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This paper introduces and explores the new concept of Time-Specific Encryption (TSE). In (Plain) TSE, a Time Server broadcasts a key at the beginning of each time unit, a Time Instant Key (TIK). The sender of a message can specify any time interval during the encryption process; the receiver can decrypt to recover the message only if it has a TIK that corresponds to a time in that interval. We extend Plain TSE to the public-key and identity-based settings, where receivers are additionally equipped with private keys and either public keys or identities, and where decryption now requires the use of the private key as well as an appropriate TIK. We introduce security models for the plain, public-key and identity-based settings. We also provide constructions for schemes in the different settings, showing how to obtain Plain TSE using identity-based techniques, how to combine Plain TSE with public-key and identity-based encryption schemes, and how to build schemes that are chosen-ciphertext secure from schemes that are chosen-plaintext secure. Finally, we suggest applications for our new primitive, and discuss its relationships with existing primitives, such as Timed-Release Encryption and Broadcast Encryption.