# Paillier scheme : Encoding floats into integers impact on computations

In Privacy Preserving Processing Over Encrypted Images, I could understand that appropriate encoding of floats into integers (required in Paillier) only incur negligible error in computations.

Any other references supporting this ?

• Are you planning to $E( int(f_1)) * E(int(f_2))$ – kelalaka Feb 10 at 17:07
• Yes, multiplication between ciphertexts is used but probably only one time per inference round ... Other operations needed to run the neural network do not normally require multiplication between ciphertexts .. But maybe you can explain the difference between the case of many multiplications and only few ones ? – witdev Feb 10 at 17:20
• Actually, when you run the neural network over encrypted data, normally the operations that are the most performed will be multiplication between ciphertexts and plain-texts, or additions ... Well I submit it here because it's about paillier, its encoding process and the impact on computations ! I read in a [ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7860550&tag=1] that proper encoding only incur negligible error which may suggest negligible impact on accuracy in neural networks .. ?! – witdev Feb 10 at 17:28
• We are not interested in the errors of NN. Yes you can multiply a ciphertext and a plaintext by taking the power with Parlier. Instead of NN, you can use some example operations to exhibit your actual problem. – kelalaka Feb 10 at 17:32
• A better link to the article. The claim that the encoding of floats as mantissa+exponent has negligible cost seems credible to me. For large data sets, I'm more dubious on performance of the encryption and decryption itself, see this question; also on size expansion; and if the inputs of the neural network, and it's nature, would be hidden from the holder of the private key. – fgrieu Feb 11 at 7:10