I have a confusion
This is a confusing topic.
How to extract a private key from it?
You do not need. The signature tool accepts the key file. He is smart enough to retrieve the private key, if necessary.
does it need to publish the key to use this assembly?
The public key is built into the assembly. You can see this by looking at the strong name of the assembly. However, you must somehow tell the client what the correct public key is, if you think that someone might try to impersonate you! See next bit for more details.
if someone can use the meaning of encryption with a private key?
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