Koblitz Curve- A Mapping Technique to Encipher/Decipher the Text message using Elliptic Curve Cryptography

Wireless Sensor Networks (WSNs), comprising of tiny nodes with limited energy, computational and communication resources, are being widely used in various application areas ranging from pollution and weather monitoring to military. Even though every application may not require data to be exchanged in a secure manner, few WSN applications may have certain security requirements. The data is encrypted by a sender and sent over the wireless links and the same is decrypted at the receiver. To meet this purpose, symmetric key cryptographic (SKC) algorithms may be used. Such SKC primitives require keys to be made available before carrying out the data transfer between the nodes. Alternately, Public Key Cryptographic techniques, such as RSA algorithm can be considered. Even though, RSA is a popular algorithm providing good security level, it is computationally intensive involving large key sizes. The RSA can not be used in WSNs, as the nodes have limited resources. Presently, it is infeasible to implement the RSA algorithm using any of the WSN nodes commercially available. Elliptic curve cryptography (ECC), another public key cryptographic (PKC) algorithm providing same level of security with smaller key size requirements, can be used as an alternative in order to provide security in WSN applications. ECC encryption and decryption use domain parameters, which includes the Generator point to be published. In most of the outdoor WSN applications, the deployment of the nodes is random and the nodes could be captured and an attacker could launch man-in-middle (MIM) attack, and break the public key thereby leading to security breach in the network. A technique to overcome such an attack is proposed in this work and the same is compared with two other similar approaches.

This paper introduces the ECC (Elliptic Curve Cryptography) processor, in which the τ-NAF converter and Square-Square-Add Algorithm are utilized, for point multiplication on Koblitz curves. The proposed ECC processor operates over GF(2163). The τ-NAF converter can turn the complicated point double to simple point square, and the Square-Square-Add Algorithm can decrease the number of point addition. With the proposed design, the execution time for executing point multiplication will decrease by 21%, and the AT value (Area-Time product) will be lowered by 15% than the state-of-the-art design, which achieves better efficiency on the execution of ECC over Koblitz curves.

The use of public-key cryptosystems (PKC) received considerable attention. They are beneficial in encryption as well as signing which play an essential role in electronic banking and financial transactions. Elliptic Curve Cryptography (ECC) is one of best public key techniques because of its small key size and high security. Secure applications in smart cards present implementation challenges particular to the platform's memory, bandwidth, and computation constraints. ECC's unique properties make it especially well suited to smart card applications. ECC systems provide the highest strength per bit of any cryptosystem known today. The paper presents a new method for smart card implementation of elliptic curves, explaining how ECC can not only significantly reduce the cost, but also accelerate the deployment of smart cards in new applications. ECC permits reductions in key and certificate size that translate to smaller memory requirements (especially for EEPROM), which represent significant cost savings. This added functionality can play an effective role in electronic payment and online banking technologies.

Elliptic curve cryptography (ECC) is an excellent candidate for secure embedded multimedia applications due to its small key size and high security protection. The performance profiling of the ECC implementation, such as execution time and data cache stalls, on TriMedia TM1300 and Intel Pentium 4 is conducted in this research. Based on this study, we identify the main bottlenecks of the EEC implementation, and propose some favorable micro-architecture for this application. Moreover, several integer multiplication schemes are presented for the TM1300 processor for performance enhancement. In particular, the FIR-based multiplication is built with the special FIR instruction provided by TM1300. The performance improvement of the proposed schemes is reported and discussed. Overall, we aim at providing a good understanding of the system architecture of secure embedded multimedia applications, hardware and software cryptography implementation with ECC as an example.

