Does Android locally encrypt your fingerprint?
Looks like the answer is in Google's Android 6.0 Compatibility Requirements, section 7.3.10:


MUST have a hardware-backed keystore implementation, and perform the fingerprint matching in a Trusted Execution Environment (TEE) or on a chip with a secure channel to the TEE.
MUST have all identifiable fingerprint data encrypted and cryptographically authenticated such that they cannot be acquired, read or altered outside of the Trusted Execution Environment (TEE) as documented in the implementation guidelines on the Android Open Source Project site [Resources, 96].
MUST prevent adding a fingerprint without first establishing a chain of trust by having the user confirm existing or add a new device credential (PIN/pattern/password) using the TEE as implemented in the Android Open Source project.
MUST NOT enable 3rd-party applications to distinguish between individual fingerprints.