Why traditional metrics are no longer enough

Caesar, Vigenère, alphabetic substitution: all these ciphers share a weakness that frequency analysis lays bare. They retain the structure of the language. A frequent ‘E’ remains a frequent letter once encrypted, and that is enough to give you away.

What a computer changes

Cracking Caesar by hand takes a few minutes. A computer tests all 25 shifts in a fraction of a second. Even the general substitution cipher, with its 26! keys (approximately 4 × 10^26), is cracked in a matter of seconds: the number of keys is enormous, but you never need to try them all. Statistical analysis leads directly to the correct one.

Bear this idea in mind: a large number of keys does not make for a strong cipher. What matters is that there is no shortcut to avoid trying them one by one.

Modern specifications

A robust cipher must withstand an attacker who:

• knows the algorithm inside out (Kerckhoffs’ principle: only the key is secret);
• has plaintext/ciphertext pairs of their own choosing;
• possesses considerable computing power.

In the face of this, the ciphertext must be indistinguishable from random data. Change a single bit of the plaintext: half the bits in the ciphertext must flip. This is the avalanche effect.

Terminology

We denote encryption as E (encrypt) and decryption as D (decrypt):

C = E_K(P)          P = D_K(C)

P is the plaintext, C is the ciphertext, and K is the key. ‘Symmetric’ means that the same key, K, is used in both directions — this is what distinguishes this family from RSA, which you’ll come across elsewhere.