Cloud computing represents a significant challenge for securing data due to its inherently distributed model. Elliptic Curve Cryptography (ECC) will provide substantial security with smaller key sizes, creating a strong candidate for cloud-based environments. This review critically examines ECC based security architectures in cloud computing with the aim of reducing the cipher space for efficiency and scalability. A comprehensive examination of recent ECC implementations guided this review, including identity-based and lightweight ECC Architectures. Specific consideration was given to cipher space reduction techniques incorporating point compression and optimized scalar multiplication. The review provided evidence of a gap in the literature regarding the ability to counterbalance strength of security with the compactness of the cipher across a range of cloud scenarios and use cases. Most models considered provide little flexibility for real-time or post-quantum alternatives. None of the literature considered cipher space optimization for ECC to date. The ongoing optimization of cipher space is essential to progressing security based on ECC implementations for cloud scenarios. Future research efforts must centre on adaptive, efficient, quantum resilient ECC schemes, in ways that yield high security with minimum impacts on the operational scale, and the associated computational loads.

The image watermarking technology is a vital facet about multimedia authentication and copyright protection to improve its reliability and security. This paper proposes an embedment of encrypted watermark in a JPEG image to address the issues of proprietorship of digital images. Amongst the cryptographic solutions, the most satisfactory cryptography method is Elliptic Curve Cryptography because of its small usage of bandwidth, low computational time and small key size. DWT and SVD are used as a scientific means to implant watermark in the image. The quality of watermarked image is measured by Peak signal to noise ratio (PSNR) and to compare the recovered watermark and the original watermark Normalized correlation (NC) is used.

With hardware support and software optimization, Public Key Cryptography (PKC) has been announced feasible on micro sensors recently [1][2][22][23]. A number of experiments proved that the Elliptic Curve Cryptography (ECC) is more suitable for resource constraint motes compared with RSA [2][3]. But even ECC based protocols still cost too much energy. In this paper, we propose C4W, an identity-based public key infrastructure specially designed for wireless sensor networks (WSNs), in which all nodes can generate others' ECC public keys directly from their identities. Without certificates, no energy will be consumed for certificates communication and verification, which makes C4W especially energy efficient. C4W uses a protocol without certificates to realize mutual authentication and key agreement. Compared with a simplified SSL (SSSL) protocol using an abbreviated certificate, C4W consumes lower than 35% energy, and the communication consumption of C4W is only 28.5% of that consumed by SSSL. Furthermore, the energy analysis of C4W illuminates that the expensive public key computational cost is almost neglectable compared with the heavy communication consumption in a large-scale WSNs, which gives the asymmetric key management in WSNs a bright future.

In WSN, DoS (denial of service) attack makes shortcoming system. The packets travel over and over in the sensor network. By that, all the assets like data transmission, memory, and vitality are squandered by this attack. However, the attacker ought to optimize its attacker plan for request to boost the impact on the system performance because of the deficiency of vitality at the aggressor side. Denial of service (DoS) attack on the Internet has become a squeezing issue. By staying away from these sorts of attacks, network performance can be improved. Therefore, security is a fundamental requirement for these networks. Effective routing is necessary in order to overcome the issued faced by the crosslayer in the DOS attack of the WSN network for the purpose of good transmission. This research work mainly focuses on performance evaluation using optimization methods. To establish the efficient path in the crosslayer against DoS attack, this paper has proposed enhanced lion optimization with an efficient path routing equalization technique (LOEPRE). If any failure node occurs in the network, then the node is recognized and the transfer of the data packet is done to the other node. Retransmission of data causes overload in the network. The proposed model focuses on these issues and overcomes these issues by improving the path efficiently with robust security. It consists of three phases: the initial phase includes the route discovery in the network. In the second phase, the transfer of data is done in the high router path for security purposes. Finally, the efficient path routing equalization technique is used for minimizing the overload in the network; it provides the equalized path length in the network and is highly efficient. Hence, the proposed LOEPRE technique is used to achieve energy efficiency in wireless network for prolonged network lifetime and minimum packet latency and minimize consumption of energy. Moreover, the simulation outcome of the proposed LOEPRE method is highly robust while comparing to the existing methods EFCRS, SSPRA ELOER, EFLOR, and TSTP. It achieves better performance than existing algorithms in comparing metric connectivity ratio, end-to-end delay, overhead, throughput, and packet delivery ratio.

