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I am currently writing a math paper for school regarding RSA encryption my focus lies on the importance of prime and co-prime numbers within the algorithm.

I understand that this is a "trap-door" algorithm which means that it is difficult to find the prime factors of a large number n as non-quantum computers without the correct algorithm are unable to perform this within a reasonable amount of time. However, if you have the prime factors of the number n it is simple to apply the algorithm.

Currently, I have looked at another question which gave me a deeper insight into the topic but I feel although there is crucial information missing.

Hence, my question is whether there is something I could add to increase the complexity of my answer with regards to why prime and co-prime numbers are of such importance in encryption (more specifically RSA).

Jackwannsee
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  • Maybe, you can mention that the safety of this method has not been proven, not even assuming the enemy cannot factor the public number. – Peter Dec 26 '21 at 17:45
  • One needs to mention that the random number generator must be good since one can GCD them all to factor some! This happened in practice. Also, note that some bad random number generators can lead to Fermat factoring method if they are close to each other. – kelalaka Dec 26 '21 at 19:35
  • Considering also the last comment, the conclusion is that this method is after all not good and allows too many attacks to be considered to be safe. Unfortunately , it is nevertheless widely used. – Peter Dec 27 '21 at 11:25

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