Cryptography: Diffusion and Confusion

•Diffusion means that if we change a character of the plaintext, then several characters of the ciphertext should change, and similarly, i-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: +mn-cs; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: green; mso-style-textfill-type: solid;">if we change a character of the ciphertext, then several characters of the plaintext should change.

–dissipates statistical structure of plaintext over bulk of ciphertex

•Where did we see this?

•We saw that the Hill cipher has this property.

–This means that frequency statistics of letters, [digraphs], etc. in the plaintext are diffused over several characters in the ciphertext, which means that much more ciphertext is needed to do a meaningful statistical attack.

•Confusion means that the key does not relate in a simple way to the ciphertext.

–each character of the ciphertext should depend on several parts of the key.

–makes relationship between ciphertext and key as complex as possible

•For example, suppose we have a Hill cipher with an n*n  matrix, and suppose we have a plaintext-ciphertext pair of length n2 with which we are able to solve for the encryption matrix.

–If we change one character of the ciphertext, one column of the matrix can change completely.

•When a situation like that happens, the cryptanalyst would probably need to solve for the entire key simultaneously, rather than piece by piece.