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as claimed in [go]. However, a careful reading of the Sigaba manual [113] reveals that the setting of the control rotors was sent in the clear as a message indicator or MI. Therefore, assuming the MI was intercepted and its meaning was known to the attacker, the actual keyspace for Sigaba-as it was generally used in WWII-was of size
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lo! . 210 . 105
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as (correctly) stated in the article [lag]. But, on the POTUS-PRIME' link between Roosevelt and Churchill, the control and cipher rotor settings were set independently, and neither was sent in the clear, which implies a keyspace in excess of 95 bits [l28]. In the next section we provide a precise calculation of the keyspace for this particular case. A keyspace of size 248.4is small enough that today it is susceptible to an exhaustive key ~ e a r c h . But a keyspace of this magnitude would have ~ been unassailable using 1940s technology, provided no shortcut attack was available.
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For this attack, we assume that all three banks of rotors are set independently. We also assume that there is only one set of index rotors, and that these five rotors can be placed in any order, and that a total of ten rotors are available for use as cipher and control rotors. The control and cipher rotors can be inserted in any order and there are two orientations for each of these rotors. Under these assumptions, the keyspace is apparently of size
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However, due to the fact that pairs of index rotor outputs are ORed together to determine the cipher rotor stepping, effectively only
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distinct index permutations can occur. This reduces the feasible keyspace size to lo! . 210 . 2G10 . 216.8 M 295.6 or less. This full keyspace of size 295.6 was used on the POTUS-PRIME link between Roosevelt and Churchill, but not on other links. Again, this represents
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8President Qf The United States PRIME Minister. 'The Data Encryption Standard (DES) has a 56-bit key and it has been successfully attacked by an exhaustive key search.
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the largest Sigaba keyspace that was available in WWII. That is, it represents the largest practical keyspace, given the hardware that was typically available with a Sigaba machine in WWII. Increasing the number of available rotors would increase the keyspace, but we limit ourselves to the number of rotors that will fit in the device at one time, since this is typically all that was available with the cipher. Finally, we assume that all of the rotors and the inner workings of the device are known to the cryptanalyst. Our attack requires some amount of known plaintext. This attack occurs in two phases--a primary phase and a secondary phase. In the primary phase, we try all cipher rotor settings, retaining those that are consistent with the known plaintext. Then in the secondary phase, we guess the control and index rotor settings, and again use the known plaintext, this time to whittle down the number of possible keys to a very small number of candidates. Suppose that we have a Sigaba-encrypted ciphertext message, where the first several letters of the corresponding plaintext are known. Our goal in the primary phase is to recover the cipher rotors, their order, orientations and initial settings. Collectively, we refer to these cipher rotor initializations as the cipher rotor settings. In the primary phase, we strive to reduce the number of cipher rotor settings to a small number--ideally just one. We refer to an incorrect choice of cipher rotor settings as a random setting, while the correct setting is said to be causal. For each cipher rotor setting that survives the primary phase, a secondary phase is required. This secondary phase consists of trying all possible control and index rotor settings to determine which are consistent with the known plaintext. In this way, the random primary survivors are eliminated and, in the causal case, we determine the key. Primary Phase We are assuming that ten different cipher rotors are available. Also, each cipher rotor has two possible orientations and 26 possible initial positions. Therefore. the number of ways to select and initialize the five cipher rotors is
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For each of these choices, we determine whether the setting is consistent with t,he known plaintext as follows. Recall that for each letter typed, from one to four of the cipher rotor rotates. This implies that once we specify the cipher rotors, their orientations and their initial settings, the number of possible new permutations at any
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