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 Jun 14 awarded Popular Question May 22 awarded Nice Question Jul 29 awarded Teacher Jul 29 comment Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Thank you, this is a nice analogy which I should use in the future! Just for myself I required a mathematical explanation. Jul 29 awarded Scholar Jul 29 accepted Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Jul 29 comment Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Thanks Uwe this is very helpful! (I think the p in your formulas is acutally the n of n=pq.) So, if we were to decrypt the ciphertext but only had the public key, we would need to calculate the private key as I can see in the second formula. To calculate the private key we would need to determine the primes in n=pq. Then we get d using: d=(1 mod ((p-1)(q-1))/e which is computally very expensive to brute force in order to find primes p and q. That's it, right? :) Jul 29 answered How are primes generated for RSA? Jul 29 comment Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? @RickyDemer Well sorry, it's not that obvious to me from this answer. Most of this answer focuses on explaining PGP but the key to my question is how RSA encryption works. I wish that part were explained a bit more elaborated so I could understand it as well. Jul 28 awarded Student Jul 28 comment Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Decryption is only possible with the private key (i.e. with both keys) because RSA requires you to know the two primes used in the calculation. You can calculate the primes used in the RSA encryption only if you have both keys. However, the same should apply to the encryption, right? Of course not apparently, but I don't see it... Hence I'm asking the question: Where in the illustration do we have the private key in the RSA encryption process? Jul 28 comment Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Thank you for the answer! While the illustration is nice, it still leaves the question how using RSA on the encrypted key can only be decrpyted using the private key. The first tip is that RSA uses a one-way function which is the essential characteristic for its asymmetric encryption. Specifically, mathematical integer factorisation is the one-way function used here. Jul 28 asked Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key? Feb 18 awarded Supporter