Cracking the Hill Cipher: Finding the Decryption Key

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SUMMARY

The discussion centers on finding the decryption key for a Hill cipher using the matrix A = [[1,2,3],[4,5,6],[7,8,10]]. The user attempted to calculate the inverse of the encryption key, A^(-1), but encountered issues with decryption. A key insight provided by another user highlights the necessity of applying modular arithmetic to both the encrypted and decrypted messages, which is crucial for successful decryption in Hill cipher operations.

PREREQUISITES
  • Understanding of Hill cipher encryption and decryption processes
  • Familiarity with matrix operations, specifically matrix inversion
  • Knowledge of modular arithmetic
  • Experience with linear algebra concepts
NEXT STEPS
  • Study modular arithmetic in the context of cryptography
  • Learn about matrix inversion techniques for cryptographic applications
  • Explore the implementation of Hill cipher in programming languages like Python
  • Investigate common pitfalls in Hill cipher decryption
USEFUL FOR

Cryptography students, mathematicians, and software developers interested in encryption techniques and the practical application of linear algebra in cryptography.

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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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?
 

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