The Discrete Logarithm Problem on Supersingular Elliptic Curves

The elliptic curve discrete logarithm problem is an essential problem in cryptography. In general it is a very complex problem; the best known solving algorithms all have exponential running time. However, for supersingular elliptic curves there exists a sub-exponential solving algorithm called the MOV attack. The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing. The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus. This thesis deals with analyzing the MOV attack and generating examples to demonstrate its power.