The Enigma Machine

Chapter 2 closed on a bridge: Enigma is, structurally, a polyalphabetic substitution cipher — the same family as Vigenère — but instead of cycling through a short repeating keyword, it mechanically generates a new substitution alphabet on every single keystroke. This chapter is about exactly how it did that: the physical components, the electrical path a signal actually takes, and the daily settings that — per Kerckhoffs's Principle (Chapter 1) — were the only real secret in the whole system.

The Physical Machine, Component by Component

A military Enigma (the German Wehrmacht/Luftwaffe 3-rotor variant this chapter focuses on) is built from five functional parts, wired together in series:

The Electrical Pathway — Tracing a Keypress

Pressing a single key completes a circuit that travels through the entire machine in one direction, then back through most of it in the other direction, before finally lighting a lamp. In order:

Every keypress passes through the rotor stack twice — once outward toward the reflector, once back — which is exactly what makes Enigma reciprocal: with identical settings, encrypting a letter and decrypting a letter are literally the same operation run through the same circuit. That's why the same machine, same daily settings, both encrypted and decrypted — a genuinely elegant piece of engineering, and (as Chapter 4 shows) also the source of its most damaging flaw.

The Rotors — Wiring & Stepping

Each rotor is a disc with 26 electrical contacts on each face, internally wired so that entering on contact A might exit on contact F, entering on B might exit on U, and so on — a fixed, physical monoalphabetic substitution baked into the metal (echoing Chapter 2's substitution ciphers, just implemented as wiring rather than a lookup table).

What makes it more than a fixed substitution is that the rightmost rotor physically advances one position after every keypress, like the units wheel on an odometer — so the substitution it performs on the very next letter is different again. When the rightmost rotor completes a full revolution, it "kicks" the middle rotor forward one position too (with a quirky, historically fiddly detail called double-stepping, where the middle rotor can occasionally step twice in a row); the leftmost rotor advances only rarely. The practical effect: the combined substitution performed by all three rotors together doesn't meaningfully repeat until many thousands of letters have been typed — nothing like Vigenère's short, repeating keyword from Chapter 2.

The Reflector (Umkehrwalze) — Symmetric But Flawed

The reflector is wired as 13 fixed pairs covering all 26 letters (A always reflects to, say, Y and vice versa), and critically, it has one structural property: no letter can ever reflect back to itself. That single design choice — which is what makes the machine reciprocal at all — turns out to be Enigma's single most exploitable weakness, covered in full in Chapter 4.

The Plugboard (Steckerbrett) — Extra Scrambling

Before the German military added it, Enigma's civilian/commercial version relied on the rotors and reflector alone. The plugboard sits at both the very start and very end of the electrical path (steps 2 and 10 above) and swaps pairs of letters via physical cables — typically 10 pairs swapped, out of 26 letters, on a standard military setup. It doesn't change the fundamental structure of the cipher at all — it's still the same rotor-and-reflector substitution underneath — but it multiplies the number of possible daily configurations enormously, which mattered a great deal for the keyspace calculation below.

The Daily Key Settings — What Was Actually Secret

Per Chapter 1's Kerckhoffs's Principle, the machine's design was not secret — the Allies had working Enigma machines. What was secret, distributed via monthly codebooks to every operator, was the daily key:

• Rotor choice & order (Walzenlage) — which 3 of the available rotors were installed, and in what left-to-right order.
• Ring settings (Ringstellung) — an offset between each rotor's internal wiring and its outer letter ring.
• Initial rotor positions (Grundstellung) — the starting letter each rotor was turned to before the message was typed.
• Plugboard pairs (Steckerverbindungen) — which ~10 letter pairs were physically cabled together that day.

Every operator sending or receiving a message that day used the identical settings — get any one piece wrong, and the decrypted output is unreadable garbage from the very first letter.

Enigma's Keyspace — Astronomically Large...

Combining rotor choice and order, ring settings, starting positions, and plugboard pairings, the total number of possible daily configurations for a 3-rotor military Enigma has been estimated at roughly 10¹¹⁴ — a number so large that brute-forcing every possible setting, even with modern computing power, remains completely infeasible. On paper, this looks like an unbreakable system.

Hands-On Exercises