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 HowgraveGraham.

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This paper describes a technique that exploits the statistical delay variations of wires and transistors across ICs to build a secret key unique to each IC. To explore its feasibility, we fabricated a candidate circuit to generate a response based on its delay characteristics. We show that there exists enough delay variation across ICs implementing the proposed circuit to identify individual ICs. Further, the circuit functions reliably over a practical range of environmental variation such as temperature and voltage.

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A Physical Random Function (PUF) is a random func-