Question

What is the number of possible 3 x 3 affine cipher transformations ?

(a) 168

(b) 840

(c) 1024

(d) 1344

This question was addressed to me at a job interview.

Origin of the question is Overview in section Cryptography Overview, TCP/IP and Communication Networks of Cryptograph & Network Security

Answer 1

Correct option is (d) 1344

To elaborate: Since ‘A’ cannot have columns of ‘0’s. so there are ‘7’ choices i.e. 001/010/011/100/101/110/111. ‘a1’ is chosen for first column of ‘A. We have ‘6’ choices for second column, let ‘a2’ be chosen for second column. The final column can be any 3-tuple except 0, a1, a2, a1+a2. That means any one of the remaining ‘4’ 3-tuples may be chosen for the final column.

(Total number of@ possibilities for A)}=k=7×6×4=168

(Number of affine@ block cipher transformation)}=k×t=8×168 =1344.