431 Enigma - 52-bit Key Length :: Quicker, easier and cheaper to make your own chip!

How it works

Background

This project features a silicon implementation of a 52-bit equivalent key model of the WWII-era Enigma code machine used by the Germans. The British, led by Alan Turing (as depicted in The Imitation Game), cracked this code, giving the Allies a crucial advantage in the war.

This electronic version is accurate and will match any simulator you can find on the web^1. Although almost every Enigma operates on similar principles, the particular model implemented here is the Enigma I^3 used by the German Army and Air Force; it comes with 3 rotor slots, the 5 original Rotors, the UKW-B Reflector, and plugboard. The only limitation is that the plugboard only supports 3 wires, whereas the actual wartime procedure was to use up to 10 wires. This limits the key length of this implementation to 52-bits. The calculation is shown below.

Key-length Calculation

The Enigma is a symmetric^4 encryption engine, and the equivalent key length is comprised of the different settings and ways the rotors and plugboard can be arranged. See the excellent analysis^5 from Dr. Ray Miller at NSA for more details on the calculations below:

Selecting the three rotors, which can be arranged from right to left in any order:

5 x 4 x 3 = 60 possible ways
Starting position of each rotor:

26 * 26 * 26 = 17576
Ring of each rotor (only two right rotors matter):

26*26 = 676
Plugboard with 3 wires (see table on p.9 for p=3^3):

= 26! / (26-6)! / 3! / 8 = 3,453,450 ways to plug in 3 wires

The total ways (# of keys) to set up this particular Enigma is therefore:

60 * 17576 * 676 * 3,453,450 =  2,461,904,276,832,000 ways

yielding a key length of ~52-bits.

Implementation

Using the Python-based hardware description tool Amaranth HDL^7 for the first time made building, testing, and generating the Verilog implementation much easier. Given the complexity of the rotors’ input-output mappings, I would’ve needed to write Python scripts anyway to generate Verilog logic. Amaranth streamlined this process and allowed seamless integration with my reference Python implementation for test generation.

Rotor design:
- Meeting the tight area requirements involved several design iterations that narrowly missed targets late in the cycle. Amaranth’s flexibility made re-architecting much simpler. For example, my initial approach of implementing three separate combinational hardware rotors was too large and lacked configurability. I ultimately created a single reconfigurable rotor block that processes data over six cycles, effectively forming a six-rotor pipeline (three forward, three backward after reflection).

Plugboard Design:
- Initial Attempt: A 26-entry, 5-bit lookup table using DFFs, which proved too large.
- Next Approach: A scan-chain-based design, but the hold-fix buffers and comparison logic made it even larger.
- Final Solution: A 26-entry, 5-bit lookup table using Skywater 130 standard-cell latches. This worked well since the plugboard functions like a ROM, with only a few initial writes to set the configuration. These writes are precisely pulsed using the state machine.

Key statistics
Utilization	81%
Cells	1583
DFF	67
Latches	130
Frequency	35MHz

Operation

The Enigma is designed to accept an 8-bit input (command plus data) at the clk edge. The internal state machine then takes a varying number of clk cycles to respond, raising the "Ready" signal when it's ready to accept the next command. If the command generates an output, the raw value will be output on the bidir pins, and the LCD display will show the character generated.

Pinouts

Description	Width	Direction	Signal(s)
Command	3	in	ui_in[7:5]
Data	5	in	ui_in[4:0]
Scrambled output char	5	out	uio_out[4:0]
Ready	1	out	uio_out[5]
7-segment LCD	7	out	uo_out[6:0]

Commands

The machine accepts the following 8 commands:

