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BFV

Load libraries that will be used.

library(polynom)
library(HomomorphicEncryption)

Set some parameters.

d  =   4
n  =   2^d
p  =   (n/2)-1
q  = 874

Set a working seed for random numbers

set.seed(123)

Here we create the polynomial modulo.

pm = polynomial( coef=c(1, rep(0, n-1), 1 ) )
print(pm)
#> 1 + x^16

Create the secret key and the polynomials a and e, which will go into the public key

# generate a secret key
s = GenSecretKey(n)
print(s)
#> 1 + x + x^2 + x^4 + x^8 - x^9 - x^12 + x^14 - x^15
# generate a
a = GenA(n, q)
print(a)
#> 91 + 348*x + 649*x^2 + 355*x^3 + 840*x^4 + 26*x^5 + 519*x^6 + 426*x^7 + 649*x^8  
#> + 766*x^9 + 211*x^10 + 590*x^11 + 593*x^12 + 555*x^13 + 871*x^14 + 373*x^15

Generate the error for the public key.

e = GenError(n)
print(e)
#> -4 - x - 2*x^2 - 6*x^3 + 6*x^5 - x^6 - 6*x^7 - 4*x^8 + 4*x^9 - 2*x^10 - 7*x^11  
#> - 3*x^12 - x^13 + 5*x^14 - x^15

Generate the public key.

pk0 = GenPubKey0(a, s, e, pm, q)
print(pk0)
#> 560 + 287*x + 70*x^2 + 788*x^3 + 534*x^4 + 150*x^5 + 43*x^6 + 331*x^7 + 328*x^8  
#> + 318*x^9 + 184*x^10 + 519*x^11 + 504*x^12 + 783*x^13 + 79*x^14 + 425*x^15
pk1 = GenPubKey1(a)

Create a polynomial message

# create a message
m = polynomial( coef=c(6, 4, 2) )

Create polynomials for the encryption

# polynomials for encryption
e1 = GenError(n)
e2 = GenError(n)
u  = GenU(n)
print(u)
#> x^3 - x^5 + x^9 + x^11 + x^13 - x^14

Generate the ciphertext.

ct0 = EncryptPoly0(m, pk0, u, e1, p, pm, q)
print(ct0)
#> 157 + 787*x + 337*x^2 + 236*x^3 + 454*x^4 + 575*x^5 + 87*x^6 + 14*x^7 + 448*x^8  
#> + 640*x^10 + 747*x^11 + 711*x^12 + 564*x^13 + 866*x^14 + 678*x^15
ct1 = EncryptPoly1(   pk1, u, e2,    pm, q)
print(ct1)
#> 760 + 698*x + 679*x^2 + 477*x^3 + 329*x^4 + 414*x^5 + 487*x^6 + 165*x^7 +  
#> 111*x^8 + 642*x^9 + 409*x^10 + 565*x^11 + 660*x^12 + 644*x^13 + 469*x^14 +  
#> 297*x^15

Decrypt

decrypt = (ct1 * s) + ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)

# rescale
decrypt = decrypt * p/q

Round (remove the error) then mod p

# round then mod p
decrypt = CoefMod(round(decrypt), p)
print(decrypt)
#> 6 + 4*x + 2*x^2

Which is indeed the message that we first encrypted.

Next, look at the vignette BFV-2 which does the exact same process, but unpacks all the functions used here into basic mathematical operations.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.