In this thesis we examine the Ball Collision algorithm for decoding generic linear codes presented by Bernstein et al. in 2010. This algorithm has been proven to be asymptotically faster than any previous attacks on the McEliece code-based cryptosystem. We first conduct a review of relevant coding theory concepts and information set decoding algorithms. We then present a description of the algorithm, discuss best practices for implementation, and look at its asymptotic computational complexity. Finally we test how the algorithm performs on Goppa codes and present statistics gathered over a large number of trials. We find that Ball Collision decoding is faster than the previous best attack (Stern’s Method) for a [1600,720] t = 80 Goppa code with large error pattern weights.
