Does decryption with a wrong key creates a new encryption? I'm wondering if decrypting with a wrong key is the same a encrypting in a different way.
For example if I encrypt the message &quot;hello&quot; with Caesar cipher with key = 3 it will give the message &quot;khoor&quot; but if I decrypt it with key = 2 the result will be &quot;ifmmp&quot;. So we can say, decrypting a message encrypted with Cesar cypher will be the same as encrypting the encrypted message with -wrongKey.
But in a general way, if I decrypt a message with a wrong key, do I encrypt the encrypted message in a different way?
In general this is a moot point, as modern encryption schemes are designed so that the recipient knows if they have used the correct key or not. It is an interesting question to ask about encryption primitives, like a block cipher. Put more precisely, you are asking whether there is always a $k_3$ such that
$D_{k_2}(E_{k_1}) = E_{k_3}$
This is essentially asking if encryption forms a group, and in general the answer is no. See e.g. Is Triple-DES a group?. There are notable exceptions. You've seen that Caesar cipher is one, and Vigenere is another.