homomorphic encryption in R

Homomorphic encryption is allows computations to be performed on encrypted data. This has enormous potential in areas of machine learning that deal with private data, such as medical records.

Below is an implementation of homomorphic encryption in R.

It encrypts two pieces of data m=10 and m1=2, once they are encrypted (as cipher and cipher2 respectively), the two encrypted forms can be added up together (cyphertotal).

They can then be descrypted to reveal mess2 to equal 12 (i.e. the sum of 10 and 2).

Note that the “computation” could be done by a other party that does not have access to the unencrypted data.

This can be used e.g. to send medical records to another party that has experience building machine learning models, without revealing the private medical data to this other party.

library(numbers)

# greater common divisor function
gcd <- function(a,b) {
  rk_1 <- a
  rk_2 <- b
  while (rk_2 > 0) {
    rk   <- rk_1 %% rk_2
    rk_1 <- rk_2
    rk_2 <- rk
  }
  return( rk_1 )
}

# least common multiplier function
lcm <- function(a,b) {
  (a*b)/gcd(a,b)
}

# extended_euclidean_algorithm
extended_euclidean_algorithm <- extGCD
 
# inverse_of
inverse_of <- modinv

p = 17
q = 19

# define the message
m = 10

n = p * q

gLambda = lcm(p-1,q-1)

r = floor(runif(1, 20, 150))

g = floor(runif(1, 20, 150))

l <- floor( (modpower(g, gLambda, n*n)-1)/n )
gMu = inverse_of(l,n)

k1 = modpower(g, m, n*n)
k2 = modpower(r, n, n*n)

cipher = (k1*k2) %% (n*n)

l <- floor( (modpower(cipher, gLambda, n*n)-1)/n )

mess = (l * g)

m1 = 2

k3 = modpower(g, m1, n*n)

cipher2 = (k3*k2) %% (n*n)
ciphertotal = (cipher*cipher2) %% (n*n)
l = floor( (modpower(ciphertotal, gLambda, n*n)-1)/n )
mess2 = (l * gMu) %% n