# AI News, Encrypt your Machine Learning

- On Sunday, September 30, 2018
- By Read More

## Encrypt your Machine Learning

We have a pretty good understanding of the application of machine learning and cryptography as a security concept, but when it comes to combining the two, things become a bit nebulous and we enter fairly untraveled wilderness.

Let me explain this in a bit more detail with another quote: Let’s define out notation for message, ciphertext, encryption, and decryption: Assuming homomorphism, we then get: It might have been obvious to some of you, but it’s important here to mention another feature: Operations between clear texts and cipher texts are homomorphic as well: The operation of the structures was preserved, despite the value being encrypted.

more realistic example: If the RSA public key is mod r and exponent e, then the encryption of a message x is given by: The homomorphic property is then: When implementing a cryptographic algorithm, you have to consider various ways to attack the cipher.

Without semantic security, the algorithm is vulnerable to chosen-plaintext attacks: One way to protect against CPA is the introduction of a random component so that encrypting a message twice results in two different ciphers.

While we build algorithms to remove the random component in the decryption step, there is an upper limit of randomness after which we are unable to recover the message.

If you consider the amount of operations involved in training a model or inferring data with an encrypted model, we quickly end up unable to decrypt the noise-polluted cypertext.

Recrypt encrypts the ciphertext with the new private key (pk2) and then removes the first encryption (pk1) in the evaluation step using the encrypted secret key (sk).

Keeping in mind that all arithmetic is binary (i.e., modulo 2), such a function produces the following truth table: If you haven’t guessed already, this is a big deal.

Such a system was proposed in 2009 by Craig Gentry using lattice-based cryptography, and described the first plausible construction for a fully homomorphic encryption scheme.

Although the literature tends to be a bit vague or hard to compare, here are a couple of quotes in rough chronological order: 100 trillion?

Okay, this isn’t even feasible for a calculator… While IBM’s numbers are a significant improvement over the initial implementation, their solution is still at least 50 million times slower than working with plain text.

While the increased size of an encrypted model might not have a considerable impact, an industry who’s value is based on large amounts of data might struggle if their training data needs to be homomorphically encrypted.

- On Tuesday, January 22, 2019

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