A timed- release cryptosystem allows a sender to encrypt a message so that only the intended recipient can read it only after a specified time. We formalize the concept of a secure timed- release public- key cryptosystem and show that, if a third party is relied upon to guarantee decryption after the specified date, this concept is equivalent to identity- based encryption; this explains the observation that all known constructions use identity- based encryption to achieve timed- release security. We then give several provably- secure constructions of timed- release encryption: a generic scheme based on any identity- based encryption scheme, and two more efficient schemes based on the existence of cryptographically admissible bilinear mappings. The first of these is essentially as efficient as the Boneh- Franklin Identity- Based encryption scheme, and is provably secure and authenticated in the random oracle model; the final scheme is not authenticated but is provably secure in the standard model ( i. e., without random oracles).