Cracking the Hill Cipher: Finding the Decryption Key

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In summary, the conversation is about finding the decryption key for a hill cipher. The person has tried using the inverse of the encryption key, but it did not work. They have attempted to find the inverse using a specific equation, but it did not properly decrypt their message. Another person suggests that they may have forgotten to take the mod of the encrypted text and the decrypted text.
  • #1
sfskseg32
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Homework Statement



I cannot figure out how to find the decryption key for a hill cypher. My textbook and a bunch of websites say that is just the inverse of the encryption key, but that is not working for me.

Homework Equations



A =
[1,2,3]
[4,5,6]
[7,8,10]

The Attempt at a Solution



A^(-1) =
[-2/3, -4/3, 1]
[-2/3, 11/3, -2]
[1, -2, 1]

But this does not properly decrypt my message. Anyone know what I'm missing?
 
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  • #2
Seems to work just fine

>> [1 2 3; 4 5 6; 7 8 10]*[0;2;19]

ans =

61
124
206

>> inv([1 2 3; 4 5 6; 7 8 10])*[61;124;206]

ans =

0.0000
2.0000
19.0000


Perhaps you simply forgot to take the mod of the encrypted text, and then take the mod of the decrypted text again. What is the 'message' to encrypt here?
 

1. How does the Hill Cipher work?

The Hill Cipher is a polygraphic substitution cipher that works by breaking the plaintext into blocks of fixed size, and then using a matrix to encrypt each block of letters. The resulting ciphertext is then decrypted using the inverse matrix to reveal the original message.

2. How do you find the decryption key for the Hill Cipher?

To find the decryption key for the Hill Cipher, you need to know the size of the matrix used for encryption and have access to a known plaintext-ciphertext pair. From there, you can use matrix algebra to calculate the inverse matrix, which will serve as the decryption key.

3. What is the importance of finding the decryption key for the Hill Cipher?

Finding the decryption key for the Hill Cipher allows you to decrypt any message that has been encrypted using this method. It also allows you to break the cipher and potentially uncover any hidden messages or information.

4. Are there any limitations to cracking the Hill Cipher and finding the decryption key?

Yes, there are limitations to cracking the Hill Cipher. The most significant limitation is that you need to have access to a known plaintext-ciphertext pair and know the size of the matrix used for encryption. Without this information, it is nearly impossible to find the decryption key.

5. Can the Hill Cipher be used for secure communication?

Yes, the Hill Cipher can be used for secure communication if the encryption key is kept secret and the matrix used for encryption is large enough. However, this method is vulnerable to known plaintext attacks, so it may not be the most secure option for sensitive information.

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