Problem 44956. Determine RSA keys (public and private) given two prime number character strings (p and q)

Created by David Hill

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Given two prime number character strings (p and q), generate the RSA public and private keys (n and d) with e = 65537. The more difficult part is doing this without the use of symbolic numbers. Example: p = '3355335697481001330501721', q = '5955344080483688912855719' n='19982178584029090861856118769095354822153154192399' d='3270348772331599380262578849367006078599068947553'

https://simple.wikipedia.org/wiki/RSA_algorithm

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Last Solution submitted on Mar 20, 2025

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Tim on 28 Aug 2019

I get different results for d in test cases 2, 3, and 4 (in particular, d=929660805638728623653 for test case 2).

Tim on 28 Aug 2019

If I understand correctly, we should have mod(d*e,phi)=1, where phi=(p-1)*(q-1). My answers seem to satisfy that condition, but test cases 2, 3, and 4 do not.

Joel Hottinger on 9 Jul 2021

Could someone help me out with the modular inversion. I can't seem to get it to work for any large numbers. I've been stuck for a while

Joel Hottinger on 9 Jul 2021

I think my main issue is that I cannot use the mod function with large numbers, what is a way around this?

Joel Hottinger on 28 Jul 2021

@David Hill. Thanks, that worked a lot better for me

Jeremy Perez on 6 Aug 2021

One should first consider if MATLAB is even adapted for these kinds of calculations. Still, I had a lot of fun.

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Problem 44956. Determine RSA keys (public and private) given two prime number character strings (p and q)

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Problem 44956. Determine RSA keys (public and private) given two prime number character strings (p and q)

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Last 200 Solutions

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