Created
October 9, 2022 17:21
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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 | |
n = 4 | |
d = 2^n | |
t = 7 | |
q = 874 | |
# load library to create polynomials | |
library(polynom) | |
# create secret key | |
s = polynomial( coef=c(-1, 1, 1, 0, -1, 0, 1, 0, 1, -1, 0, -1, -1, -1, 0, 1 ) ) | |
# define a | |
a = polynomial( coef=c(84, -60, -282, 186, 322, -138, 70, 52, 107, -212, -369, 447, -229, -393, -256, 42) ) | |
# define the error | |
e = polynomial( coef=c(1, 4, 0, 4, -4, 3, -1, 0, 4, 1, -6, -6, 7, 1, 1, -3) ) | |
# create the public key | |
pk0 = -a*s + e | |
pk1 = a | |
# remove the error term | |
rm(e) | |
# create a message | |
m = polynomial( coef=c(3, 0, 0, 0, 0, 0, 0, 0, 4) ) | |
# polynimials for encryption | |
e1 = polynomial( coef=c(4, -6, 2, -3, -3, -4, 5, 4, 4, 1, 3, -4, -1, 3, -2, -5) ) | |
e2 = polynomial( coef=c(2, -2, -4, 1, -2, 2, -3, -4, 4, -1, 2, 5, -4, 0, 2, -7) ) | |
u = polynomial( coef=c(1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 1, 1, 1, 0) ) | |
# create cyphertext | |
ct0 = pk0*u +e1 +m*floor(q/t) %% q | |
ct1 = pk1*u +e2 %% q |
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