Elliptic Curves and Their Applications to Cryptography

With the advent of public key cryptography in the 1970s, the role of mathematics in real-world applications entered a new and exciting phase. Indeed, many well-established mathematical problems were thrust into the limelight with many computational problems taking on an added significance. Essentially, at the heart of a public key scheme is a pair of public/private keys such that we can be reasonably assured that the private key (kept hidden from all but the originator) cannot be computed from the public key (accessible to all) using the available resources.