Any proposal to provide security for implantable medical devices (IMDs), such as cardiac pacemakers and defibrillators, has to achieve a trade-off between security and accessibility for doctors to gain access to an IMD, especially in an emergency scenario. In this paper, we propose a finger-to-heart (F2H) IMD authentication scheme to address this trade-off between security and accessibility. This scheme utilizes a patient's fingerprint to perform authentication for gaining access to the IMD. Doctors can gain access to the IMD and perform emergency treatment by scanning the patient's finger tip instead of asking the patient for passwords/security tokens, thereby, achieving the necessary trade-off. In the scheme, an improved minutia-cylinder-code-based fingerprint authentication algorithm is proposed for the IMD by reducing the length of each feature vector and the number of query feature vectors. Experimental results show that the improved fingerprint authentication algorithm significantly reduces both the size of messages in transmission and computational overheads in the device, and thus, can be utilized to secure the IMD. Compared to existing electrocardiogram signal-based security schemes, the F2H scheme does not require the IMD to capture or process biometric traits in every access attempt since a fingerprint template is generated and stored in the IMD beforehand. As a result, the scarce resources in the IMD are conserved, making the scheme sustainable as well as energy efficient.