Question

In the Feistel structure, show proof that LD2 = RE14 and RD2=LE14. (Hint: LD1 and RD1 )

Please show the detailed steps in your solution.

Answer 1

To Prove: LD2=RE14;

Proof:

In Fiestal encryption algorithm, the right part of a round is copied as left part of the next round. i.e

LE15=RE14--------------------------- (i)

Now For decryption the output of the 16th round is reversed and fed into decryption algorithm. which implies LD0=RE16 AND RD0=LE16

Also for decryption the same algorithm is used so the right part of a round is copied as left part of next round. which implies

LD2=RD1---------------------------(ii)

Now consider the encryption process. we see that

LE16=RE15

RE16=LE15 XOR F(RE15,K16)

On decryption part

LD1=RD0=LE16=RE15.

RD1=LD0 XOR F(RD0,K16)

= RE16 XOR F(RE15,K16)

Putting value of RE16 from above

RD1=[LE15 XOR F(RE15,K16)] XOR F(RE15,K16).

XOR has following properties

[A XOR B] XOR C = A XOR [B XOR C]

A XOR A = 0

A XOR 0 = A

Thus RD1= LE15.

Now LD2= RD1 (as per the algorithm)

which implies LD2=LE15.

Now from equation (i)

LD2= RE14.

Hence proved.