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LetM1 = {0000 0001, 0101 0000, 1111 1000} be a message space andM2 = {1010 0100, 1110 0011, 1011 0101} be another. (In case the typesetting is unclear, these are sets containing three bitstrings of length 8.) Suppose two ciphertexts are received c1 = 1011 1011 and c2 = 0101 1110. Suppose you know c1 is a one-time pad encryption of a message in M1 with key k and that c2 is one-time pad encryption of a message in M2 with the same key k. What are the two messages and what is the key?

Question

LetM1 = {0000 0001, 0101 0000, 1111 1000} be a message space andM2 = {1010 0100, 1110 0011, 1011 0101} be another. (In case the typesetting is unclear, these are sets containing three bitstrings of length 8.) Suppose two ciphertexts are received c1 = 1011 1011 and c2 = 0101 1110. Suppose you know c1 is a one-time pad encryption of a message in M1 with key k and that c2 is one-time pad encryption of a message in M2 with the same key k. What are the two messages and what is the key?

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Solution

To solve this problem, we need to use the properties of the XOR operation, which is used in one-time pad encryption. The properties we need are:

  1. A XOR A = 0
  2. A XOR 0 = A
  3. A XOR B XOR A = B

We know that a one-time pad encryption is done by XORing the message with the key. So, if M1 is the message and K is the key, then the ciphertext C1 is:

C1 = M1 XOR K

Similarly, for the second message and ciphertext:

C2 = M2 XOR K

We can XOR the two ciphertexts together, which will give us the XOR of the two messages, because the keys will cancel out (since the same key is used for both messages):

C1 XOR C2 = M1 XOR K XOR M2 XOR K = M1 XOR M2

Now we can XOR this result with each message in M1 and M2. The results that are in M1 and M2 are the original messages, and the key can be found by XORing the message with the corresponding ciphertext.

Let's do the calculations:

C1 XOR C2 = 1011 1011 XOR 0101 1110 = 1110 0101

Now XOR this with each message in M1:

1110 0101 XOR 0000 0001 = 1110 0100 (which is in M2) 1110 0101 XOR 0101 0000 = 1011 0101 (which is in M2) 1110 0101 XOR 1111 1000 = 0001 1101 (which is not in M1 or M2)

So the message from M1 is 1111 1000.

Now XOR the result with each message in M2:

1110 0101 XOR 1010 0100 = 0100 0001 (which is not in M1 or M2) 1110 0101 XOR 1110 0011 = 0000 0110 (which is not in M1 or M2) 1110 0101 XOR 1011 0101 = 0101 0000 (which is in M1)

So the message from M2 is 1011 0101.

Finally, to find the key, we can XOR the message with the corresponding ciphertext:

K = M1 XOR C1 = 1111 1000 XOR 1011 1011 = 0100 0011 K = M2 XOR C2 = 1011 0101 XOR 0101 1110 = 1110 1011

Both calculations give the same key, as expected. So the key is 0100 0011.

This problem has been solved

Similar Questions

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Question No. 1: (Marks 10) Suppose a Station A transmits a message containing five characters to Station B using Even Parity encoding to ensure data integrity during transmission. Each character consists of 8 bits encoded in the ASCII. Station B receives the message of five 9-bit data elements and needs to extract the 8-bit data message from each element and decode it using ASCII to form meaningful words. The data elements received by Station B are: Received 9-bit Data Elements: 010101100 010101010 010011001 010011010 010100110 Assuming the data is received correctly without any errors by Station B, you are required to do the following tasks: 1. Extract 8-bit Data Message: Remove the Parity bits to extract the 8-bit data message from each 9-bit received element. 2. Decode and Extract using ASCII: Convert each 8-bit data message into its corresponding ASCII character to extract the meaningful words. Give your answer in the following table: Received Message 010101100 010101010 010011001 010011010 010100110 Data message (Bits)? Decoded Message?

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