Elliptic Curve Cryptography and Smart Cards

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems (for example, a 160 bit ECC has roughly the same security strength as 1024 bit RSA). In addition, ECC satisfies smart cards requirements in terms of memory, processing and cost. In this report, I will present a background on ECC including the basics and some ECC techniques. Then, I will talk about smart cards, their constraints and ECC implementation options.