Fully Homomorphic Encryption: Secret Key Homomorphic Encryption Over Integers

by madrafion 4/27/2018, 2:53:46 PM with 9 comments
  • by pieguyon 4/27/2018, 4:10:57 PM

       (c(mod p)) (mod 2) = (p * q + 2 * r + m (mod p)) (mod 2) = 2r + m (mod 2) = m
    This breaks if 2*r > 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 "from a different interval than the private key one". This should be made more clear.

  • by 8bitsruleon 4/27/2018, 7:19:37 PM

    Top of article mentions 'In the previous post...' (which is an intro to homomorphic encryption)

    That post is here: https://radicalrafi.github.io/posts/homomorphic-encryption/

  • by admax88qon 4/27/2018, 4:41:22 PM

    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 "cloud."

  • by archi42on 4/27/2018, 9:29:23 PM

    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 :(

    (And yeah, HE "noise" is a pain)

  • by ddtayloron 5/6/2018, 10:21:08 AM

    > c is odd if m = 1 c is even if m = 0 ( Yes 0 is even ).

    If c is the ciphertext than can't someone simply mod 2 and "decrypt" it?

  • by zebra9978on 4/27/2018, 5:36:49 PM

    is this the same technology that Numerai uses... or is it multi party computation (https://mortendahl.github.io/2017/04/17/private-deep-learnin...) ?

  • by olliejon 4/27/2018, 4:45:44 PM

    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?

  • by gesmanon 4/27/2018, 6:48:42 PM

    The best way to encrypt any data is to make adversary think the data does not exist.

    For everything else rubber hose cryptanalysis will work.