HILL CIPHER
HILL CIPHER
1. Background: Matrices
[pic]
A is 2X2 matrix
2. Matrix multiplication:
[pic]
3. Matrix by vector multiplication
[pic]
4. Determinant of the 2X2 Matrix
[pic]
5. Theorem: 2X2 matrix A is invertible modulo m if and only if det(A) is relatively prime to m. In this case the inverse matrix is given by:
[pic]
Hill Cipher
Key Matrix: 2X2 matrix
Condition: The key matrix has to be invertible mod 26
Given Plaintext: p1p2p3p4…..pn-1pn
Given Key Matrix: [pic]
Encryption:
1. Form vectors as follows:
[pic]
2. Multiply each vector by A to obtain a pair of ciphertext letters:
[pic]
3. The ciphertext is: c1c2….cn
Decryption:
1. Calculate A-1
2. For each pair of ciphertext find a plaintext by:
[pic]
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