In this paper, we present a novel framework for the generic construction of biometric Identity Based Encryption (IBE) schemes, which do not require bilinear pairings and result in more efficient schemes than existing fuzzy IBE systems implemented for biometric identities. Also, we analyze the security properties that are specific to biometric IBE namely anonymity and identity privacy. Considering these notions, we present generic constructions for biometric IBE and ID-KEM based on weakly secure anonymous IBE schemes, error correcting codes and generic conversion schemes. Finally, we describe concrete applications of our framework and compare them to the existing fuzzy IBE systems in terms of time complexity.