inst/doc/BFV-relinearization.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 and d need to be renamed throughout the package
n  =      2^d
p  =      11
q  =  p * 15000
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/10) # need to figure out how this division can be removed, by scaling q/p

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

## -----------------------------------------------------------------------------
ek0 = GenEvalKey0(a, s, e)
ek1 = 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) # the rounding should come before the mod (both of the mods)

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)

## -----------------------------------------------------------------------------
ct0hat = CoefMod(multi_ct0 + ek0 * multi_ct2 %% pm, q)
ct1hat = CoefMod(multi_ct1 + ek1 * multi_ct2 %% pm, q)

## -----------------------------------------------------------------------------
decrypt = ct0hat + ct1hat * s
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)

# rescale
decrypt = decrypt * p/q

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