novel key management scheme for wireless sensor networks using elliptic curve public key cryptosystem. The proposed key management scheme uses multiple private keys and a pair of public keys. Findings: The proposed key management scheme was tested for performance evaluation using various elliptic curves of different parameters. The experimental results showed that our scheme performed well in spite of using multiple private keys and a pair of public keys. Applications/Improvements: The proposed key management scheme can be used in wireless sensor networks as elliptic curve cryptosystem uses small key length or size in contrast to other public key cryptosystems.

Design and FPGA implementation of an efficient security mechanism for mobile pay‐TV systems

SummaryA mobile pay‐TV service is one of the ongoing services of multimedia systems. Designing an efficient mechanism for authentication and key distribution is an important security requirement in mobile pay‐TV systems. Until now, many security protocols have been proposed for mobile pay‐TV systems. However, the existing protocols for mobile pay‐TV systems are vulnerable to various security attacks. Recently, Wang and Qin proposed an authentication scheme for mobile pay‐TV systems using bilinear pairing on elliptic curve cryptography. They claimed that their scheme could withstand various attacks. In this paper, we demonstrate that Wang and Qin's scheme is vulnerable to replay attacks and impersonation attacks. Furthermore, we propose a novel security protocol for mobile pay‐TV systems using the elliptic curve cryptosystem to overcome the weaknesses of Wang and Qin's scheme. In order to improve the efficiency, the proposed scheme is designed in such a way that needs fewer scalar multiplication operations and does not use bilinear pairing, which is an expensive cryptographic operation. Detailed analyses, including verification using the Automated Validation of Internet Security Protocols and Applications tool and implementation on FPGA, demonstrate that the proposed scheme not only withstands active and passive attacks and provides user anonymity but also has a better performance than Wang and Qin's scheme.

Montgomery curves and their arithmetic

Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryptosystems. This article surveys the theory and cryptographic applications of Montgomery curves over non-binary finite fields, including Montgomery's x-only arithmetic and Ladder algorithm, x-only Diffie–Hellman, y-coordinate recovery, and 2-dimensional and Euclidean differential addition chains such as Montgomery's PRAC algorithm.

Efficient and low‐complexity hardware architecture of Gaussian normal basis multiplication over GF(2 m ) for elliptic curve cryptosystems

In this paper, an efficient high-speed architecture of Gaussian normal basis (GNB) multiplierover binary finite field GF(2m) is presented. The structure is constructed by using some regular modules for computation of exponentiation by powers of 2 and low-cost blocks for multiplication by normal elements of the binary field. For the powers of 2 exponents, the modules are implemented by some simple cyclic shifts in the normal basis representation. As a result, the multiplier has a simple structure with a low critical path delay. The efficiency of the proposed multiplier is examined in terms of area and time complexity based on its implementation on Virtex-4 field programmable gate array family and also its application specific integrated circuit design in 180 nm complementary metal–oxide–semiconductor technology. Comparison results with other structures of the GNB multiplier verify that the proposed architecture has better performance in terms of speed and hardware utilisation.

Securing the Internet of Things in a Quantum World

Currently, we rely on cryptographic algorithms such as elliptic curve cryptosystems (ECCs) as basic building blocks to secure the communication in the IoT. However, public key schemes like ECC can easily be broken by the upcoming quantum computers. Due to recent advances in quantum computing, we should act now to prepare the IoT for the quantum world. In this article, we focus on the current state of the art and recent developments in the area of quantum-resistant cryptosystems for securing the IoT. We first demonstrate the impacts of quantum computers on the security of the cryptographic schemes used today, and then give an overview of the recommendations for cryptographic schemes that can be secure under the attacks of both classical and quantum computers. After that, we present the existing implementations of quantum-resistant cryptographic schemes on constrained devices suitable for the IoT. Finally, we give an introduction to ongoing projects for quantum-resistant schemes that will help develop future security solutions for the IoT.

Provable Identity Based User Authentication Scheme on ECC in Multi-server Environment

With non-stop development of e-commerce and different internet-based applications’ demands, service providers include many physical servers scattering all over the world. If some users would like to use various services, they have to repeatedly register. Therefore, they must remember all these information such as, user-names or passwords. To solve this problem, many authentication schemes in multi-server environment are proposed. Furthermore, to prevent the adversary from keeping track of another user when he or she logins, many schemes apply dynamic identity, but they have some limitations with popular kinds of attacks such as, replay attack, impersonation attack, or man-in-the-middle attack... In 2014, Yeh (Department of Information Management, National Dong Hwa University) proposed multi-server scheme using Rivest–Shamir–Adleman (RSA). However, we discover this scheme cannot achieve two basic properties, mutual authentication and session-key agreement. In this paper, we concretely demonstrate that discovery and propose a different provable version using elliptic curve cryptosystem in multi-server environment which overcomes the limitation of Yeh’s scheme and satisfies security and efficiency.

