inst/doc/BFV-multiply.R

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

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

## ----libraries----------------------------------------------------------------
library(polynom)
library(HomomorphicEncryption)

## ----params-------------------------------------------------------------------
d  =      4
n  =      2^d
p  =     (n/2)-1
q  = 424242
pm = GenPolyMod(n)

## -----------------------------------------------------------------------------
set.seed(123)

## -----------------------------------------------------------------------------
# generate a secret key
s = GenSecretKey(n)

# generate a
a = GenA(n, q)

# generate the error
e = GenError(n)

## -----------------------------------------------------------------------------
# generate the public key
pk0 = GenPubKey0(a, s, e, pm, q)
pk1 = GenPubKey1(a)

## -----------------------------------------------------------------------------
# polynomials for encryption
e1 = GenError(n)
e2 = GenError(n)
u  = GenU(n)

## -----------------------------------------------------------------------------
m1 = polynomial(c(3, 2, 2))
m2 = polynomial(c(0, 2   ))

## -----------------------------------------------------------------------------
m1_ct0 = EncryptPoly0(m1, pk0, u, e1, p, pm, q)
m1_ct1 = EncryptPoly1(    pk1, u, e2,    pm, q)
m2_ct0 = EncryptPoly0(m2, pk0, u, e1, p, pm, q)
m2_ct1 = EncryptPoly1(    pk1, u, e2,    pm, q)

## -----------------------------------------------------------------------------
multi_ct0 = m1_ct0 * m2_ct0 * (p/q)
multi_ct0 = multi_ct0 %% pm
multi_ct0 = CoefMod(multi_ct0, q)
multi_ct0 = round(multi_ct0)

multi_ct1 = (m1_ct0 * m2_ct1 + m1_ct1 * m2_ct0) * (p/q)
multi_ct1 = multi_ct1 %% pm
multi_ct1 = CoefMod(multi_ct1, q)
multi_ct1 = round(multi_ct1)

multi_ct2 = (m1_ct1 * m2_ct1) * (p/q)
multi_ct2 = multi_ct2 %% pm
multi_ct2 = CoefMod(multi_ct2, q)
multi_ct2 = round(multi_ct2)

## -----------------------------------------------------------------------------
decrypt = (multi_ct2 * s^2) + (multi_ct1 * s) + multi_ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)

# rescale
decrypt = decrypt * p/q

# round then mod p
decrypt = CoefMod(round(decrypt), p)
print(decrypt)