Custom RSA implementation in Javascript (NodeJS)

Question

I've tried to implement the basics of RSA into a simple NodeJS / javascript file.

For encrypting I've used c = m^e % n.
For decrypting I've used m = c^d % n.

const p = 7; // choice prime
const q = 13; // choice prime
const n = p * q;
const e = 5; // choice
const Ke = [e, n]; // the private key
const d = 29; // choice
const Kd = [d, n]; // the public key

let message = 'hello'
let encrypted = []

message = message.toUpperCase()

for (let i = 0; i < message.length; i++) {
  const char = message.charCodeAt(i) - 64 // m
  const pow = Math.pow(char, e) // m^e
  const mod = pow % n // mod n
  encrypted[i] = mod
}

encrypted.forEach(char => {
  const pow = Math.pow(char, d) // c^d
  const mod = pow % n // mod n
  console.log(String.fromCharCode(mod + 64))
})

The encrypting goes well. However, the decrypting has some issues. It shows other characters then I've put in in the let message = 'hello' part

What am I doing wrong with decrypting?

set0gut1 · Accepted Answer · 2018-05-18 10:16:48Z

2

encrypted.forEach(char => {
  const pow = Math.pow(char, d) // c^d
  const mod = pow % n // mod n
  console.log(String.fromCharCode(mod + 64))
})

In above function, pow is too large and precision is lost. For example, in the case of 'L':

{ char: 38, d: 29, pow: 6.512148596632774e+45, mod: 81 }

Using a technique to calculate the mod of pow without losing precision, it can decode correctly.

encrypted.forEach(char => {
  let mod = 1
  for (let i = 0; i < d; i++) {
    mod = (mod * char) % n
  }
  console.log(String.fromCharCode(mod + 64))
})

output:

H
E
L
L
O

answered May 18, 2018 at 10:16

set0gut1

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