Question

Hi i am trying to set up an RSA cryptosystem i have all the values except d selected prime numbers: p=1889, q=2003, n=3783667, phi=3779776, e= 61

i got stuck finding d could anyone help me to figure it out?

Setting up an RSA cryptosystem

• Two large distinct prime numbers p and q are selected, and n = pq and Φ(n) = (p − 1)(q − 1) are calculated.

• An integer e is selected such that gcd(Φ(n), e) = 1 and the multiplicative inverse d = e^(−1) in ZΦ(n) is calculated, i.e.

  ed ≡ 1 (mod Φ(n)).

• The numbers p, q, and Φ(n), are then discarded.

• The pair (e, n) is published as the public encryption key
• The number d is the secret decryption key.

Answer 1

Here’s the algo, step by step, including finding d.
m from the article is your Φ(n).
Now, you try to find a d = (1 + nm) / e, working through values of n until an integer solution for e is found.

Edit:
Here you’ll find a more detailed explanation of the whole algorithm.