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Figure 10: Type 8 Safe Locker [5]

Figure 11: Army Field Safe CH 76 [5]

2.5 Theoretical Keyspace

First, we will discuss the theoretical keyspace of the SIGABA machine. We consider a key 

to include the follow.

1. The choice of the five cipher rotors.

2. The choice of the five control rotors.

3. The choice of the five index rotors.

Each cipher and control rotor permute the 26 letters of the alphabet. This means that each 

cipher and control rotor have 26! different possible permutations. Similarly, the index 

rotors permute the digits to another digit. This means the index rotors each had 10! different 

permutations. Combining these different permutations gives a theoretical keyspace of (26!)

5 

* (26!)

5

 * (10!)

5

 ≈ 2

993

 different keys for the machine. We do not need to consider the 

starting positions of the 15 rotors in this calculation since we are considering all possible 

rotor wirings. A different starting position would be equivalent to another rotor wiring. For 

15

---

this reason, we can treat all the possible rotor wirings as being set to some standard starting 

position. Since the index rotors do not step at all during the operation of the machine, the 

(10!)

5

 permutations for the index rotors reduce down to 10! distinct permutations. This 

reduces the theoretical keyspace down to (26!)

10

 * 10! ≈ 2

906

.

The theoretical keyspace seems to indicate that the key is the equivalent of a modern cipher 

key that is 906 bits long, which is over three and a half times longer than the largest 

encryption key today of 256 bits. If this were true, it would certainly explain why there are 

no recorded instances of SIGABA ever being broken during the war by enemy forces. 

However, is this keyspace accurate? Unfortunately, the answer is no. SIGABA did not have 

a real keyspace of 906 bits. Several factors limited the actual keyspace of the machine 

during its operation lifetime.