To enhance the security and authentication processes, this extension integrates Elliptic Curve Cryptography (ECC) for image encryption and Local Binary Pattern Histogram (LBPH) for live face authentication during registration and login. ECC, known for its high security with smaller key sizes, is incorporated to securely encrypt images, addressing the growing need for efficient and lightweight image encryption in resource-constrained environments. By employing ECC, the encryption algorithm ensures that visual data transmitted and stored remains confidential, with reduced computational overhead compared to traditional encryption methods like AES. Additionally, LBPH is employed for real-time face authentication, allowing users to authenticate themselves via facial recognition during both registration and login. This biometric system leverages LBPH’s robustness against variations in lighting and facial expressions, ensuring reliable face recognition in diverse environments. By the integrity of user access control, offering a combining ECC for image encryption and LBPH for face authentication, the extended system strengthens both the confidentiality of transmitted data and seamless and secure authentication process. The enhanced system was evaluated for speed, accuracy, and efficiency, showing significant improvements in real-time security applications.

Radio‐frequency identification (RFID) technology has proliferated over the last few years and being deployed as identification technology in numerous domains like intelligent transportation systems (ITS) and Internet of Vehicles (IoV) for applications like road safety, efficient traffic management, automatic toll collection, intelligent parking, etc. As RFID devices, as well as the possible domains of ITS and IoV onto which the RFID technology can be deployed, are usually resource‐constrained, thus, security and privacy become a major concern. So, public‐key cryptography becomes the better choice for enhancing the security of RFID based systems. Elliptic curve cryptography (ECC) is one of the dominant and secure asymmetric‐key cryptosystems being used for RFID security due to its smaller key size. Numerous RFID authentication schemes based on ECC have been suggested in literature, however, the majority has various serious security weaknesses. To bridge those existing security weaknesses, an enhanced ECC based light weight protocol for RFID systems has been proposed in this article. An extensive security analysis has been performed to demonstrate various secure features offered by our proposed protocol, and formal security analysis is being conducted using Automated Validation of Internet Security Protocols and Applications tool. The performance of our proposed RFID protocol has been compared with various existing RFID based security solutions on the basis of parameters, that is, computational cost, communication cost, and storage requirement. Simulation results indicate that the proposed lightweight protocol is more secure and performance efficient than the existing RFID protocols, and is well suited for practical applications.

Wireless Sensor Networks (WSNs) are used in many applications in military, environmental, and health-related areas. These applications often include the monitoring of sensitive information such as enemy movement on the battlefield or the location of personnel in a building. Security is important in WSNs. However, WSNs suffer from many constraints, including low computation capability, small memory, limited energy resources, susceptibility to physical capture, and the use of insecure wireless communication channels. These constraints make security in WSNs a challenge. In this paper, we try to explore security issue in WSN. First, the constraints, security requirements and attacks with their corresponding countermeasures in WSNs are explained. Individual sensor nodes are subject to compromised security. An adversary can inject false reports into the networks via compromised nodes. Furthermore, an adversary can create a Gray hole by compromised nodes. If these two kinds of attacks occur simultaneously in a network, some of the existing methods fail to defend against those attacks. The Ad-hoc On Demand Distance (AODV) Vector scheme for detecting Gray-Hole attack and Statistical En-Route Filtering is used for detecting false report. For increasing security level, the Elliptic Curve Cryptography (ECC) algorithm is used. Simulations results obtain so far reduces energy consumption and also provide greater network security to some extent.

