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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.(John Mitchell)I 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.

Cryptographers have accumulated a long assortment of \killer" applications for fully homomorphic encryption since then. (See Section 1.8.) However, until now, we did not have a viable construction. 1.1 A Very Brief and Informal Overview of Our Construction Imagine you have an encryption scheme with a \noise parameter" attached to each ci-

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  Applications, Encryption, Homomorphic, Homomorphic encryption

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