Elliptic Curve Cryptography

In early 2016, Tobias wrote a paper on elliptic curve cryptography. This paper has now been published as an e-book by GRIN Verlag. The e-book is available for tablets, smartphones, Kindles, and many other devices. It can be purchased at http://www.grin.com/de/e-book/337700/elliptische-kurven-kryptographie among others. Elliptic curves are a subfield of cryptography and have a high significance in IT security.

What exactly is the paper about?

Elliptic curves in cryptography are an example of the high usefulness of pure mathematics. Elliptic curves have been researched for a long time. For 30 years, elliptic curves have been applied in cryptographic systems. The methods are secure as long as discrete logarithms in the group of points of the elliptic curve cannot be efficiently computed. Methods based on the discrete logarithm in finite fields can be transferred to elliptic curves with points. These include the Diffie-Hellman key exchange, the Digital Signature Algorithm, and the Elgamal encryption scheme. Companies like the NSA develop, standardize, and use these encryptions for their Top-Secret data. The method is also used in many countries in the EU for various purposes. Most people have already come into contact with this type of cryptography in some form, even if most don’t know it. Some other well-known applications in 2016 are:

• Signing PlayStation 3 games
• Access protection of chips in European passports
• Access to the chip of the German identity card
• Key exchange in WhatsApp (Curve25519)

The goal of the paper is to explain the basics of Elliptic Curve Cryptography.