Add Additive/Multiplicative Depth Tracking

[iamtrask]

Add Additive/Multiplicative Depth Tracking

[mortendahl]

for noise estimation, some inspiration might be found in the SEAL library and its documentation (section 6), which comes with an estimator for the FV scheme

[dipanshunagar]

If it helps, I found that Paillier fails to decrypt to accurate numbers after multiplication at a depth of 20, for all tensor shapes and sizes that I tried.

Here's what I did(this one for a simple tensor):

from syft.he.paillier import KeyPair, PaillierTensor
from syft import TensorBase
import numpy as np

pubkey, privkey = KeyPair().generate()

arr1 = np.ones(3, dtype=float)

a = PaillierTensor(pubkey, arr1)
b = TensorBase(arr1)
c = a * b
for i in range(25):
    c = b * c
    if c.decrypt(privkey).data.all() == arr1.all():
        print(i, '_mul_depth =', c._mul_depth, '    decryption functional:', c.decrypt(privkey))
    else:
        print(i, ' _mul_depth =', c._mul_depth, '    decryption failed:', c.decrypt(privkey))
        break

But addition goes on for way longer...