We initiate a study of on-line ciphers. These are ciphers that can take input plaintexts of large and varying lengths and will output the ith block of the ciphertext after having processed only the first i blocks of the plaintext. Such ciphers permit length-preserving encryption of a data stream with only a single pass through the data. We provide security definitions for this primitive and study its basic properties. We then provide attacks on some possible candidates, including CBC with fixed IV. We then provide two constructions, HCBC1 and HCBC2, based on a given block cipher E and a family of computationally AXU functions. HCBC1 is proven secure against chosenplaintext attacks assuming that E is a PRP secure against chosen-plaintext attacks, while HCBC2 is proven secure against chosen-ciphertext attacks assuming that E is a PRP secure against chosen-ciphertext attacks. © International Association for Cryptologic Research 2011.