Classical Ciphers Summary

Cryptography · Axiom Academy

Key takeaways from the Classical Ciphers unit in cryptography. Cipher Types & Basic Techniques Substitution Ciphers: Replace plaintext characters with ciphertext characters (monoalphabetic or polyalphabetic) Transposition Ciphers: Rearrange the order of plaintext characters without changing them Caesar Cipher: Simple shift cipher with only 25 possible keys, easily broken by brute force Substitution Cipher: Has 26! (approximately 4×10 26 ) possible keys but vulnerable to frequency analysis Vigenère Cipher: Polyalphabetic cipher considered "unbreakable" for centuries, uses repeating keyword Affine Cipher: Uses linear function E(x) = (ax + b) mod 26, requires gcd(a,26)=1 for invertibility Hill Cipher: Matrix-based cipher that encrypts blocks of letters, vulnerable to known-plaintext attacks One-Time Pad: The only cipher with mathematically proven perfect secrecy when used correctly Breaking Ciphers: Frequency Analysis Al-Kindi's Breakthrough: 9th century mathematician discovered that letter frequencies in ciphertext match plaintext language patterns Single-Letter Frequencies: In English, 'E' appears ~13%, 'T' ~9%, 'A' ~8% - these patterns reveal substitutions Digraphs & Trigraphs: Common pairs ('TH', 'HE', 'IN') and triples ('THE', 'AND', 'ING') provide additional clues Kasiski Examination: Find repeated sequences in Vigenère ciphertext to determine key length, then apply frequency analysis to each alphabet Historical Impact & Real-World Applications

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