3.3 WHAT IS ELLIPTIC CURVE CRYPTOGRAPHY?
Elliptical curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller, and more efficient cryptographic keys. ECC generates keys through the properties of the elliptic curve equation instead of the traditional method of generation as the product of very large prime numbers. The technology can be used in conjunction with most public key encryption methods, such as RSA, and Diffie- Hellman. According to some researchers, ECC can yield a level of security with a 164-bit key that other systems require a 1,024-bit key to achieve. Because ECC helps to establish equivalent security with lower computing power and battery resource usage, it is becoming widely used for mobile applications. ECC was developed by Certicom, a mobile e-business security provider, and was recently licensed by Hifn, a manufacturer of integrated circuitry (IC) and network security products. RSA has been developing its own version of ECC. Many manufacturers, including 3COM, Cylink, Motorola, Pitney Bowes, Siemens, TRW, and VeriFone have included support for ECC in their products.
3.4 HISTORY OF ELLIPTIC CURVE CRYPTOGRAPHY
Elliptic Curve Cryptography (ECC) was discovered in 1985 by Victor Miller (IBM) and Neil Koblitz (University of Washington) as an alternative mechanism for implementing public-key cryptography. Public-key algorithms create a mechanism for sharing keys among large numbers of participants or entities in a complex information system. Unlike other popular algorithms such as RSA, ECC is based on discrete logarithms that is much more difficult to challenge at equivalent key lengths. They implemented existing public key algorithms like Diffie-Hellman using elliptic curve. Since then, a lot of scholars have researched into this area from different perspectives and for different applications. For instance, Chen et al. Designed and implemented fast algorithms using elliptic curve cryptography over the field GF(p) in relation with modular addition, subtraction, point addition, point production and choice of embedding plaintext to a point. Recently, Hedabou et al. proposed a security scheme to avoid side channel at-tacks using ECC by combining an optimized use of space memory with high level of security and efficiency. Shi and Yan studied and identified the problems in the software implementation of ECC and explored techniques that can accelerate the software implementation, however, their work was based on ECC in GF(2m). In addition, Vijayalakshmi and Palanivelu used elliptic curve cryptography to investigate secure localization in wireless sensor networks. The challenges imposed on wireless sensor networks with regards to communication between authenticated neighbor’s and their precise locations in a secure manner were identified; and furthermore, the problem of insecurity in sensor networks was addressed. Vijayalakshmi and Palanivelu also showed that ECC satisfies all the constraints of the sensor networks- minimum bandwidth, power, energy and computational speed; and thus suitable for secure localization in sensor networks. Jena et al., proposed a novel protocol for smart card using ECDLP (Elliptic Curve Discrete Logarithm Problem) for securing entity authentication, data integrity and confidentiality. The secure channel protocol described by Jena et al. uses a combination of secure public key system and secret key to achieve the desired output. This proposed scheme however, was not implemented for payment system. Another related work to this paper, is the one of Vivek et al, which described ECC and compared its strength with that of RSA. In Vivek et al., a possible scheme for RSA encryption was presented and its performance was compared with that of ECC.
At the time of its discovery, the ECC algorithm was described and placed in the public domain. What others found was that while it offered greater potential security it was slow. Certicom focused its efforts on creating better implementations of the algorithm to improve its performance. After many years of research, Certicom introduced the first commercial toolkit to support ECC and make it practical for use in a variety of applications. Other cryptographers have also become interested in ECC. Today Certicom sponsors the Centre for Advanced is a consortium of leading providers of cryptography and information security solutions who have united to address the lack of interoperability between today's different cryptographic solutions. On February 16, 2005 the National Security Agency (NSA) presented its strategy and recommendations for securing U.S. Government sensitive and unclassified communications. The strategy included a recommended set of advanced cryptography algorithms known as Suite
Below, we define the nomenclature and then provide a general overview of security protocols based on elliptic curve cryptography.
