i need help solving this homework problem any help is appreciated. thanks in adv

Question

i need help solving this homework problem any help is appreciated. thanks in advance

Suppose a message has been encrypted using an old system with the basic DES algorithm under key k. (i) If the receiver of the message is running a new system with 3DES implemented. Can the receiver decrypt the ciphertext by setting k1=k2=k3=k and why? (ii) If the encryption of 3DES used the EEE mode instead of EDE and the decryption used the DDD mode instead of DED, can the receiver decrypt the ciphertext by setting k1=k2=k3=k and why?

Explanation / Answer

(i)Before We start quick facts that 3DES =3 Diffarent DES operation with 3 Diffarent key K1,K2,K3 .each key is 8octate.
Yes the Reciever can dicipher the cipher text usingm 3 DES that is encypted in DES preveously.
Because the decryption operation in 3DES is eual to
P=D3(K1||K2||K3,C)=D(K1,E(K2,D(K3,C)))
C=Cipher Text
P=Plain Text.
means first it decrypt the ciphered text (C) with key=K3 ,then the result will again
encrypted using key K2 then the resulted Encypted text again Decrypted using Key
K1.
There is 3 layer of encyption and Decryption ,But if we make all keys equal i.e(k=K1=K2=K3) we can get same Diciphered text that a normal DES methord Does.

(ii)
Generally we Do encyption like E(K3,D(K2,E(K1,P))) in 3DES .
First Encrypt Plain Text (p ) with key K1
secoendly Decrypt that encrypted text with key K2
Thirdly Again Encypt the outcome of above step with key K3

Here we need 3 diffarent key to do the same .
BUT If we find K=K1=K2=K3.
then we can do EEE instead of EDE ,and in Decryption we can use DDD to Dicipher the 3 layer of Encryption.
Because
EEE means applying SIMPLE DES 3 times and inthis keys are also equal in all encryption So
it is obvious that the final encrypted text will be decrypted using SIMPLE DES DECRYPTION 3 times.

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