Notes - Block Cipher

The following are notes from Introduction to Cryptography with Coding Theory.

• also known as the hill cipher
• choose an integer n, the key is an n x n matrix
• M =
• (1   2 3)
• (4   5 6)
• (11 9 8)
• Message is written as a series of row vectors
• abc becomes (0 1 2) which gets 
• (012)(1   2 3)
•         (4   5 6)
•         (11 9 8)
• mod 26
• (0,23,22)
• In order to decrypt we need the determinant of matrix M to satisfy
• gcd(det(M),26)=1
• Find the inverse of matrix M
•       (-14 11 -3)
• -1/3(34 -25  6)
•       (-19 13 -3)
• Since 17 is the inverse of -3 mod 26
•      (22 5  1 )
•      (6 17 24)
•      (15 13 1)
• can return plaintext by mulitplying inverse matrix by (0,23,22) mod 26
• In order to perform the block cipher we just divide the plaintext into blocks of n characters and if the ciphertext does not divide evenly, the blanks are left as 0 but the matrix multiplication is still done
• changing one letter changes n letters of plaintext therefore frequency decryption is very difficult
• Claude Shannon
• the fundamental foundations of cryptography include
• Diffusion
• means that changing one character of the plaintext, then several characters
• Confusion
• means that key does not relate in a simple way to the ciphertext
• each ciphertext should depend on several parts of the key

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