How to protect an iOS application linked to an accessory with a serial number?

Question

Objective-C

I have my iPad app (objective C, iOS 9) that needs to be protected.
iPad will only be used with an accessory that has a unique serial number.
It is necessary that the program does not work in the absence of an accessory or with an accessory with a different serial number.
The idea of ​​protection is this: the
user presses the “Activation” button, downloads a certain text file from my server, puts it on the iPad.
When the program starts (offline), it reads the serial number, performs calculations with a text file and starts or does not start.
What is the best way to encrypt/sign?
I looked in the direction of asymmetric encryption in order to use the serial number of the accessory as a public key for decryption. But in RSA two keys are generated, they cannot be set manually?