Lorenz 2

Alice: So, before we jump into some of the specifics of the Lorenz codebreaking efforts, two key points worth reiterating:

Wheel settings refer to the rotor configurations, while wheel patterns refer to the pin configurations.

The χ-wheels are used for the first set of XOR operations and rotate every time a key is pressed, while the ψ-wheels are used for the second set of XOR operations and sometimes rotate and sometimes stay still.

It can be easy to confuse wheel settings with wheel patterns and χ-wheels with ψ-wheels, so do your best to keep these distinctions in mind, as we'll be using these terms often.

Hanne: Okay.

Alice: Also, we should mention the difference in how the wheel settings and wheel patterns were changed in Lorenz. Basically:

• The wheel settings were changed for every message.
• The wheel patterns were changed every month.

The twelve-letter message indicator at the start of every message was used to communicate the wheel settings, and changing these was straightforward—the German operators simply had to rotate each rotor to the desired starting configuration.

Hanne: Right.

Alice: However, changing the wheel patterns was more involved—it required setting the pins on all 501 rotor teeth to the desired configuration, and doing this for every message would have been impractical. So instead, the Germans updated the wheel patterns once a month and communicated them via key sheets—although later in the war, they started changing them daily. But at least in the early days, the fact that the wheel patterns were only updated monthly made things much easier for the British codebreakers.

Hanne: Got it.

Alice: Awesome. So, let's jump in and explore some of the key events in the British Lorenz codebreaking operations. After Tutte and his colleagues successfully worked out the internal structure of the Lorenz machine in January of 1942, they began developing methods to tackle messages that had what they called a "depth". These were basically the cases where the twelve-letter message indicator was repeated. And messages could have a depth of two, three, or more, depending on how many times the same indicator was repeated.

Hanne: Hmm… but couldn't the British have always broken messages that had a depth—like in the Tiltman Break?

Alice: Well, yes, but remember, the Tiltman Break was just one successful case, and there were many other in-depth Lorenz messages that the British failed to break. However, now that they understood the machine's design, they were able to develop new techniques to tackle these in-depth messages.

Hanne: Ah, I see.

Bob: And one of these early techniques used to tackle depths relied on a weakness in how the ψ-wheels rotated. Tutte discovered this weakness when he was working out the machine's internal structure and later said that without it, he likely wouldn't have succeeded in reverse engineering the Lorenz machine.

Hanne: Interesting. What was the weakness?

Bob: The weakness was simply that the ψ-wheels did not rotate as often as they should have. In some cases, five, six, or even seven characters were encrypted without the ψ-wheels ever moving. These stretches of static ψ-wheels reduced the complexity of the Lorenz machine and made the codebreakers' jobs a lot easier.

Hanne: Huh… lazy ψ-wheels.

Bob: However, within a few weeks, Tutte and his colleagues noticed that this method for attacking depths was not as effective as before. They realised that the Germans had caught on to the ψ-wheels' weakness and corrected it, ensuring that they now rotated more regularly.

Hanne: Oh… so much for the lazy ψ-wheels. Back to work.

Bob: Indeed. And while the British were lucky that this change came after they had figured out the machine's design, they now had to refine their codebreaking techniques to keep up. Fortunately, they managed to do so.

Hanne: Sweet.

Alice: So, by early 1942, the British were successfully breaking most of the in-depth Lorenz messages. However, these messages made up only a small portion of the total Lorenz traffic, and the codebreakers needed to expand on this.

Hanne: Right.

Alice: One day, while reviewing a list of message indicators, Tutte noticed two that were almost identical. This sparked in him the idea of attacking "near-depths"—messages whose indicators weren't identical but similar. Tutte shared his idea with his colleagues, and together they developed methods to tackle these near-depth messages as well. And although it was a much more complex and time-consuming process compared to breaking regular depths, at least it allowed the British to break a larger portion of Lorenz messages.

Hanne: Yay!

Bob: Now, at this point, while the British had made some progress in breaking in-depth and near-depth Lorenz messages, they still hadn't made any headway on the monthly wheel patterns. This was because those early successes merely exploited the weakness of using a repeated key in the Vernam cipher; they didn't reveal what the monthly wheel patterns actually were. However, if the British could figure out how to deduce those patterns, they could then use that information to break even more Lorenz messages.

Hanne: Right.

