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.

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