

Fully Homomorphic Encryption over the Integers - sweis
http://eprint.iacr.org/2009/616

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sweis
Paper by van Dijk, Gentry, Halevi, and Vaikuntanathan.

Abstract: "We construct a simple fully homomorphic encryption scheme, using
only elementary modular arithmetic. We use Gentry's technique to construct
fully homomorphic scheme from a "bootstrappable" somewhat homomorphic scheme.
However, instead of using ideal lattices over a polynomial ring, our
bootstrappable encryption scheme merely uses addition and multiplication over
the integers. The main appeal of our scheme is the conceptual simplicity.

We reduce the security of our scheme to finding an approximate integer gcd --
i.e., given a list of integers that are near-multiples of a hidden integer,
output that hidden integer. We investigate the hardness of this task, building
on earlier work of Howgrave-Graham."