Elliptic Curve Cryptography and Coding Theory

From the earliest days of history, the requirement for methods of secret communication and protection of information had been present. Cryptography is such an important field of science developed to facilitate secret communication and safeguard information. Cryptography is based on mathematics. It is an application of different disciplines such as Algebra, Number Theory, Graph etc. Private key cryptography and Public key cryptography are the two main types of cryptography. Public key cryptosystems offer more security and convenience for the users. The main objective of this study is to explore the possibilities of further improvement of Curve Cryptography (ECC) by studying the mathematical aspects behind the Elliptic curve cryptosystem which is one of the latest of this kind and develop a computer program to generate the cyclic subgroup of a given elliptic curve defined over a finite field Ζp, where p is a prime, which is the major requirement to perform ECC and then use the same to illustrate how data security is achieved from this. For an elliptic curve defined over a field, the points on an elliptic curve naturally form an abelian group. curve arithmetic can be employed to develop a variety of curve cryptographic schemes such as key exchange, encryption, digital signatures and specific construction of a keyed-Hash Message Authentication Code (HMAC) which are illustrated through this study. Moreover this study proposes an improvement for the encryption of a message through utilization of a concept in Coding Theory of Abstract algebra which offers an additional shield for the transmitted message.

Implementation of Elliptic Curve Arithmetic Operations for Prime Field and Binary Field using Java BigInteger Class

The security of elliptic curve cryptosystems depends on the difficulty of solving the Elliptic Curve Discrete Log Problem (ECDLP). Elliptic curves with large group order are used for elliptic curve cryptosystems not to solve ECDLP. We implement elliptic curve arithmetic operations by using java BigInteger class to study and analyze any elliptic curve cryptographic protocol under large integer for prime field and binary field.

Security and Privacy-Preserving Metering Service in the Smart Grid

The deployment of smart metering provides an immense amount of data for power grid operators and energy providers. By using this data, a more efficient and flexible power grid can be realized. However, this data also raises privacy concerns since it contains very sensitive information about customers. In this paper, we present a security and privacy-preserving metering scheme for the community customers, by utilizing the password authenticated key exchange (PAKE) protocol and Elliptic Curve Cryptosystem (ECC). The proposed scheme will protect the community network from possible malicious behavior, and security analysis is also given in the paper.

A secure ID-based signcryption scheme based on elliptic curve cryptography

Signcryption is a cryptographic primitive which at the same time give both the capacity of digital signature and public key encryption in a single logical step. Identity based cryptography is a distinct option for the traditional certificate based cryptosystem. Its principal thought is that every client utilises his identity information as his public key. Elliptic curve cryptosystem (ECC) have new received consistent attention because of their higher security per bit as compare to other cryptosystem. This paper presents a new identity based signcryption based on elliptic curve cryptography. Its security is dependent on elliptic curve discrete logarithm problem (ECDLP) and elliptic curve Diffie-Hellman problem (ECDHP). The proposed scheme can be very useful in low-end resource devices such as mobile communication, mobile banking, personal digital assistant (PDA) and internet of things (IoT).

A secure ID-based signcryption scheme based on elliptic curve cryptography

Signcryption is a cryptographic primitive which at the same time give both the capacity of digital signature and public key encryption in a single logical step. Identity based cryptography is a distinct option for the traditional certificate based cryptosystem. Its principal thought is that every client utilises his identity information as his public key. Elliptic curve cryptosystem (ECC) have new received consistent attention because of their higher security per bit as compare to other cryptosystem. This paper presents a new identity based signcryption based on elliptic curve cryptography. Its security is dependent on elliptic curve discrete logarithm problem (ECDLP) and elliptic curve Diffie-Hellman problem (ECDHP). The proposed scheme can be very useful in low-end resource devices such as mobile communication, mobile banking, personal digital assistant (PDA) and internet of things (IoT).

