I'm interested in two following processes:

1) Perform deep learning on homomorphic encrypted data

2) Perform deep learning predictions with a homomorphic encrypted model on unencrypted data. By this I mean encrypting weights of a deep learning model, sending them to the owner of the data, and perform an encrypted prediction. The owner of the data will return back to me the encrypted prediction. See for instance this blog post for an example with logistic regression.

I'm wondering if it's possible to do deep learning (with many hidden layers) with PHE (partially homomorphic encryption, e.g. Paillier) or if I need a FHE (fully homomorphic encryption).

References are welcome!

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    $\begingroup$ You might be able to do very simple things (e.g. linear regression) from Paillier and the like, but for deep learning, I can think of only two alternatives: SHE/FHE, or MPC (with interactions). $\endgroup$ – Geoffroy Couteau Feb 13 '18 at 11:33

There are very few (somewhat practical) results about homomorphic deep learning currently. As a good starting point, you might want to have a look at this recent paper from my former colleagues, and references therein. It focuses on optimizing lattice-based somewhat homomorphic encryption schemes, for evaluating deep neural networks.

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  • $\begingroup$ After re-thinking about it, and facing contrary evidence, I have retracted my answer. $\endgroup$ – fgrieu Sep 10 '19 at 12:28

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