ii DEDICATION This endeavor, and indeed my entire existence, is dedicated to my daughter: my best and most beloved work. You are the reason for everything and the center of my Universe, and

ii iii DEDICATION I dedicate this thesis to my father and my mother in recognition of their endless help; support and encouragement also dedicate this work to my beloved wife, I will not forget my brothers and sisters.

We present an algorithm for implementing a secure oblivious RAM where the access pattern is perfectly hidden in the information theoretic sense, without assuming that the CPU has access to a random oracle. In addition we prove a lover bound on the amount of randomness needed for information theoretically secure oblivious RAM.

We give the rst example of systolic freedom over torsion coefcients. The phenomenon is a bit unexpected (contrary to a conjecture of Gromov’s) and more delicate than systolic freedom over the integers. Dedicated to Rob Kirby, a lover of Mathematics and other wild places. Thank you for your inspiration. AMS Classi cation 53C22