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Figure 2.9: Purple encryption. of using permutations wired to rotors-which only requires one permutation per rotor-each step of Purple s S , L , M , and R switches t o a different, unrelated, hardwired permutation. Consequently, we refer to S , L , M , and R as switches and Purple as a stepping switch machine. While the distinction between rotors and switches might seem relatively minor, it is actually a major difference. For one thing, a stepping switch machine like Purple is inherently more complex and difficult to engineer than a rotor machine. From a cryptanlytic point of view, a rotor machine provides an elegant way to generate a large number of permutations, while a comparable stepping switch machine must be far more complex. There are also significant differences between the types of permutations that can be generated by Purple and Enigma, as discussed below and in Problem 16. The Purple encryption formula depending on whether the letter being encrypted corresponds to a six or twenty . Let x be the given input letter and let y be the corresponding output letter. Then we can denote the encryption by

where PI is the input plugboard permutation (when going from the input keyboard to the switches), PO is the output plugboard permutation (from

Leaving out the imaginary part ([Durbin and Rumelhart 1989] show that the added complexity of including the imaginary part does not help with increasing performance) ,

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the output keyboard to the plugboard). Note that PI and PG1 follow the direction of the arrows in Figure 2.9. Also, PL, P ~ Iand PR are the left, , middle, and right twenties permutations, respectively, and Ps is the sixes permutation. As mentioned above, the Japanese always selected PI = PO. A major practical difference between Purple and Enigma is that Purple is not its own inverse (Problem 6 asks you to show that Enigma is its own inverse). This means that decryption with Purple is more complicated than with Enigma. Since decryption requires the inverse permutations, Purple can be decrypted by reversing the flow through the diagram in Figure 2.9, as illustrated in Figure 2.10. This implies that the output plugboard is used for input and the input plugboard for output. Of course, if the plugboards have identical permutations (as, apparently, was always the case with Purple), then it does not matter which plugboard is used for input and which is used for output.

Type the project name. Select the Move selected items to new project check box if you want to move your selected images into the new project.

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Since the decryption formula works for any choice of PI and PO, why did the Japanese always select PI = PO If PI = PO, then a single plugboard

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Another very common task in Aperture is to make a new, empty album at the project or library level and then move images into it. For example, we might make a Submit to Agency album and then drag whatever images we want to submit to our stock agent into that album. Another common task is to make a new album at the project level prepopulated with the images you ve selected in Browser, such as if you select all the images of a certain subject and want to make a new album just for that subject. These tasks are straightforward and similar to making a new project.

can be used Assuming there were two physical plugboards present in Purple, perhaps it was the case that it was easy t o swap the input and output keyboards, but not the plugboards If so, then it would still be possible t o decrypt when PI # Po, but the plugboards would have t o be wired with the inverse permutations t o do so This would have necessitated different encryption and decryption settings and, in particular, would have made it difficult t o do trial encryptions and decryptions, which could be used t o verify the key settings In contrast t o the Enigma, Purple plugboards are not necessarily their own inverse, since the plugboards do not connect pairs of letters, as is the case with Enigma Instead, the Purple plugboards connect 26 letters t o 26 letters so they can implement any permutation.

Since there are 25 steps on each of the switches S, L , M , and R, each switch has a cycle length of 25 Since exactly one of the switches L , M , or R steps with each letter, overall, the twenties have a cycle length of 25 2525 = 15,625, while the sixes have a cycle length of 25 As mentioned above, the S switch determines which of L , M , or R steps When setting the Purple cipher, it is necessary t o specify which of L , M and R are fast, medium, and slow switches The fact that only one of the twenties switches steps with each letter leads t o a somewhat complicated stepping process, which we now describe.

Choose one of the following options to begin creating an album:

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