# Determine the RSA private key from public key

I was told that you can determine the private key of an RSA encryption with the public key.

I thought the point of a public key was to avoid letting people find the private key, but anyway, they said I could find it by simply factoring the public key modulus? Were they joshing me or can it be done? If so, how would I do that (need to acquire $$p,q$$ somehow?)?

So with with example Public Key $$( e, n ) = ( 13, 119 )$$ or any other valid key you want to use...

• Note that solving a Sudoku is also considered a hard problem, given large enough dimensions of the Sudoku. Hard problems are not impossible problems; they are just hard to solve for large enough puzzles. – Maarten Bodewes Oct 21 '19 at 14:26