Abstract

In the early 90's, pairings were used to attack elliptic curve cryptosystems. But in recent years, they have been used to design cryptographic protocols for such tasks as identity-based encryption and group signature. Suitable pairings can be constructed from the Weil and Tate pairings for specially chosen elliptic curves.We will give an introduction to public-key cryptography, and describe the applications of pairings in cryptography. We will also explain how suitable elliptic curves can be selected, and how the Tate pairing can be efficiently computed.
Prerequisites: Familiarity with finite fields, elliptic curves, and public-key cryptography, for example as covered in Chapters 1, 2 and 6  of Neal Koblitz's book "A Course in Number Theory and Cryptography" will be helpful.