Spatial Encryption a Dissertation Submitted to the Department of Computer Science and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Dan Boneh) Principal Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (DavidMazì eres) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. iii Dedication For the glory of God. iv Acknowledgements There are many people without whom this work would not have been possible. I would never have entered graduate school at Stanford, and having entered would never have finished, without the support of my family and friends. Beyond my family, I would especially like to thank the entering class of 2006 for their friendship throughout our five years here, and the Society for Freedom and Service to Humanity for being such a wonderful community. For the material itself, I owe many thanks to Adam Barth, who proposed some of the central problems addressed here; to Lewko and Brent Waters, upon whose work the solutions are built; and to the rest of the security and theory groups, who have listened and contributed to many iterations of those solutions. Of course, Dan Boneh deserves the greatest acknowledgement in this area: not only did he teach me cryptography and guide my study of it, he also worked directly on spatial encryption. Finally, the credit for this work belongs to the Lord Almighty. Beyond the " ordinary " miracles of creation and providence, His inspiration at key points in this work paved the path from a short, mediocre paper to a full thesis.