the present invention provides encryption schemes and apparatus which securely generate a cipher - text which in itself contains checks for assuring message integrity . it also provides compatible decryption schemes confirming message integrity . the encryption scheme generates a cipher - text with message integrity in a single pass with little additional computational cost , while retaining at least the same level of security as schemes based on a mac . one embodiment encrypts a plain - text message by dividing the plain - text message into a multitude of plain - text blocks and encrypting the plain - text blocks to form a multitude of cipher - text blocks . a single pass technique is used in this process to embed a message integrity check in the cipher - text block . a message integrity check is embedded in the cipher - text blocks by embedding a set of pseudo random numbers , which may be dependent , but are pair - wise differentially uniform . we also describe an embodiment which is highly parallelizable .