Abstract. In this work, we take a closer look at anonymity and robustness in encryption schemes. Roughly speaking, an anonymous encryption scheme hides the identity of the secret-key holder, while a robust encryption scheme guarantees that every ciphertext can only be decrypted to a valid plaintext under the intended recipient's secret key. In case of anonymous encryption, we show that if an anonymous PKE or IBE scheme (in presence of CCA attacks) is used in a hybrid encryption, all bets regarding the anonymity of the resulting encryption are off. We show that this is the case even if the symmetric-key component is anonymous. On the positive side, however, we prove that if the keyencapsulation method is, additionally weakly robust the resulting hybrid encryption remains anonymous. Some of the existing anonymous encryption schemes are known to be weakly robust which makes them more desirable in practice. In case of robust encryption, we design several efficient constructions for tr...