Classical and Polyalphabetical Ciphers

Classical Substitution Ciphers

• Every plaintext character in A is replaced (substituted) by another suitable character from the secret text B.
• There are two alphabets: a - plaintext, b - secret text and f is unique.
• f(a) = b, where f is the substitution function.
• Each plaintext letter maps to a different random cipher text letter, making the key 26 letters long.
• The total number of keys is 26! (4 x 10^26).
• Despite the large number of keys, it is not secure because of language redundancy and characteristics.

Language Redundancy and Cryptanalysis

• Human languages are redundant, meaning some letters and combinations occur more frequently than others.
• In English, the most frequent letters are e, t, r, n, i, o, a, s.
• Less frequent letters include z, j, k, q, x.
• Frequency tables exist for single, double, and triple letter sequences.

Polyalphabetical Ciphers

• Each plaintext character a is converted into many secret alphabets b1, b2,…, fi : a → Bi.
• i = 1, 2, 3, …
• A special case is a Polyalphabetical cipher with period p: fi : a → Bi, where i = 1, 2, 3, …, p.
• p is the period of the cipher.
• When p = 1, the cipher is a monoalphabetical cipher.

Vigenere Cipher

• It is the simplest polyalphabetic substitution cipher.
• Uses a set of all Caesar ciphers: {Ca, Cb, Cc, …, Cz}.
• The key is a word, e.g., "security".
• Each letter is encrypted using the Caesar ciphers in turn based on the key letters (Cs, Ce, Cc, Cu, Cr, Ci, Ct, Cy).
• The process repeats from the beginning after reaching the end of the key.
• Decryption works in reverse.
• Formula for Vigenère cipher:
  • Encryption: c = (m + ki) mod n
  • Decryption: m = (c - ki) mod n where:
  • c is the ciphertext character
  • m is the plaintext character
  • ki is the key character at position i
  • n is the size of the alphabet (26 for English).

Transposition Ciphers

• Hide messages by rearranging letter order without changing the letters themselves.
• They preserve the original text's frequency distribution.
• They do not change the characters in the plaintext; they simply reorder them.

Rail-Fence Cipher

• A simple, easy-to-crack cipher.
• The key is the number of rails.
• The message letters are written diagonally over a number of rows.
• The ciphertext is read row by row.
• Example: the message "meet me after the toga party" is written as:
  • mematrhtgpry
  • etefeteoaat
• The ciphertext is: MEMATRHTGPRYETEFETEOAAT.

Column Transposition Ciphers

• A more complex scheme.
• The message letters are written in rows over a specified number of columns.
• The columns are reordered based on a key.
• The ciphertext is read off row by row.
• Algorithm:
  1. Create a table with specified columns and index them from 1.
  2. Fill each cell in turn with a character from the plaintext, reading from left to right and moving to the next row when a row is full.
  3. If there are any empty cells in the last row, fill them with character 'X'.
  4. Read the cells in turn based on the order specified in the key.
• This process produces the ciphertext.

This quiz explores the concepts of classical substitution ciphers and polyalphabetical ciphers. It covers how plaintext characters are substituted with secret characters, the implications of language redundancy on cryptanalysis, and the use of multiple alphabets in cipher creation. Test your understanding of these cryptographic techniques and their vulnerabilities.