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MobileMe is a set of online services offered by Apple for $99 per year (as of this writing). One of its nice features is that it provides a sophisticated gallery system, where you can view slide shows and upload new images, which are synced back to Aperture, right from your Browser. Aperture 3 makes it easy to create a MobileMe Gallery album.

(3,4) (4,l) 4

(O,9) 1

To set up a new MobileMe Gallery album, follow these steps:

(5,6)

The function h m n , k j ( t ) in equation (4.19) is referred to as the neighborhood function. Thus, only those neurons within the neighborhood of the winning neuron mn have their codebook vectors updated. For convergence, it is necessary that hmn,kj (t) > 0 when t -> oo.

(7,8) (9,O) (2,5) (3,7) 4 7

Assuming the control rotors generate random permutations, the expected number of steps for cipher rotor i depends solely on the number of control rotor output letters that feed into C,, as illustrated in Figure 2.22. All of the 45 possible input pairs and the corresponding number of control rotor output letters are tabulated in Table 2.10. Table 2.10: Index Permutation Input Pairs Letters 1 Count 3 Pairs (0 1) (0 9)

1. 2.

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If we have sufficimt known plaintext available, we obtain information on the count column of Table 2.9 for each cipher rotor simply based on a count of the number of times that cipher rotor i steps. Then from the pairs column, we obtain putative restrictions on the index permutation. Other restrictions apply which further reduce the number of cases that must be considered; see Problem 27. Using the available information, we can reduce the number of possible index perniutations to a small fraction of the 10!/32 216 permutations that

The neighborhood function is usually a function of the distance between the coordinates of the neurons as represented on the map, i.e.

we would otherwise need to consider In fact, with sufficient known plaintext, the average number of permutations that we need to check is about 27 (the range is about 24 to 21 ) However, there is significant variability in the amount of known plaintext required to distinguish the control rotor counts, depending on the actual underlying index permutation With this refinement, the average work factor for the secondary phase of the attack is about 27 5 ! 25 2G5 N 2424 which is somewhat less than the primary phase of the attack However, this work factor applies to each survivors from the primary phase, and we expect a large number of primary survivors Consequently, we could improve the attack by either reducing the number of primary survivors or making the secondary phase more efficient (or both).

Select the images to initially include in your gallery. Choose File Share MobileMe Gallery. Aperture opens the New MobileMe Gallery Album sheet, as shown in Figure 8.25.

Note that in this secondary phase, the actual index rotor settings are not-and in fact cannot be--recovered Several details of this phase of the attack are explored more fully in Problems 27 and 28 Thc typical secondary work factor for each primary survivor is on the order of 243, assuming sufficient known plaintext is available This amount of work is clearly feasible, although the attack is not trivial to implement The primary phase of this attack has a similar work factor and it is also feasible However, for the attack described in this chapter, the primary phase yields a larger number of survivors, which makes the overall cost of the secondary phase high In any case, either phase of this attack would have been far beyond the realm of 1940s technology.

Nevertheless, the attack outlined above offers a dramatic shortcut as compared to an exhaustive key search, which, under the assumptions of this section, would have a work factor of about 295 Problem 33 suggests one method for improving the attack described in this chapter For the definitive treatment of this attack-including several improvements over the outline given in this chapter-see [28]..

hmn,kj(t) = h(\\Cmn - Ckj\\2,t)

3. 4.

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