Achieving fully-homomorphic encryption, under any kind of reasonable computational assumptions (and under any reasonable definition of “reasonable”) was a holy grail of cryptography for over 30 years. In 2009, Craig Gentry [Gen09a, Gen09b, Gen10] proposed the first fully-homomorphic encryption scheme that is secure under a reasonable assumption. Craig Gentry and Shai Halevi have already implemented the scheme, and are working on optimizations [GH10]. In the next two lectures, we will describe a somewhat simplified variant of Gentry’s construction
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