Encoding[^6]	Command	Data	Description
000	NOP	N/A	Do nothing
001	LOAD_START	Setting 0-25 (A-Z)	Set the start position of a rotor. Do this three times in succession to set each of the three rotors (right to left)
010	LOAD_RING	Setting 0-25 (A-Z)	Set the ring setting of a rotor. Do this three times in succession to set each of the three rotors (right to left)
011	RESET	N/A	Go back to the initial state
100	SCRAMBLE	Input char 0-25 (A-Z)	Run a letter through the rotor. The Ready signal will be asserted when the scrambled character is output
101	LOAD_PLUG_ADDR	Src 0-25 (A-Z)	Set an internal register to where the start of the plug should go. This command should be followed by LOAD_PLUG_DATA to set the destination
110	LOAD_PLUG_DATA	Dst 0-25 (A-Z)	Set the other end of the plug. Note that this connection is unidirectional, so if you want A,B connected, then you need to do two sequences of these commands to first set A->B and then B->A
111	SET_ROTORS	Rotor 0-4	Pick the Rotor type for each slot where Rotor I=0, Rotor II=1, ... Rotor V=4. Do this three times in succession to pick each of the rotors (right to left). Default is Rotor I, II, III from right to left, where Rotor I is closest to the plugboard

Sample run

At some point, I'll have some code ready for running on the RPi on the PC, but for now, here is the pseudo code for setting up and scrambling/descrambling with this machine:

    # Install the rotors
    send_command(SET_ROTORS, 0)   # Set slot 0 to Rotor I
    send_command(SET_ROTORS, 1)   # Set slot 0 to Rotor II
    send_command(SET_ROTORS, 2)   # Set slot 0 to Rotor III

    # Dial start position of the rotors
    send_command(LOAD_START, 15)  # Set rotor 0 start position to P
    send_command(LOAD_START, 5)   # Set rotor 1 start position to F
    send_command(LOAD_START, 1)   # Set rotor 2 start position to B

    # Dial ring position of the rotors
    send_command(LOAD_RING, 18)  # Set rotor 0 start position to S
    send_command(LOAD_RING, 5)   # Set rotor 1 start position to F
    send_command(LOAD_RING, 24)  # Set rotor 2 start position to Y

    # Set up the plugboard
    # First, configure the plugboard default configuration with 
    # no swizzling of letters
    for i in range(26):
        send_command(LOAD_PLUG_ADDR, i)
        send_command(LOAD_PLUG_DATA, i)

    # Now, plug in three wires
    send_command(LOAD_PLUG_ADDR, 0)    # connect A -> N
    send_command(LOAD_PLUG_DATA, 13)

    send_command(LOAD_PLUG_ADDR, 13)   # connect N -> A
    send_command(LOAD_PLUG_DATA, 0)

    send_command(LOAD_PLUG_ADDR, 3)    # connect D -> E
    send_command(LOAD_PLUG_DATA, 4)

    send_command(LOAD_PLUG_ADDR, 4)   # connect E -> D
    send_command(LOAD_PLUG_DATA, 3)

    send_command(LOAD_PLUG_ADDR, 25)    # connect Z -> B
    send_command(LOAD_PLUG_DATA, 1)

    send_command(LOAD_PLUG_ADDR, 1)   # connect D -> Z
    send_command(LOAD_PLUG_DATA, 25)

    # Now, enter letters into the machine and watch the coded char
    # appear on the display
    send_command(SCRAMBLE, 11)  # 'L' -> 'X'
    send_command(SCRAMBLE, 14)  # 'O' -> 'K'
    .
    .
    .

[^6]: See the src/defines.py file

Control FSM

alt text

The state machine diagram source can be found on github^8.

How to test

Design verification

Generate the verilog from the Amarangth HDL source
```
 cd tt10-enigma
 python -m src.top
```
This will write a file src/am_top.v with the Enigma block. This block is connected to the TinyTapeout harness using src/project.v
Run the functional test
```
 cd test
 make
```
Run the gate-level tests: After hardening (synthesis/pnr/gds), copy the gate_level_netlist.v into the test/ directory. Then:
```
 make -B GATES=yes
```

External hardware

None. Uses the built-in 7-segment display on the PCB.

#	Input	Output	Bidirectional
0	din[0]	seg[0]	dout[0]
1	din[1]	seg[1]	dout[1]
2	din[2]	seg[2]	dout[3]
3	din[3]	seg[3]	dout[4]
4	din[4]	seg[4]	dout[5]
5	cmd[0]	seg[5]	ready
6	cmd[1]	seg[6]
7	cmd[2]	GND

431 Enigma - 52-bit Key Length