Computer Security and Cryptography

1.11 AN EXAMPLE OF THE INFERENCE PROCESS IN CRYPTANALYSIS

Although statistical characteristics provide information to aid in cryptanalysis, more often internal constraints in the cryptographic system provide a great deal of information. We give an example in this section of the inference process.

A PUZZLE

Each of the nine symbols appearing in the array below stands for a unique encoding of one of the digits 1 through 9. The rightmost column gives the sum in each row; the bottom row gives the sum in each column. A question mark can stand for any one- or two-digit number and not necessarily the same number in each instance. Find the encoding of the digits 1 through 9!

Solution The row 2 and column 3 sums give the equations

As

is even,

are distinct and each are ≤9, and

it follows that •• ...