CKKS encode 3

In HomomorphicEncryption: BFV, BGV, CKKS Schema for Fully Homomorphic Encryption

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Load libraries that will be used.

library(polynom)
library(HomomorphicEncryption)

Set a working seed for random numbers (so that random numbers can be replicated exactly).

set.seed(123)

Set some parameters.

M     <- 8
N     <- M / 2
scale <- 4
xi    <- complex(real = cos(2 * pi / M), imaginary = sin(2 * pi / M))

Create the (complex) numbers we will encode.

z <- c(complex(real=3, imaginary=4), complex(real=2, imaginary=-1))
print(z)

Now we encode the vector of complex numbers to a polynomial.

pi_z                <- pi_inverse(z)
scaled_pi_z         <- scale * pi_z
rounded_scale_pi_zi <- sigma_R_discretization(xi, M, scaled_pi_z)
p                   <- sigma_inverse(xi, M, rounded_scale_pi_zi)
coef                <- as.vector(round(Re(p)))
p                   <- polynomial(coef)

Let's view the result.

print(p)

Let's decode to obtain the original number:

rescaled_p <- coef(p) / scale
z          <- sigma_function(xi, M, rescaled_p)
decoded_z  <-pi_function(M, z)

print(decoded_z)

The decoded z is indeed very close to the original z, we round the result to make the clearer.

round(decoded_z)

Next, work through the CKKS-encode-2 vignette, which breaks down the encode and decode functions into the individual steps.

HomomorphicEncryption documentation built on May 29, 2024, 9:59 a.m.