Bob: This is where Alan Turing came in. In July of 1942, he took a few weeks' break from tackling Enigma to see what he could contribute to the Lorenz operations.

Hanne: Huh… on his "break" from Enigma, he chose to tackle Lorenz. What a guy.

Bob: Yep. And Turing's genius proved decisive yet again, as he developed a method to figure out the monthly wheel patterns in Lorenz. His method became known as "Turingery"—though some called it "Turingismus" or simply "Turing's method". At a high level, it involved:

• Analysing the plaintext and ciphertext of already broken messages in a month.
• Guessing the wheel patterns on a specific χ-wheel.
• Calculating the wheel patterns on the corresponding ψ-wheel.
• Figuring out when the ψ-wheel rotated and when it stayed still.

It was a very challenging and time-consuming process, as contradictions often emerged that required the initial guesses and subsequent deductions to be refined. However, once the wheel patterns for a χ-wheel and its ψ-wheel pair were determined, the information could then be used to work out the wheel patterns in the remaining rotors. And the fact that the ψ-wheels always rotated in unison made this process a lot easier.

Alice: Bill Tutte, however, later remarked that while others were able to get Turing's method to work, he did not have any success with it himself. He described it as being "more artistic than mathematical", and to be fair, it did rely on a lot of heuristics. Still, Tutte acknowledged its immense value and considered Turing's contributions crucial to the overall success of the Lorenz codebreaking efforts.

Hanne: Remarkable.

Bob: So, by August of 1942, thanks to contributions from Turing, Tutte, and others, the Lorenz codebreaking operations had made significant strides. The British could now break in-depth and near-depth Lorenz messages and even work out the machine's monthly wheel patterns. The final challenge was coming up with a technique to break all Lorenz messages—regardless of whether they had a depth, a near-depth, or no depth at all.

Hanne: Right… the depthless Lorenz messages… dun dun duuun!

Alice: To break some of these non-depth Lorenz messages, the British initially began using cribbing. However, this cribbing technique relied heavily on information gained from the in-depth and near-depth messages broken earlier in the month. This meant it was usually only possible to break these non-depth messages later in the month—after enough information had been gained from earlier decrypts.

Hanne: Right.

Alice: Still, things were progressing nicely, and it felt like an all-encompassing Lorenz codebreaking technique was within reach.

Hanne: Ooooh…

Alice: But then, in October of 1942, the Lorenz codebreaking operations faced a major setback, all stemming from a simple change that the Germans made. Instead of sending the twelve-letter indicator at the start of each Lorenz message, the Germans now sent a single number—which mapped to the actual message indicator in a German codebook. However, the British didn't have access to this codebook, and the number gave them much less information than the original twelve-letter indicator did. As a result, the volume of Lorenz decrypts plummeted, and it looked like it would take some time for the operations to recover… if they ever could recover.

Hanne: Oh no.

Alice: And yet—almost as if they needed a greater challenge to overcome, as if a blow had to be struck against them for them to strike back—the very next month, the British developed a technique to break all Lorenz messages!

Hanne: Wow! The old "make it harder for me and then I'll succeed". Amazing!

Alice: Yes. It was called the "1+2 break-in", and it came from none other than Bill Tutte.

Hanne: I see… Bill Tutte really stepped up for the Lorenz problem.

Alice: He certainly did. And even though the British had to keep refining their techniques to keep up with the constant improvements that the Germans made to Lorenz throughout the war, it was Tutte's 1+2 break-in that marked the major breakthrough. Many of the subsequent codebreaking techniques either built on or borrowed ideas from Tutte's method.

Hanne: Got it.

Bob: Also, it's worth pointing out that while Tutte's method worked in theory, because of the sheer number of calculations that it required, it couldn't be reliably implemented in practice—at least, using only manual methods. As a result, just like how the Bombes had to be built to automate the breaking of Enigma, machines had to be built to automate the breaking of Lorenz. We'll say a bit about what those machines were in a bit, but first, let's give you a little insight into some of the principles behind Tutte's 1+2 break-in method.

Hanne: Sounds good.

Bob: Tutte's method made use of the XOR operator, which—just to recap—takes two inputs, either 0 or 1, and returns 0 if they are the same and 1 if they differ. That is:

\(\mathbf{A}\)	\(\mathbf{B}\)	\(\mathbf{A \oplus B}\)
\(1\)	\(1\)	\(0\)
\(1\)	\(0\)	\(1\)
\(0\)	\(1\)	\(1\)
\(0\)	\(0\)	\(0\)

Hanne: Right.

