cloudy understanding of asymmetric cryptography

[Felipe Alvarez]

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Someone today shook my understanding of asymmetric ciphers.

_Bob performs symmetric encryption on message with_
_key "K" (generated randomly). He then encrypts "K" _
_with Alice's public key, and sends both the symetrically _
_encrypted message and asymmetrically encrypted key to Alice_

Is this what happens during most/some/all of public-key
communications? I had always thought that the message is encrypted
with public key, and decrypted with secret key. I was not aware that
key "K" was encrypted with public key, but message encrypted with
__symmetric_cipher__.

To help my understanding a little futher, if this does not always
occur, or does not usually occur, when does it occur (not occur)?
Using what ciphers (algorithms)?

I was unable to find adequate explanations online.

Thanks
Felipe

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