University of Birmingham Hardware assisted fully homomorphic function evaluation and encrypted search

In this paper we propose a scheme to perform homomorphic evaluations of arbitrary depth with the assistance of a special module <italic>recryption box</italic>. Existing somewhat homomorphic encryption schemes can only perform homomorphic operations until the noise in the ciphertexts reaches a critical bound depending on the parameters of the homomorphic encryption scheme. The classical approach of bootstrapping also allows for arbitrary depth evaluations, but has a detrimental impact on the size of the parameters, making the whole setup inefficient. We describe two different instantiations of our recryption box for assisting homomorphic evaluations of arbitrary depth. The recryption box refreshes the ciphertexts by lowering the inherent noise and can be used with any instantiation of the parameters, i.e. there is no minimum size unlike bootstrapping. To demonstrate the practicality of the proposal, we design the recryption box on a Xilinx Virtex 6 FPGA board ML605 to support the FV somewhat homomorphic encryption scheme. The recryption box requires 0.43 ms to refresh one ciphertext. Further, we use this recryption box to boost the performance of encrypted search operation. On a 40 core Intel server, we can perform encrypted search in a table of <inline-formula><tex-math notation="LaTeX">$2^{16}$</tex-math><alternatives> <inline-graphic xlink:href="sinharoy-ieq1-2686385.gif"/></alternatives></inline-formula> entries in around 20 seconds. This is roughly 20 times faster than the implementation without recryption box.