Bob: Now, in a way, XOR can be thought of as addition since:

• Two 0s give 0.
• 0 and 1 give 1.
• Two 1s "wrap around" to 0.

Hanne: Yeah… I can see that.

Bob: And because of this similarity to addition, the codebreakers used the '+' symbol instead of '\(\oplus\)' to represent XOR. So, the '+' in Tutte's "1+2 break-in" method actually means XOR and not standard addition.

Hanne: Ohhh…

Bob: And here are some of the key ideas involved. In November of 1942, Tutte began exploring something called "deltaing". Deltaing is a technique that involves XORing each character in a string with the one that follows it. For example, if the string is "LORENZ", then deltaing means calculating L ⨁ O, then O ⨁ R, and so on.

Hanne: Right.

Bob: This deltaing technique was used because it was thought to reveal patterns that weren't obvious in the raw ciphertext. Turing was the one who came up with it, and it was first used in his method for finding the wheel patterns in Lorenz. However, Bill Tutte took it further. Tutte analysed the main equation that described Lorenz:

\[C = P\ \oplus\ \chi\ \oplus\ \psi\]

where \(C\) is ciphertext, \(P\) is plaintext, χ is the χ-wheel stream, and ψ is the ψ-wheel stream.

And he took the delta of it:

\[\Delta C = \Delta P\ \oplus\ \Delta\chi\ \oplus\ \Delta\psi\]

where \(\Delta\) is the symbol for capital delta—another Greek letter.

Hanne: I see… these mathematicians sure do like their Greek letters.

Bob: Yes, they're quite fond of them. For simplicity, just like he did when solving the design of Lorenz, Tutte analysed the characters on an impulse-by-impulse basis. Thus, he formed the equation:

\[\Delta C_{i} = \Delta P_{i}\ \oplus\ \Delta\chi_{i}\ \oplus\ \Delta\psi_{i}\]

where \(i\) refers to the \(i^{th}\) impulse.

Tutte then took the delta of the first two impulses:

\[\Delta C_{1} = \Delta P_{1}\ \oplus\ \Delta\chi_{1}\ \oplus\ \Delta\psi_{1}\]

\[\Delta C_{2} = \Delta P_{2}\ \oplus\ \Delta\chi_{2}\ \oplus\ \Delta\psi_{2}\]

and XORed them together to get the equation:

\[(\Delta C_{1}\oplus\ \Delta C_{2}) = (\Delta P_{1}\oplus\ \Delta P_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2})\ \oplus\ (\Delta\psi_{1}\oplus\ \Delta\psi_{2})\]

Hence the name "1+2 break-in".

Hanne: Cool.

Alice: And it should be noted that Tutte was analysing already-broken Lorenz messages, so he had all the variables in the equation. And here's what he discovered. Tutte noticed that there was a slight relationship between the delta of the ciphertext and the delta of the χ-wheels. Specifically, he found that their values were the same around 55% of the time. That is:

\[(\Delta C_{1}\oplus\ \Delta C_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2}) = 0\]

55% of the time.

Hanne: Okay…

Alice: This is where the weakness of the pseudorandom nature of the Lorenz machine comes into play. In a truly random system, we would expect there to be no relationship between the different components—that is, there should be a roughly 50-50 split of 0s and 1s.

Hanne: Right.

Alice: However, Tutte found that while there was indeed a roughly 50-50 split for the incorrect χ-wheel settings, for the correct χ-wheel settings it was closer to a 55-45 split. This slight skew gave the codebreakers something to work with, as they could try the different settings for the first two χ-wheels and then calculate:

\[(\Delta C_{1}\oplus\ \Delta C_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2})\]

for each combination. The χ-wheel combination that made this expression 0 around 55% of the time was most likely the correct wheel setting for the first two χ-wheels.

Bob: Right. However, do realise exactly what doing these calculations for the different χ-wheel combinations actually entails. The periods of the first two χ-wheels are 41 and 31, so that is 41 × 31 = 1271 different combinations that the codebreakers would have to try. And this is just to find the wheel settings for the first two χ-wheels.

Hanne: Wow!

(Hanne thinks.)

