A method and 
system for encrypting a first piece of information M to be sent by a sender [100] to a 
receiver [110] allows both sender and 
receiver to compute a secret message key using identity-based information and a bilinear map. In a one embodiment, the sender [100] computes an identity-based 
encryption key from an identifier ID associated with the 
receiver [110]. The identifier ID may include various types of information such as the receiver's e-
mail address, a receiver credential, a message identifier, or a date. The sender uses a bilinear map and the 
encryption key to compute a secret message key gIDr, which is then used to encrypt a message M, producing 
ciphertext V to be sent from the sender [100] to the receiver [110] together with an element rP. An identity-based decryption key dID is computed by a private 
key generator [120] based on the ID associated with the receiver and a secret 
master key s. After obtaining the private decryption key from the 
key generator [120], the receiver [110] uses it together with the element rP and the bilinear map to compute the secret message key gIDr, which is then used to decrypt V and recover the original message M. According to one embodiment, the bilinear map is based on a Weil 
pairing or a Tate 
pairing defined on a subgroup of an elliptic curve. Also described are several applications of the techniques, including 
key revocation, 
credential management, and return 
receipt notification.