We present group encryption, a new cryptographic primitive which is the encryption analogue of a group signature. It possesses similar verifiability, security and privacy properties, but whereas a group signature is useful whenever we need to conceal the source (signer) within a group of legitimate users, a group encryption is useful whenever we need to conceal a recipient (decryptor) within a group of legitimate recievers. We introduce and model the new primitive and present sufficient as well as necessary conditions for its generic implementation. We then develop an efficient novel number theoretic construction for group encryption of discrete logarithms whose complexity is independent of the group size. To achieve this we construct a new public-key encryption for discrete logarithms that satisfies CCA2-key-privacy and CCA2-security. Applications of group encryption include settings where a user wishes to hide her preferred trusted third party or settings where verifiable well-formed ciphertexts are kept in a storage server that must be prevented from, both, learning the content of records and analyzing the identities of their retrievers