Used the ECB mode (with block length 4) to encrypt the message m = 1011000101001010 into c = 0010011001001101 using the key π = ( 1 2 3 4 2 3 4 1 ) and initialisation vector I V = 1010. Now I to decrypt it we used the key π − 1 = ( 1 2 3 4 4 1 2 3 ) however isn't the inverse of a permutation it written backwards? In this case shouldn't we have π − 1 = ( 1 2 3 4 1 4 3 2 ) Why is it the first one?

Question

Used the ECB mode (with block length   4) to encrypt the message   m  =  1011000101001010 into   c  =  0010011001001101 using the key  π  =      (                            1                          2                          3                          4                                      2                          3                          4                          1                      )  and initialisation vector   I  V  =  1010. Now I to decrypt it we used the key      π          −      1        =      (                            1                          2                          3                          4                                      4                          1                          2                          3                      )  however isn&#039;t the inverse of a permutation it written backwards? In this case shouldn&#039;t we have      π          −      1        =      (                            1                          2                          3                          4                                      1                          4                          3                          2                      )  Why is it the first one?

Misael Li · Accepted Answer

If you are using cyclic notation,   π  =  (  1234  ). And       π          −      1        =  (  4321  ), which is just   π written backwards. But in the matrix notation that you are using, you form the inverse by exchanging the top and bottom rows. So      π          −      1        =      (                            2                          3                          4                          1                                      1                          2                          3                          4                      )  which, after rearranging the columns, is the same as      (                            1                          2                          3                          4                                      4                          1                          2                          3                      )

Ayanna Trujillo · Accepted Answer

No. The inverse permutation is the one that puts everything back where it came from (  π  (  1  )  =  2, so       π          −      1        (  2  )  =  1, and so on), which means that you get the inverse by swapping the two rows:      π          −      1        =      (                            2                          3                          4                          1                                      1                          2                          3                          4                      )  Usually one also sorts the columns for easy readability, so that we get      π          −      1        =      (                            1                          2                          3                          4                                      4                          1                          2                          3                      )

Used the ECB mode (with block length 4 ) to encrypt the message m = 1011000101001010 into

Answered question

Answer & Explanation

New Questions in Descriptive Statistics