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Question: A cryptography student has accidentally used the same keystream to encrypt two different messages, 𝑀1 M 1 and 𝑀2 M 2 . We know that the ciphertexts are 𝐢1=0π‘₯𝑑45𝑏63𝑑𝑑3𝑑𝑓604𝑐2 C 1 = 0 x d 45 b 63 d d 3 d f 604 c 2 and 𝐢2=0π‘₯56𝑑𝑒𝑏𝑓1𝑓49𝑓7𝑑1𝑓𝑒 C 2 = 0 x 56 d e b f 1 f 49 f 7 d 1 f e . We also happen to know that 𝑀1=0π‘₯π‘Ž4329136𝑑26𝑏2𝑐54 M 1 = 0 x a 4329136 d 26 b 2 c 54 . a) What is 𝑀2 M 2 in hexadecimal? Please give your answer a leading 0x and use lowercase letters only. b) What is the keystream? Please give your answer a leading 0x and use lowercase letters only. Hint: These are all 8 byte numbers and will fit in an unsigned long type on most systems. – Free Chegg Question Answer

A cryptography student has accidentally used the same keystream to encrypt two different messages, 𝑀1 M 1 and 𝑀2 M 2 . We know that the ciphertexts are 𝐢1=0π‘₯𝑑45𝑏63𝑑𝑑3𝑑𝑓604𝑐2 C 1 = 0 x d 45 b 63 d d 3 d f 604 c 2 and 𝐢2=0π‘₯56𝑑𝑒𝑏𝑓1𝑓49𝑓7𝑑1𝑓𝑒 C 2 = 0 x 56 d e b f 1 f 49 f 7 d 1 f e . We also happen to know that 𝑀1=0π‘₯π‘Ž4329136𝑑26𝑏2𝑐54 M 1 = 0 x a 4329136 d 26 b 2 c 54 . a) What is 𝑀2 M 2 in hexadecimal? Please give your answer a leading 0x and use lowercase letters only. b) What is the keystream? Please give your answer a leading 0x and use lowercase letters only. Hint: These are all 8 byte numbers and will fit in an unsigned long type on most systems.

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Step 1

a) A message can be recovered with the help of XOR operation if two messages are encrypted by the using the same keystream.

Computer Engineering homework question answer, step 1, image 1

Once we get (M1 XOR M2) we can easily recover M2 since we already know M1. All that we need to do is another XOR with M1.

First calculating C1 XOR C2 by using an online XOR calculator: –

Computer Engineering homework question answer, step 1, image 2

Now, determining M2 = (C1 XOR C2) XOR M1, that is: –

Computer Engineering homework question answer, step 1, image 3

Step 2

b) In the same way, the keystream can be recovered by performing the XOR operation on any Ciphertext & corresponding message: –

Computer Engineering homework question answer, step 2, image 1


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