Hanne: Wait. But isn't this essentially brute force—since the codebreakers are trying all the possible combinations?

Bob: Well, kind of, but not entirely.

Hanne: Huh?

Bob: While this technique is similar in principle to brute force, the analysis is broken up bit by bit, and it is the individual components that are being brute forced as opposed to the entire key itself.

Alice: Right. In a secure system, this should not be possible; the only option should be a brute force attack on the entire key. This was the situation with Lorenz initially, but Tutte's analysis revealed relationships between some of the components that allowed them to be brute forced individually. This made the problem much more manageable compared to brute forcing the entire key in one go, as once the codebreakers can brute force bits of the key, it can reveal information that makes it easier to solve the rest.

Hanne: I see… kind of like brute force, but not entirely.

Bob: Indeed. But still a lot of calculations are involved.

Alice: So, going back to the equation that Tutte formed:

\[(\Delta C_{1}\oplus\ \Delta C_{2}) = (\Delta P_{1}\oplus\ \Delta P_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2})\ \oplus\ (\Delta\psi_{1}\oplus\ \Delta\psi_{2})\]

The next insight that he got was related to the delta of the plaintext. Specifically, Tutte found that:

\[(\Delta P_{1}\oplus\ \Delta P_{2}) = 0\]

60% of the time.

This was because the plaintext wasn't a random string of letters—it was German. And German, like all languages, has structure and patterns. For instance, things like double letters would have always resulted in the delta operation producing 0 and would have played a major role as to why there were slightly more 0s overall compared to 1s.

Hanne: Right.

Alice: And with respect to the ψ-wheels, Tutte found that

\[(\Delta\psi_{1}\oplus\ \Delta\psi_{2}) = 0\]

70% of the time.

If you think more deeply about how the deltaing technique works and how the ψ-wheels rotate irregularly, this high number of 0s makes sense. Deltaing calculates the XOR of a character with the one after it.

• In the cases where the ψ-wheels do not rotate, the pin values remain unchanged, and the deltaing operation always produces 0.
• In the cases when the ψ-wheels do rotate, the pin value might be the same on the next tooth, again resulting in the delta operation producing 0.

Hanne: Hmm…

Alice: Yes… it does take some time to understand this bit. The key takeaway, however, is that the irregular rotation of the ψ-wheels gave the codebreakers another statistical insight into Lorenz because deltaing the ψ-wheels produced 0 about 70% of the time, as opposed to a truly random 50%.

Hanne: Okay. Got it.

Bob: So, just to recap. In the equation that Tutte formed in his 1+2 break-in method:

\[(\Delta C_{1}\oplus\ \Delta C_{2}) = (\Delta P_{1}\oplus\ \Delta P_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2})\ \oplus\ (\Delta\psi_{1}\oplus\ \Delta\psi_{2})\]

He found that:

\[\begin{array}{r c l l} (\Delta C_{1}\oplus\ \Delta C_{2})\ \oplus\ (\Delta\chi_{1}\ \oplus\ \Delta\chi_{2}) & = & 0 & \text{ (55\% of the time)} \\[5pt] (\Delta P_{1}\oplus\ \Delta P_{2}) & = & 0 & \text{ (60\% of the time)} \\[5pt] (\Delta\psi_{1}\oplus\ \Delta\psi_{2}) & = & 0 & \text{ (70\% of the time)} \end{array}\]

Thus, by applying the deltaing method on an impulse-by-impulse basis and analysing the statistical relationships between the deltas of ciphertext, plaintext, χ-wheel, and ψ-wheel streams, Tutte found a way to break Lorenz without relying on depths!

Hanne: Amazing! The complex Lorenz machine had finally been broken.

Bob: That's right. And Tutte later extended this method to tackle the wheel patterns as well. This was extremely useful because Turing's method became less effective when the Germans started changing the Lorenz wheel patterns daily.

Hanne: I see.

Bob: So, that was a basic insight into Tutte's 1+2 break-in method. Hopefully, you now have a better appreciation of just how many calculations it entailed and why relying solely on manual methods was out of the question.

Hanne: Yes, I see why the British needed machines to automate the breaking of Lorenz.

Alice: And with respect to those Lorenz codebreaking machines, it's worth noting that the problem was not as simple as building a codebreaking machine like the Bombe—only adapted to tackle Lorenz instead of Enigma.

Hanne: Why not?

