A new algorithm for signed binary representation and application in mobile phones

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.

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.

Elliptic Curve Cryptography (ECC) is a promising public key cryptography, probably takes the place of RSA. Not only ECC uses less memory, key pair generation and signing are considerably faster, but also ECC's key size is less than that of RSA while it achieves the same level of security. However, the magic behind RSA and its friends can be easily explained, is also widely understood, the foundations of ECC are still a mystery to most of us. This paper's aims are to provide detailed mathematical foundations of ECC, especially, the subgroup and its generator (also called base point) formed by one elliptic curve are researched as highlights, because they are very important for practical ECC implementation. The related algorithms and their implementation details are demonstrated, which is useful for the computing devices with restricted resource, such as embedded systems, mobile devices and IoT devices.

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.

An entire chapter is dedicated to elliptic curves since there is great hope that advances in this area will bring higher levels of security to many embedded devices. Compared to previous public key systems, elliptic curve cryptography (ECC) promises equivalent security strength with smaller key sizes. Since key size impacts storage and in general has been shown to impact performance and thus energy dissipation, these elliptic curves are of great interest to embedded systems. The notion of using elliptic curves in cryptography is generally agreed to have emerged from two famous papers: those of Miller (1986) and Koblitz (1987).

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.

Rivest, Shamir, and Adleman (RSA) is one of the most important types of asymmetric cryptography. In RSA, the key size is larger compared to algorithms in cryptography. In this concept, keys are generated with any two prime numbers. An unauthorized person can easily obtain the keys using a Greatest Common Delvisor (GCD) attack. This is one of the main disadvantages of RSA cryptography. Elliptic Curve Cryptography (ECC) is also an asymmetric cryptography with a small key size. The proposed work aims to overcome the disadvantage of GCD attack in RSA. An RSA private and public key can be combined with an ECC private and public key using Exclusive OR(XOR) to generate a new hybrid private and public key. RSA encryption can be done using a new hybrid public key. RSA decryption can be done using a new hybrid private key. The advantage of the proposed work is to create three key levels for cryptography to prevent GCD attack in RSA. The key strength is higher compared to simple RSA key generation.

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.

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.

The data everywhere was being transferred for each second using domain of Internet of Things (IoT). To secure data using the Internet of Things (IoT) is a tedious task. When the data is being transferred using Internet of Things (IoT), more security can be provided using elliptic curve cryptography. Asymmetric cryptography is used by most of the applications for providing secure communication between two parties (Weber in Comput Law Secur Rev 26:23–30, 2010). The purpose of this type of cryptography is the requirement of huge amount of computation and storage. This is where the use of elliptic curve cryptography comes into picture, as it needs less storage and can be used in small computational devices. ECC needs smaller key sizes and provides stronger encryption compared to various asymmetric cryptographic algorithms like RSA. The usage of power required is low but the performance of the devices using ECC is high for different types of devices like IoT, sensors, etc. This paper shows how ECC must be implemented strongly for providing communication securely to encode the data on an elliptic curve, in IoT devices. The encryption of the data must be done securely while mapping the data on to the elliptic curve. This paper shows how the data is encrypted and mapped on to the curve securely. The work shows how the data can be encrypted with ECC and how it can be visible to only authorized users. In the field of cryptography, ECC is a method for asymmetric cryptography which is dependent on the algebraic structure of an elliptic curve on the finite field.

Elliptic Curve Cryptography (ECC) is studied to be very powerful and secured asymmetric technique which uses small key sizes and efficiently uses power and bandwidth. Wired and wireless sensor networks are prone to attacks like node capture, physical tampering, eavesdropping, denial of service, etc. ECC curves being resistant to these kinds of attacks, are used for secured data transmission. ECC uses Koblitz’s curve mapping methodology for encoding and decoding of user’s information over public environment and thus is efficient for secured computations. Koblitz curves are also used for secured exchange and ownership of cryptocurrency which is very popular nowadays. The research paper aims to discuss and implement Koblitz mapping technique on a given ECC curve and it is also proved to be secured to encode and decode the textual information during data transfer. The method, if used with parallel multipliers, does faster computations than other curves and saves time and space.

Elliptic curve cryptography (ECC) is widely used for secure communications, because it can provide the same level of security as RSA with a much smaller key size. In constrained environments, it is important to consider efficiency, in terms of execution time and hardware costs. Modular inversion is a key time-consuming calculation used in ECC. Its hardware implementation requires extensive hardware resources, such as lookup tables and registers. We investigate the state-of-the-art modular inversion algorithms, and evaluate the performance and cost of the algorithms and their hardware implementations. We then propose a high-radix modular inversion algorithm aimed at reducing the execution time and hardware costs. We present a detailed radix-8 hardware implementation based on 256-bit primes in Verilog HDL and compare its cost performance to other implementations. Our implementation on the Altera Cyclone V FPGA chip used 1227 ALMs (adaptive logic modules) and 1037 registers. The modular inversion calculation took 3.67 ms. The AT (area–time) factor was 8.30, outperforming the other implementations. We also present an implementation of ECC using the proposed radix-8 modular inversion algorithm. The implementation results also showed that our modular inversion algorithm was more efficient in area–time than the other algorithms.

Elliptic curve cryptography (ECC) can ensure an equivalent security with much smaller key sizes. Elliptic curve scalar multiplication (ECSM) is a fundamental computation used in ECC. This paper focuses on ECSM resisting simple power attack and safe error attack of side-channel attack specifically. Elliptic curve complete addition (CA) formulae can achieve secure ECSM algorithms but are inefficient from memory and computational cost perspectives. Another secure ECSM, which uses (extended) affine, is more efficient for both memory and computational costs. However, it scans input scalars from right to left. In this paper, our developed scalar multiplication algorithms also use their extended affine, but scan from left to right (LR). We also prove the security of our LR ECSM algorithms and analyze them both theoretically and experimentally. Our new LR ECSM algorithms can reduce the amount of memory by \(37.5\%\) and reduce the computational time by more than \(40\%\) compared to Joye’s regular 2-ary LR algorithm with CA formulae.

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