# How is message length involved in public/private-key encryption?

I've just read this question regarding why to sign only the hash of a message. I kind of understood the answer, but the question arisen is now:

Why can I encrypt any text messages with the same method while it is needed to split up the message in order to sign it?

I mean, signing is taking the private key and encrypting e.g. message A and on the other side taking the encrypted message and using the public key to decrypt it. What is the difference that makes the other way around (public key for encryption, private key for decryption) (more) secure?

• Signing is not "taking the private key and encrypting". $\:$ See this answer. $\;\;\;\;$ – user991 Aug 8 '15 at 6:27
• The first one is a great answer and explanation. Anyways, it still does not answer my question entirely. What about the message sizes? The answer states that the message length is limited to keysize - 11bytes. I tested one implementation which threw me an error (message too long), but how is that handled in e.g. PGP for mail encryption? – user2084865 Aug 8 '15 at 6:41
• – user991 Aug 8 '15 at 6:44
• @RickyDemer, bing.com/search?q=hybrid+cryptosystem – SEJPM Aug 8 '15 at 18:15
• What do you mean with "with the same method?" What do you mean with "split up the message"? – Maarten Bodewes Aug 9 '15 at 9:05

That said, in both cases (signature & public key encryption) schemes are designed for fixed message sizes. For RSA signatures and encryption the maximum message length is determined by the size of $N = pq$ (assuming the school book notation for RSA). You can neither sign longer messages nor encrypt them.