Elliptic Curve Cryptography - Maple Application Center
Application Center Applications Elliptic Curve Cryptography

Elliptic Curve Cryptography

Author
: Pauline Hong
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!
In this report, we provide an elementary exposition of elliptic curve cryptography (ECC), which was invented around 1985 independently by Miller and Koblitz. Since then there has been extensive research on it and recently it is being used in commercial cryptosystems. In order to see where elliptic curves are used in cryptography, we begin by reviewing the abstract version of the ElGamal scheme, which can be used for arbitrary groups. Then we introduce groups based on elliptic curves. Additionally, we discuss how to encode and decode between text and points on an elliptic curve. Then we present an efficient method of performing iterated group operations. We briefly discuss how to choose the elliptic curves so that the resulting cryptosystem is secure. Finally we briefly describe the routines in the program written in Maple, that implements the algorithm.

Application Details

Publish Date: January 26, 2004
Created In: Maple 9
Language: English

More Like This

The Advanced Encryption Standard and its modes of operation
Frequency Analysis and the Kama Sutra Substitution Cipher
The SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions
RSA with maple
Secure Symmetric-Key Block Cipher Based on Generalized Finite Fields
Elliptic Curve Arithmetic over the Real Numbers
User-Friendly ElGamal Public-Key Encryption Scheme
A Symmetric-Key Block Cipher Generating Cryptograms Containing Characters Belonging to the Definite Set
Exploring the Modified IDEA Using the topicIDEA Package
Mersenne Primes-Based Symmetric-Key Masquerade Block Cipher
CBC Mode Fast AES Directory Encryption/Decryption