Alice: Well, with Enigma, there was a daily key, and once that was broken, the British could comfortably read all the messages in a day. However, with Lorenz, each message had its own unique wheel setting, which meant that every message had to be broken individually. In this manner, not only did breaking Lorenz require far more calculations than breaking Enigma, but these calculations had to be done to tackle each message as opposed to a single daily key! Thus, the Lorenz codebreaking machines needed to be significantly more powerful than the Bombes for the British to have any chance of reading Lorenz messages.

Hanne: Ohhh… they had to bring out the big guns.

Alice: That's right. And here's a bit about what those big guns—the Lorenz codebreaking machines—were all about. From the onset, Tutte realised that manually implementing his method would have been far too slow. So, after developing it, he approached another mathematician at Bletchley Park by the name of Max Newman. Newman had long been interested in mechanising the codebreaking operations, and when he learnt about Tutte's method, he eagerly took on the task. His section became known as the "Newmanry", and it would become the home of the Lorenz codebreaking machines.

Hanne: The Newmanry… neat. One of these days, I'll have a section of my own, and I'll call it the Hannery.

Alice: Sensational. So… once the requirements for the codebreaking machine were laid out, a design was proposed, and construction began. Around this time, Alan Turing introduced Max Newman to a young engineer named Tommy Flowers. Turing had previously encountered Flowers when exploring the possibility of building additional machines to support the Bombes. Although nothing major came out from that endeavour, Turing recognised that Flowers was a brilliant engineer, so he recommended him to Newman to help with the construction of the Lorenz codebreaking machine.

Bob: And just a bit on Tommy Flowers—before the war, he worked as a telephone engineer for the British General Post Office, where he specialised in switching systems and early electronics. Here, he gained a reputation for his innovative thinking and technical skill. He also did a lot of work at Dollis Hill—the research section of the General Post Office. And it just so happened that Bletchley Park worked closely with Dollis Hill during the war. In fact, the Lorenz codebreaking machine that was under construction was not being built at Bletchley Park but rather at Dollis Hill.

Alice: Indeed. So, when Flowers was introduced to Newman, he was shown the design of the Lorenz codebreaking machine that was under construction. However, after reviewing it, Flowers could tell that the machine wouldn't be fast enough to meet the codebreaking requirements. This was because it relied heavily on relays—mechanical switches that controlled the flow of electricity—and only made use of a few dozen valves, which performed the same function as relays but were fully electronic.

Bob: Right. To put it simply, relays and valves were two devices used to control the flow of electricity. But:

• Relays were slower because they had a mechanical component.
• Valves were faster because they were fully electronic devices with no mechanical component.

However, at the time, it was widely believed that valves were unreliable, as they tended to blow and needed frequent replacement. This is why relays were used instead. But from his pre-war work, Flowers had discovered that valves could be reliable so long as they weren't switched off. It was the constant switching on and off that caused the valves to blow. If, when not in use, the current flowing through the valves was reduced as opposed to being cut off entirely, then valves could last a long time without blowing.

Hanne: Interesting.

Bob: However, it is no exaggeration when we say that Flowers may have been the only person in Britain at that time who understood this about valves. So, when he tried to explain to Newman and the other engineers about building a fully electronic machine using valves rather than relays, his proposal was met with scepticism. It was believed the relay-based machine already under construction had a higher chance of success, and Flowers was left deciding what to do with his vision of the faster, valve-based machine.

Hanne: Oh.

Alice: With minimal support from Newman and Bletchley Park, Flowers assembled a separate team and began working on his valve-based machine—also at Dollis Hill, where the relay-based machine was being built.

Hanne: Good old competition.

Alice: Yep. And it was the relay-based machine that was completed first. It was installed at Bletchley Park in May of 1943 and had a rather elaborate design. The WRNS—Women's Royal Naval Service—who operated the machine at Bletchley Park named it "Heath Robinson", after the popular British cartoonist known for drawing complex and whimsical machines. Just as Flowers had predicted, the Heath Robinson was not fast enough to meet Bletchley Park's codebreaking requirements. It was also unreliable—occasionally producing different results for the same input—and was prone to overheating, sometimes to the point of smoking.

Hanne: Huh! Too slow, unreliable, and prone to overheating… not the best combination.

Alice: That's for sure. But Tommy Flowers and his valve-based machine were largely an afterthought at this point, so Bletchley Park ordered more Heath Robinsons in the hopes of speeding things up.

