Previous | ToC | Next Labs: Cryptography. Part 1. Math Alive

HBO Application

You just studied binary and parity addition because these operations are used in many applications, in cryptography and elsewhere. The encryption method that you will be learning here uses parity addition.

We discuss a toy example here: in order to be able to transmit some movie channels to their customers, local cable companies subscribing to the movie service must have a password to unscramble the signal sent to them by the television station. As explained in class, the password is broadcast itself, encrypted differently for each subscriber. Each subscriber has a key, consisting of a binary string of (say) 20 digits. The password itself is also a binary string with 20 entries. The television station sends out an enormous string that contains, in successive 20-digit strings, the XOR addition of the password and every acceptable key, in random order.

Therefore the concatenated string may look like this:

(password oplus key3) (password oplus key6) (password oplus key1) (password oplus key7) (password oplus key5) (password oplus key4)

Parity addition has the neat property that if you parity add the (password oplus key) to the key, then you will get back the password.

For example:

your key:01011011110011
password oplus your key:11101101001001

password oplus your key :11101101001001
your key :01011011110011
(password oplus your key) oplus your key10110110111010

NOTE: password = (password oplus key) oplus key

You can exploit this as follows: parity add your 20-digit keyword to every one of the 20-digit pieces in the long string sent out by the station. One of them will be the password. We denote password by pwd.

password oplus key2password oplus key4password oplus key7password oplus your keypassword oplus key1
pwd oplus key2 oplus your keypwd oplus key4 oplus your keypwd oplus key7 oplus your keypwd oplus your key oplus your keypwd oplus key1 oplus your key
junk junk junk passwordjunk

In a tool below you see a stream of 45 binary strings; they respresent the TV station transmission. Enter the key you got in class (or in email) in the text field and click on one of the strings (If you did not get one you can use the key: 00001000000100010010). You will see the parity addition of these numbers. If you get the password, the signal will get unscrambled.
After you get the password you can use it to calculate other subscribers' passwords. Calculate three passwords from the first column.

Previous | ToC | Next Last Modified: August 2008