Answer:
IP−1(IP(x))=x
the initial permutation IP and the final permutation IP ⁻¹ are bitwise permutations.
Initial Permutation IP is as per below table
58 50 42 34 26 18 10 2
60 52 44 36 28 20 12 4
62 54 46 38 30 22 14 6
64 56 48 40 32 24 16 8
57 49 41 33 25 17 9 1
59 51 43 35 27 19 11 3
61 53 45 37 29 21 13 5
63 55 47 39 31 23 15 7
Final Permutation IP ⁻¹ is as per below table
40 8 48 16 56 24 64 32
39 7 47 15 55 23 63 31
38 6 46 14 54 22 62 30
37 5 45 13 53 21 61 29
36 4 44 12 52 20 60 28
35 3 43 11 51 19 59 27
34 2 42 10 50 18 58 26
33 1 41 9 49 17 57 25
that input bit 58 is mapped to output position 1, input bit 50 is mapped to the second output position, and so forth. The final permutation IP ⁻¹ performs the inverse operation of IP.
When x=1 then IP ⁻¹ (IP(1) ) is as below. and for all x to 2 to 5 are as below as well.
IP ⁻¹ (IP(1) ) = IP ⁻¹ (40) = 1
Similarly IP ⁻¹ (IP(2) ) = IP ⁻¹ (8) = 2
IP ⁻¹ (IP(3) ) = IP ⁻¹ (48) = 3
IP ⁻¹ (IP(4) ) = IP ⁻¹ (16) = 4
IP ⁻¹ (IP(5) ) = IP ⁻¹ (56) = 2
Explanation:
Explanation is given in the answer section.
