No , it does not depend on the computer.
Make sure you copy the Keystore that you used to sign it from the old computer to the new one, and everything will be exactly the same.
Keystore is just a file in which all your keys are stored (and usually has a .jks extension).
The main documentation states:
A keystore is a binary file containing a set of private keys. You should store the vault in a safe and secure place.
A private key is an object that must be identified with the application, such as a person or company.
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