The Wireless Sensor Networks (WSNs) are characterized by their widespread deployment due to low cost, but the WSNs are vulnerable to various types of attacks. To defend against the attacks, an effective security solution is required. However, the limits of these networks’ battery-based energy to the sensor are the most critical impediments to selecting cryptographic techniques. Consequently, finding a suitable algorithm that achieves the least energy consumption in data encryption and decryption and providing a highly protected system for data remains the fundamental problem. In this research, the main objective is to obtain data security during transmission by proposing a robust and low-power encryption algorithm, in addition, to examining security algorithms such as ECC and MD5 based on previous studies. In this research, the Energy Saving and Securing Data algorithm (ESSD) algorithm is introduced, which provides the Message Digest 5 (MD5) computation simplicity by modifying the Elliptic Curve Cryptography (ECC) under the primary condition of power consumption. These three algorithms, ECC, MD5, and ESSD, are applied to Low Energy Adaptive Clustering Hierarchy (LEACH) and Threshold-sensitive Energy Efficient Sensor Network Protocol (TEEN) hierarchical routing algorithms which are considered the most widely used in WSNs. The results of security methods under the LEACH protocol show that all nodes are dead at 456, 496, and 496, respectively, to ECC, MD5, and ESSD. The results of security methods under the TEEN protocol show that the test ends at 3743, 4815, and 4889, respectively, to ECC, MD5, and ESSD. Based on these results, the ESSD outperforms better in terms of increased security and less power consumption. In addition, it is advantageous when applied to TEEN protocol.

Wireless Sensor Network (WSN) is a spatially distributed network. It contains many numbers of distributed, self-directed, small, battery powered devices called sensor nodes or motes. In recent years the deployment of WSN in various application domains are growing in a rapid pace as with the upcoming boom of Internet of Things (IoT) and Internet of Everything (IoE). However, the effectiveness of the WSN deployment is restricted due to the constrained computation and power source. Hence, many researchers have been proposing new approaches and models to improve the efficiency of the domain specific WSN deployment procedures. Though, many research communities addressing various issues in WSN deployment, still the privacy and security of such networks are susceptible to various network attacks. Thus, it is necessary to practice different models for authentication and privacy preservation in a highly dynamic resource constrained WSN environment to realize the effectiveness and efficiency of the deployment. Hence, this paper addressing an authentication scheme that can reduce energy consumption without compromising on security and privacy. In order to provide a light weight authentication mechanism, this paper proposing an authentication mechanism for WSN deployment by combining the features of Elliptic Curve Cryptography (ECC) and Hexagonal numbers. The feature of ECC is used to reduce the key size and the effectiveness of generating hexagonal numbers is used for minimizing the energy consumption in a resource constrained WSN environment. The results of the proposed approach are evaluated with the different authentication models and the results were indicating that the proposed approach can perform better than the other approaches.

This paper discusses parallelization of elliptic curve cryptography hardware accelerators using elliptic curves over binary fields F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m</sub> . Elliptic curve point multiplication, which is the operation used in every elliptic curve cryptosystem, is hierarchical in nature, and parallelism can be utilized in different hierarchy levels as shown in many publications. However, a comprehensive analysis on the effects of parallelization has not been previously presented. This paper provides tools for evaluating the use of parallelism and shows where it should be used in order to maximize efficiency. Special attention is given for a family of curves called Koblitz curves because they offer very efficient point multiplication. A new method where the latency of point multiplication is reduced with parallel field arithmetic processors is introduced. It is shown to outperform the previously presented multiple field multiplier techniques in the cases of Koblitz curves and generic curves with fixed base points. A highly efficient general elliptic curve cryptography processor architecture is presented and analyzed. Based on this architecture and analysis on the effects of parallelization, a few designs are implemented on an Altera Stratix II field-programmable gate array (FPGA).

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987(Koblitz, ) in 1985. .At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique.As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely.Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem.The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group.The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem.The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = g x , where given the l and g, it is infeasible to compute the x.Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG.Given the point P and the point G, then it is very hard to find the integer n.To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve.Computation to find the number of points on a curve, has given rise to several point counting algorithms.The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter.This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed.Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples.Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm.Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms.Section 7 gives some brief literature on these two point counting algorithms.Finally, section 8 is the concluding remarks for this chapter. Elliptic curvesElliptic curves obtained their name from their relation to elliptic integrals that arise from the computation of the arc length of ellipses (Lawrence & Wade, 2006).Elliptic curves are www.intechopen.com Cryptography and Security in Computing1 1 2 3 4 2 2 4 Fig. 1.1. 2(1 ) (1 ) yx x x   www.intechopen.com