Schneier on Security

Bear • December 9, 2016 2:30 PM

The M4 Naval model is extremely rare. The ones on the vessels mostly sank with the vessels (or were thrown overboard the instant it looked like the vessels might be boarded) and the naval shore stations were built in well-protected positions well behind the lines, where the Allies weren’t likely to make a pinch.

In point of fact the codebooks that gave the operators their daily keys for the month (destroyed with about the same reliability as the machines) were hundreds of times more important from an intelligence POV; the guys at Bletchley and Arlington knew the the mechanical details and rotor wirings of the M4 from a few months after it went into service.

There’d have been an exception for about three months after the M4 went into service – before they’d figured out the wirings, getting a machine in hand would have been a significant shortcut.

I’ve thought about the Enigmas way too much, and if the designers had been just a bit more savvy about the math they could have been utterly impossible to break. A redesign of the Enigma (mostly reusing the same parts) would have made it effectively immune to anything possible during WWII.

Encoding the letters as a positive and negative impulse to make two paths through the maze, instead of using a reflector to make two paths through the maze, would have solved the antireflexive property that the bombes used against them.

That cuts the number of I/O positions needed to express a 28-character alphabet down to 8 (assuming they didn’t care which direction the current is running. 6 positions for a 30-character alphabet if you add a bunch of diodes).

Connecting 8 positions to the keyboard on one end, and 8 positions to the light board on the other end, leaves you a significant chance that the impulses from input will come through on paths that don’t lead directly to the positions used for output. This is a good thing for security because you have a steckerboard.

Take the 18 positions not used for input, and the 18 positions not used for output, wire them together through the steckerboard, and now the impulses travel through an indeterminate number of paths through the maze. Each travels at least one path through the maze, and if it doesn’t reach an output post it just takes another trip through until it does.

Because reflexivity has been eliminated, you have to add a double-throw 8-pole switch to go from encrypting to decrypting. It would just switch the connections from keyboard to lightboard and vice versa.

Not only do the bombes not work anymore, but because of the indeterminate number of paths through the maze and stecker this is no longer a “neat and simple” problem in group theory. You can’t isolate the sequence of offsets of the first wheel, for example, because the first wheel is making two different offsets simultaneously and they are independently disrupted by the stecker settings.

There is still one way in, but it’s hard. 9.4% of the characters transmitted will not go through the stecker and additional paths, and if you can sort out the statistics and figure out which 9.4% of the characters those are, you can still solve it as a group theory problem. But it’s a very hard one, and would have been far beyond WWII cryptanalytic efforts. Also, I don’t think there was enough traffic in any one key to pull it off.

Bear • December 9, 2016 2:51 PM

I forgot to mention the last detail. The above description uses only 18 positions of the stecker I/O, leaving 8. In truth you should be using all 26 positions of the stecker input wired to all 26 positions of the last wheel, with 8 of the stecker outputs wired to output and 18 wired back to input.

So everything would go through the steckerboard at least once, and combinatorics being what they are the stecker difficulty has been squared (in addition to whatever is available from additional trips through the wiring maze).

Bear • December 9, 2016 3:00 PM

Yes, the Lorenz machine was much better, if you had the space, the weight allowance, and the reliable power source to run it. In practical terms machines that combined encryption and transmission into a single operation were less subject to operational errors. But they were not portable, not compact, not easy to hide, not easy to throw overboard, and usually not usable unless connected to ‘mainline’ electrical power supply or equivalent.

Also the Lorenz machine is still a “neat and simple” group theory problem because it doesn’t use feedback. The cryptanalyst knows that each ‘bit’ of the output has taken exactly one path through the rotors and has taken it in parallel, with the rotors at the same position that every other bit passed through, and that the keyed bit inversions are applied consistently to the same set of parallel paths. It’s a much BIGGER group theory problem than the Enigma, but it’s still ‘neat’.

Bear • December 9, 2016 5:26 PM

Of course I know about the SIGABA. Never successfully cryptanalyzed, without a doubt the strongest rotor cipher machine ever used. But not available at the time and you sure as heck couldn’t build one using the parts from an Enigma, and have it fit in the same box.