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Doubly-Efficient Private Information Retrival

A prototype implementation of Lin-Mook-Wichs doubly-efficient private information retrieval in sage

I believe with some optimizations the recent doubly-efficient private information retrieval by Lin, Mook, and Wichs [https://eprint.iacr.org/2022/1703] can be made practically efficent. I'm prototyping the optimizations here.

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depir's Issues

Allow preprocessing

Currently all polynomials are evaluated on the fly. Finally we want to have such that this evaluation is preprocessed and can just be looked up

Find good parameters

Currently everything happens over small toy number. Set the parameters s.t. the RLWE is secure

Extend to Z_q where q not prime

Currently everything happens over Z_p where p is prime with some constraint. Allow it to happen over Z_q where q is a product of many p_i where p_i fulfills the same constraints as currently p does.

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