## ----include = FALSE---------------------------------------------------------- knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ## ----setup-------------------------------------------------------------------- library(polynom) library(HomomorphicEncryption) ## ----seed--------------------------------------------------------------------- set.seed(123) ## ----params------------------------------------------------------------------- M <- 8 N <- M / 2 scale <- 200 xi <- complex(real = cos(2 * pi / M), imaginary = sin(2 * pi / M)) ## ----z------------------------------------------------------------------------ z <- c(complex(real=3, imaginary=4), complex(real=2, imaginary=-1)) print(z) ## ----encode------------------------------------------------------------------- pi_z <- pi_inverse(z) scaled_pi_z <- scale * pi_z rounded_scale_pi_zi <- sigma_R_discretization(xi, M, scaled_pi_z) m <- sigma_inverse(xi, M, rounded_scale_pi_zi) coef <- as.vector(round(Re(m))) m <- polynomial(coef) ## ----print-m------------------------------------------------------------------ print(m) ## ----params2------------------------------------------------------------------ n = 16 p = 7 q = 874 pm = polynomial( coef=c(1, rep(0, n-1), 1 ) ) ## ----seckey------------------------------------------------------------------- # generate a secret key s = polynomial( sample.int(3, n, replace=TRUE)-2 ) # generate a a = polynomial(sample.int(q, n, replace=TRUE)) # generate the error e = polynomial( coef=round(stats::rnorm(n, 0, n/3)) ) ## ----pubkey------------------------------------------------------------------- pk0 = CoefMod(-(a*s +e)%%pm,q) pk1 = a ## ----------------------------------------------------------------------------- # polynomials for encryption e1 = polynomial( coef=round(stats::rnorm(n, 0, n/3)) ) e2 = polynomial( coef=round(stats::rnorm(n, 0, n/3)) ) u = polynomial( coef=sample.int(3, (n-1), replace=TRUE)-2 ) ## ----------------------------------------------------------------------------- ct0 = CoefMod((pk0*u + e1 + m) %% pm, q) ct1 = CoefMod((pk1*u + e2 ) %% pm, q) ## ----------------------------------------------------------------------------- decrypt <- (ct1 * s) + ct0 decrypt <- decrypt %% pm decrypt <- CoefMod(decrypt, q) print(decrypt[1:length(coef(m))]) ## ----decode------------------------------------------------------------------- rescaled_p <- decrypt[1:length(m)] / scale z <- sigma_function(xi, M, rescaled_p) decoded_z <- pi_function(M, z) print(decoded_z) ## ----round-------------------------------------------------------------------- round(decoded_z)