HE-BFV.R

# 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