Matrix Cryptography: Encryption and Decryption Using Inverse and Transpose

Matrix Cryptography: Encryption and Decryption Using Inverse and Transpose
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2018-12-11 22:50
This GeoGebra example demonstrates a simple encryption and decryption scheme using matrix operations, where plaintext is encoded into matrices and transformed via linear algebra, then recovered using the inverse matrix. The core mathematical concepts include matrix multiplication, inverse matrices, transpose, and their application in cryptography. The construction uses the Invert command to compute matrix inverses and the Transpose command for transposition, with multiple matrix objects (A, B, m1-m8, n1-n8, d1-d8) storing encryption, decryption, and intermediate data to illustrate the full workflow. This is suitable for high school or undergraduate linear algebra courses to show real-world applications of matrix operations, and for introductory cryptography lessons to explain how matrix invertibility and key design ensure secure communication.

GeoGebra Commands & Parameters

  1. Invert(A) → B
  2. Transpose({{12, 1, 2}}) → m1
  3. Transpose({{9, 16, 20}}) → m2
  4. Transpose({{17, 19, 22}}) → m3
  5. Transpose({{4, 5, 14}}) → m4
  6. Transpose({{21, 5, 20}}) → m5
  7. Transpose({{20, 5, 5}}) → m6
  8. Transpose({{20, 20, 1}}) → m7
  9. Transpose({{2, 9, 16}}) → m8