Bob: Meanwhile, Flowers and his team kept on working on their valve-based machine. Flowers later described the experience as working "in the face of scepticism", saying that few people truly believed his machine would be useful. But in December of 1943, after ten months of persistent effort, Flowers and his team completed the valve-based machine. It was tested at Dollis Hill and delivered to Bletchley Park in January of 1944.

Hanne: Yay!

Bob: The machine was enormous and was much larger than the Bombes and the Heath Robinsons. It took up an entire room and used about 1500 valves. The WRNs called it "Colossus", and to everyone's surprise, it was significantly faster and more reliable than the Heath Robinsons. Flowers later remarked:

I don't think they really understood what I was saying in detail—I am sure they didn't—because when the machine was constructed and working, they obviously were taken aback. They just couldn't believe it!

Alice: The remaining orders for the Heath Robinsons were cancelled, and new orders were placed for more Colossus machines. Flowers, however, stressed that to meet Bletchley Park's urgent timeline for these additional machines, he would need more staff. He pointed out that the first machine had taken ten months to build even though his team "did nothing but work, eat, and sleep for weeks and months on end".

Hanne: Huh!

Alice: Flowers and his team also gained valuable insights from building the first Colossus and observing how it was used in practice. This allowed them to make refinements to subsequent versions, making them more flexible and easily adaptable to Bletchley Park's evolving codebreaking techniques.

Bob: The second Colossus became operational at Bletchley Park on June 1, 1944, just days before D-Day—more on D-Day later. After that, new machines were delivered to Bletchley Park roughly every seven weeks. By May 8, 1945, the end of World War II in Europe, ten Colossus machines were in operation, with two more in production.

Alice: And here's a little fact about Colossus that we'll expand on later—Colossus, first operational at Bletchley Park in January of 1944, was the world's first electronic computer.

Hanne: Oh… wow!

Alice: Indeed. So… that was a bit on Colossus—the main British Lorenz codebreaking machine.

Hanne: I see. Good thing Tommy Flowers kept on believing in his valve-based machine, despite all the scepticism.

Alice: Definitely. Without Colossus, Bill Tutte's methods couldn't have been reliably implemented, and the British would have had far less success in breaking the Lorenz machine.

Hanne: Right.

Bob: And just a reminder—since you may have forgotten it after all the technical discussions—Lorenz was reserved for use by German high command during World War II. Thus, these decrypted messages were of great strategic value to the British and played a significant role in their military campaigns—especially in the latter part of the war.

Hanne: Understood.

Bob: Awesome. So, that wraps up the Lorenz codebreaking story. In a nutshell, the British managed to break this incredibly complex cipher machine without ever actually seeing the machine or any documents related to it. Instead, they mathematically reverse engineered it, built one of their own, developed numerous techniques to break it, and ultimately had to build the world's first electronic computer to implement some of their codebreaking techniques.

Hanne: Extraordinary!

Bob: Absolutely. And it was especially thanks to the contributions of Bill Tutte and Tommy Flowers that the British were able to successfully break Lorenz.

Alice: And on that note, remember how we ranked the top three figures in the Enigma codebreaking efforts at Bletchley Park as Alan Turing, Dilly Knox, and Gordon Welchman?

Hanne: Yes.

Alice: Well, if we broaden the scope to the entire Bletchley Park operations—not just related to Enigma—we'd rank the top five most influential figures as:

• Alan Turing
• Bill Tutte
• Tommy Flowers
• Dilly Knox
• Gordon Welchman

We'd place Bill Tutte and Tommy Flowers above Dilly Knox and Gordon Welchman because Lorenz was more complex, and the decrypted messages were of greater strategic importance. Plus, Tutte's reconstruction of the Lorenz machine from a single 4000-character key and Flowers' development of the Colossus machines were truly incredible. But even so, we might still shuffle positions two through five depending on how we feel on the day. All four of those men made significant contributions to the work at Bletchley Park, and it is tough to definitively place one above the other. However, for us, Turing remains a clear number one in terms of the overall impact he had on Bletchley Park's codebreaking success.

Hanne: Indeed. He worked on both Enigma and Lorenz and made significant contributions to both operations.

Alice: Correct.

Bob: Finally, here's a timeline of the key events in the Lorenz codebreaking story to put it all together: