Created
October 10, 2022 03:21
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# HE illustrated primer | |
# define some parameters (small as an example) | |
# N.B. these parameters are not secure, they are completely insecure | |
d = 4 | |
n = 2^d | |
t = (n/2)-1 | |
q = 874 | |
# load library to create polynomials | |
library(polynom) | |
# polymod | |
pm = polynomial( coef=c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ) ) | |
# create secret key | |
s = polynomial( coef=c(-1, -1, 0, 0, -1, 1, 0, 0, 0, 1, 0, -1, -1, 1, -1, 0 ) ) | |
# define a | |
a = polynomial( coef=c(136, 239, 313, 241, 615, 37, 233, 408, 570, 8, 356, 132, 558, 110, 706, 327) ) | |
# define the error | |
e = polynomial( coef=c(2, 7, -2, -2, 8, 1, 0, 3, 6, -2, -2, 6, 3, 4, -3) ) | |
# create the public key | |
pk0 = -(a*s + e) | |
pk0 = pk0 %% pm | |
# define helper function | |
library(HEtools) | |
pk0 = CoefMod(pk0, q) | |
pk1 = a | |
# remove the error term | |
rm(e) | |
# create a message | |
m = polynomial( coef=c(1, 1, 1) ) | |
# polynomials for encryption | |
e1 = polynomial( coef=c( 6, -1, 3, 3, 9, 0, 3, -3, -5, 0, -7, 1, -5, 0, 4, 1) ) | |
e2 = polynomial( coef=c(-5, -3, -1, -1, 1, -7, 2, 0, 2, 0, -2, 6, 0, 1, 0, 1) ) | |
u = polynomial( coef=c(1, -1, 1, -1, 1, 1, 0, 0, -1, 0, 1, 1, 0, 1) ) | |
# create ciphertext | |
ct0 = pk0*u +e1 + floor(q/t) * m | |
ct0 = ct0 %% pm | |
ct0 = CoefMod(ct0, q) | |
ct1 = (pk1*u +e2) %% pm | |
ct1 = CoefMod(ct1, q) | |
# decryption | |
decrypt = (ct1 * s) + ct0 | |
decrypt = decrypt %% pm | |
decrypt = CoefMod(decrypt, q) | |
# rescale | |
decrypt = decrypt * t/q | |
# round then mod t | |
decrypt = CoefMod(round(decrypt), t) |
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