Fully Homomorphic Encryption: Secret Key Homomorphic Encryption Over Integers

<p><pre><code> (c(mod p)) (mod 2) = (p * q + 2 * r + m (mod p)) (mod 2) = 2r + m (mod 2) = m </code></pre> This breaks if 2*r &gt; p. Even if you choose r to be small during encryption, the r values accumulate with each homomorphic operation and will eventually be too big. The only restriction stated is that r is &quot;from a different interval than the private key one&quot;. This should be made more clear.

Top of article mentions &#x27;In the previous post...&#x27; (which is an intro to homomorphic encryption)<p>That post is <i>here</i>: <a href="https:&#x2F;&#x2F;radicalrafi.github.io&#x2F;posts&#x2F;homomorphic-encryption&#x2F;" rel="nofollow">https:&#x2F;&#x2F;radicalrafi.github.io&#x2F;posts&#x2F;homomorphic-encryption&#x2F;</a>

Homomorphic encryption is interesting from a mathematics perspective, but in practical terms it seems like an awful lot of effort being invested to move even more computing off of your own devices and onto the &quot;cloud.&quot;

I used HE in my informatics b.sc. thesis to do privacy preserving surveillance: Store data on multiple servers and need server majority to reconstruct (non-HE), perform face recognition on encrypted data and then use (S?)HE to query a database if that face is in it - of course without the db learning about the content of the face data. So, turns out just throwing some math on the problem works (I just applied some previous work; you know what they say about the shoulders of giants) and gives you the advantages of surveillance with less potential for abuse - but the necessary computational power is absurd :(<p>(And yeah, HE &quot;noise&quot; is a pain)

&gt; c is odd if m = 1 c is even if m = 0 ( Yes 0 is even ).<p>If c is the ciphertext than can&#x27;t someone simply mod 2 and &quot;decrypt&quot; it?

is this the same technology that Numerai uses... or is it multi party computation (<a href="https:&#x2F;&#x2F;mortendahl.github.io&#x2F;2017&#x2F;04&#x2F;17&#x2F;private-deep-learning-with-mpc&#x2F;" rel="nofollow">https:&#x2F;&#x2F;mortendahl.github.io&#x2F;2017&#x2F;04&#x2F;17&#x2F;private-deep-learnin...</a>) ?

I am unclear on this - it looks like it operates 1 but at a time, so if I have a sequence of encrypted bits I can do freq analysis. Clearly that is not the case, so what bone headed misunderstanding am I making?

The best way to encrypt any data is to make adversary think the data does not exist.<p>For everything else rubber hose cryptanalysis will work.