Seamless Key Agreement Framework for Mobile-Sink in IoT Based Cloud-Centric Secured Public Safety Sensor Networks

Recently, the Internet of Things (IoT) has emerged as a significant advancement for Internet and mobile networks with various public safety network applications. An important use of IoT-based solutions is its application in post-disaster management, where the traditional telecommunication systems may be either completely or partially damaged. Since enabling technologies have restricted authentication privileges for mobile users, in this paper, a strategy of mobile-sink is introduced for the extension of user authentication over cloud-based environments. A seamless secure authentication and key agreement (S-SAKA) approach using bilinear pairing and elliptic-curve cryptosystems is presented. It is shown that the proposed S-SAKA approach satisfies the security properties, and as well as being resilient to node-capture attacks, it also resists significant numbers of other well-known potential attacks related with data confidentiality, mutual authentication, session-key agreement, user anonymity, password guessing, and key impersonation. Moreover, the proposed approach can provide a seamless connectivity through authentication over wireless sensor networks to alleviate the computation and communication cost constraints in the system. In addition, using Burrows–Abadi–Needham logic, it is demonstrated that the proposed S-SAKA framework offers proper mutual authentication and session key agreement between the mobile-sink and the base station.

Three-Factor User Authentication and Key Agreement Using Elliptic Curve Cryptosystem in Wireless Sensor Networks.

Secure communication is a significant issue in wireless sensor networks. User authentication and key agreement are essential for providing a secure system, especially in user-oriented mobile services. It is also necessary to protect the identity of each individual in wireless environments to avoid personal privacy concerns. Many authentication and key agreement schemes utilize a smart card in addition to a password to support security functionalities. However, these schemes often fail to provide security along with privacy. In 2015, Chang et al. analyzed the security vulnerabilities of previous schemes and presented the two-factor authentication scheme that provided user privacy by using dynamic identities. However, when we cryptanalyzed Chang et al.’s scheme, we found that it does not provide sufficient security for wireless sensor networks and fails to provide accurate password updates. This paper proposes a security-enhanced authentication and key agreement scheme to overcome these security weaknesses using biometric information and an elliptic curve cryptosystem. We analyze the security of the proposed scheme against various attacks and check its viability in the mobile environment.

Blind signatures using light variations in CCD sensors as a pattern to avoid identity forging

The implementation of countermeasures to avoid licence abuse is now obligatory, especially with the burgeoning of the Internet. The protocol proposed here is implemented within the session initiation protocol (SIP); this has been selected as the official end‐to‐end signalling protocol for establishing multimedia sessions in the Universal Mobile Telecommunication Systems network. This paper introduces blind signatures, enforced with user‐specific and unique data, modelled from CCD sensors to trace users of these online services, thus avoiding licence sharing that gives access to them. Blind signatures are useful in providing anonymity and establishing a way to tag users. The proposed protocol takes advantage of elliptic curve‐based cryptosystems – smaller key sizes and lower computational resources, an interesting issue for session establishment in S‐Universal Mobile Telecommunication Systems (satellite‐linked networks), where fast and light authentication protocols are a requirement ideal. SIP is a powerful signalling protocol for transmitting media over Internet protocol. Authentication is a vital security requirement for SIP. Hitherto, many authentication schemes have been proposed to enhance SIP security; indeed, the problem of impersonation is one of the topics most discussed. Consequently, a novel authentication and key agreement scheme is proposed for SIP using an elliptic curve cryptosystem. Copyright © 2016 John Wiley & Sons, Ltd.

Message mapping and reverse mapping in elliptic curve cryptosystem

AbstractElliptic curve cryptography is used as a public‐key cryptosystem for encryption and decryption in such a way that if one has to encrypt a message, then they attempt to map the message to some distinct point on the elliptic curve by modifying the message using a mapping algorithm. Although the arithmetic involved in elliptic curve cryptography is computationally less complex than other cryptographic algorithms, but conversion of simple messages to points on the elliptic curve has always been challenging. In this paper, we discuss the different schemes of message mapping in elliptic curve cryptosystem, the flaws of each method, and how vulnerable they are to cryptanalysis. We also derive the guidelines of a good message mapping scheme in elliptic curve cryptosystem. In the later part of this paper, we will discuss about a new mapping scheme that is resistible to frequency analysis and other forms of cryptanalysis. Copyright © 2016 John Wiley & Sons, Ltd.

Optimizing {0, 1, 3}-NAF Recoding Algorithm Using Block-Method Technique in Elliptic Curve Cryptosystem

The most expensive and time-consuming operation in Elliptic curve cryptosystem is scalar multiplication operation. Optimization of scalar multiplication will substantially enhance the ECC performance. Scalar multiplication can be improved by using an enhanced scalar recoding algorithm that can decrease the number of operations in the scalar representation process. The objective of this research is to introduce an efficient design and implementation of {0,1,3}-NAF scalar recoding algorithm by applying block method technique. The base algorithm has a complex look up table. With block method application on base algorithm, a complex look up table is undesired. Instead a fix look up table is introduced with less computation required for recoding. The Big-O notation is used to measure the complexity and (µs) used to evaluate the running time of base and proposed algorithm.