This thesis studies automated methods for analyzing hardness assumptions in generic group models, following ideas of symbolic cryptography. We define a broad class of generic and symbolic group models for different settings-symmetric or asymmetric (leveled) k-linear groups-and prove ''computational soundness'' theorems for the symbolic models. Based on this… (More)
Acknowledgements First I must thank Robin Pemantle, my advisor. I have greatly enjoyed working with him for the past five years. His advice and encouragement has been crucial to my development as a mathematician. He has given me wide latitude to pursue my own interests but at the same time steered me towards problems that other people might actually care… (More)
In 2010, Lionel Levine introduced a cooperative game, and posed the question of finding the optimal strategy. We provide an overview of prior work on this question, and describe several strategies that give the best lower bound on the probability of victory. We further generalize the problem to consider the case of arbitrary color distribution.