Elliptic curve cryptography
Cryptography is the science of information security. It involves scrambling ordinary text into cipher-text in a process called encryption, and then back again, the process of decryption. This ability to securely store and transfer information is met using mathematical systems, or cryptosystems. Elliptic curves are simple functions that can be drawn as gently looping lines in the (x,y) plane. However, cryptosystems using elliptic curves are largely unused due to the complex mathematics involved. To overcome this limitation and exploit the advantages available, cryptographic procedures based on elliptic curves have been developed in the ELIAS project. Elliptic curve cryptography, or ECC, is based on algorithms that are defined on sets of points of elliptic curves. The elliptic curves are used to encrypt information, to create digital signals and to exchange keys. Thus the software developed in the project includes algorithm-primitives, digital signatures, and key exchange schemes. It also includes an elliptic curve generator. Implementation is done almost entirely in JAVA to allow the software to run on most platforms. The project is in two parts. The first part of the project involves the standardization of the procedures used against the ISO standard 15946, and the development of the relevant documentation in a format that is easy to read and easily understood by the developer. The second part of the project addresses the curve generating software. This provides fast generation of qualified elliptic curves. Different strengths of curve can be produced as needed. This software is freely available and the information is displayed on the internet. Further research and developments are being sought.
