The idea is to identify user using fingerprint. I want to bind finger with user, so that user will able to login to app using finger with any fingerprint device, so if user will change device and without entering username and password user will be able to login. How to make it? as i found so far, there is no option to make it. or i can be wrong?
i found the article about authentication using public and private keys, but it is not what i really wanted, because if user will change the device, device must generate a new pair of public and private keys.
There is no way to do this. The Android Fingerprint API (not unlike Apple's TouchID) was designed so that the fingerprints are tied to the device (from the Nexus FAQ):
Your fingerprint data is stored securely and never leaves your device. Your data is not shared with Google or any apps on your device.
Therefore there is no way for an app to access the fingerprint data to be able to save it for use across devices.