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A FULLY HOMOMORPHIC ENCRYPTION SCHEME A …

A FULLY HOMOMORPHIC ENCRYPTION SCHEMEA DISSERTATIONSUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCEAND THE COMMITTEE ON GRADUATE STUDIESOF STANFORD UNIVERSITYIN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OFDOCTOR OF PHILOSOPHYC raig GentrySeptember 2009c Copyright by Craig Gentry 2009 All Rights ReservediiI certify that I have read this dissertation and that, in my opinion, it is fullyadequate in scope and quality as a dissertation for the degree of Doctor ofPhilosophy.(Dan Boneh) Principal AdviserI certify that I have read this dissertation and that, in my opinion, it is fullyadequate in scope and quality as a dissertation for the degree of Doctor ofPhilosophy.

1 Introduction 1 1.1 A Very Brief and Informal Overview of Our Construction . . . . . . . . . . 2 ... Regev’s Quantum Reduction . . 141 ... We obviously want the server’s response here to be more concise than the trivial 1. CHAPTER 1. INTRODUCTION 2

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