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Title:
Fully Homomorphic Encryption over the Integers
Authors: Marten van Dijk, Craig Gentry, Shai Halevi, Vinod Vaikuntanathan
Abstract:We describe a very simple ``somewhat homomorphic’’ encryption scheme using only elementary modular arithmetic, and use Gentry’s techniques to convert it into a fully homomorphic scheme. Compared to Gentry’s construction, our somewhat homomorphic scheme merely uses addition and multiplication over the integers rather than working with ideal lattices over a polynomial ring. The main appeal of our approach is the conceptual simplicity. We reduce the security of our somewhat homomorphic 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.
ePrint: https://eprint.iacr.org/2009/616
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