General Monoalphabetic Substitution

An arbitrary permutation of the alphabet: 26! keys, and letter frequency still hands it over.

Monoalphabeticdemo

Objectives

Build a substitution key as a permutation of the alphabet.
Compare the keyspace against a brute-force budget.
Explain why a fixed letter-to-letter map leaks frequency no matter how large the key is.

50%

Key = an arbitrary permutation of the alphabet.

Key (26 letters, each used once)

✓ valid permutation

plain

cipher

Plaintext

ciphertext

VTIQC TQDGS TQWGK ZZITR TQS

Keyspace

26! ≈ 2^88.4 keys

Larger than DES (2⁵⁶). Larger than every key you could brute-force this decade.

A big keyspace is necessary, not sufficient. This cipher was broken by al-Kindi around 850 CE without any machine. The key is huge but the structure of the language leaks through. Frequency analysis is the tool to exploit that structure.

step 1/2

CPE 645 / CS 685

General Monoalphabetic Substitution

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