Homomorphicity over Integers

[SudharakaP]

Created methods to homomorhically add and multiply integers.

[matlink]

does that propagate the carry bit ? for example, summing 3+3 (11+11 in binary) is not the same as doing bitwise xor.

[SudharakaP]

Yes it does propagate the carry bit. That means enc(3)+enc(3) will give enc(6). Which when decrypted will give 6.

[matlink]

Okay. Do you know how the recryption is done? It's not very explicit in the paper, they say
Apply the decryption circuit to the expanded ciphertext z and the encrypted secret key bits σi. Then how can I apply the decryption circuit, since it has a modulo 2 operation and requires a lot of multiplication then?

[SudharakaP]

I am sorry, I don't know how recryption is done exactly. I am not actively involved this project anymore so its best to ask the original author (coron).

[matlink]

Shouldn't you encrypt the carrybit in the addEnc() function ? Well, it works for you because you are using the encrypt function of the Pk class, which is using the self.p secret key... But when using the PkRecrypt's encrypt_pk() function, there seems to be a mistake even if one encrypts the carrybit. I'm investigating on it.

[matlink]

I would like to implement faster multiplication like Karatsuba's algorithm (https://fr.wikipedia.org/wiki/Algorithme_de_Karatsuba), however in this algorithm you need to be able to substract integers. Could this approach be adapted for negative cipherintegers?