Question

I am trying to do some homework to crack a small-RSA key. We are given the following:

Public Key: {e=49, n=10539750919}
Cipher Text: ITG!AAEXEX
Ascii Table: AEGIORTX!0
             1234567890

I am asked to crack the key and find the plain text.

I think I have a basic algorithm figured out. It looks like if I take p = Floor(Sqrt(n)) = 102663, then I can try to find a q using n = p*q by checking if (n mod p == 0). Once we find q, I can use the formula

d*e = 1 mod (p-1)(q-1)

to find d (private exponent). After this I have all I need to crack the key! (I think). The only thing I do not get is, how is the above equation to find d actually computed? Isn't 1 mod (p-1)(q-1) ALWAYS going to be 1? 1 mod anything is 1, so what am I doing wrong?

No correct solution

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