We define a new mode of operation for block encryption which
in addition to assuring confidentiality also assures
message integrity. In contrast, previously for message
integrity a separate pass was required to compute a
cryptographic message authentication code (MAC).
The new mode of operation, called Integrity Aware CBC (IACBC),
requires a total of $m+{\log m}$ block encryptions on a plaintext
of length $m$ blocks. The well known CBC (cipher block chaining)
mode requires $m$ block encryptions. The second pass of computing
the MAC essentially requires additional $m$ block encryptions
(as in CBC-MAC), or a U-MAC like computuaion. The new scheme
derives its efficiency and simplicity by using $m$ block of
pairwise independent random variables.