The Weil Pairing on Elliptic Curves and Its Cryptographic Applications
Alex Edward Aftuck · University of North Florida Digital Commons (University of North Florida) · 2011
This thesis presents the Weil pairing on elliptic curves as a tool to implement a tripartite Diffie-Helman key exchange. Elliptic curves are introduced, as well as the addition operation that creates a group structure on its points. In leading to the definition of the Weil pairing, divisors of rational functions are studied, as well as the Weierstrass }-function, which shows the complex lattice as isomorphic to elliptic curves. Several important qualities of the Weil pairing are proved, and Miller's algorithm for quick calculation is shown. Next, the bipartite Diffie-Helman key exchange is discussed over finite fields and elliptic curves. Finally an example of a modifed Weil pairing is defined, which leads to the tripartite Diffie-Helman key exchange.