The concept of verifying the integrity of encrypted data appeared in the 1970s in the banking industry. The problem was studied in detail by the ANSI X9 committee, and later formalized by Katz and Yung [13]. Banks did not want to transmit data and allow an attacker to flip a bit undetected. In this situation, the attacker would not decrypt the message, instead he would only flip a bit so that the encrypted message "Post $100" would be changed to "Post $700".
