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The results in Table 3.8 show that Trudy can expect to reduce the numher of surviving fills to one single candidate using only six keystream bytes. However, to completely determine the 32 bits in each register will require at least 25 keystream bytes, since ko is used to determine bits 24 through 31, while each subsequent k , determines only a single bit of registers A and X , while, on average, each keystream byte determines 1.5 bits of register B . Since t,he registers step before the first keystream byte is generates, this attack does not recover the original fills ( X ,A , B ) ,but instead, it recovers the fills ( X >> l , A >> l , B > s ) , where s is one or two, depending on whether B > steps once or twice on the first iteration. In any case, given the recovered fills, it is a simple matter to determine the actual initial fills-although it is not necessary to do so t o decrypt the message. Assuming that !keystream bytes are used, the expected work required for this attack is

1.18 c 1

1 20

11.00 1.19602 2 d 0.68088

1 2 . (65,536

99 Oxygen purity y (%)

Figure 11-8 Scatter diagram of oxygen purity data from Example 11-1 with tted regression line, 95% prediction limits (outer lines) and 95% con dence limits on Y 0 x0.

The Trimming feature allows you to crop parts of an image and save it as a new image le. This is a great adjustment you can make in-camera before e-mailing without the need of a computer and image-processing software. RAW, Wide, or Stitch-Assist images cannot be trimmed. To trim an image on the G11, follow these steps: 1. Place the camera in Playback mode. 2. Press the Menu button and use the 4-Way Controller to navigate to Trimming. 3. Press the Function/Set button.

+ 6144 + 576 + 54 + l) < 22"

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Minitab will also calculate prediction intervals. Refer to the output in Table 11-2. The 95% PI on the future observation at x0 1.00 is shown in the display. By repeating the foregoing calculations at different levels of x0, we may obtain the 95% prediction intervals shown graphically as the lower and upper lines about the tted regression model in Fig. 11-8. Notice that this graph also shows the 95% con dence limits on Y 0 x0 calculated in Example 11-5. It illustrates that the prediction limits are always wider than the con dence limits.

EXERCISES FOR SECTIONS 11-6 AND 11-7

This is an extremely efficient attack to recover a 96 bit key. The space requirement for the attack is also minimal, as explored further in Problem 13 at the end of this chapter.

11-31. Refer to the data in Exercise 11-1 on y intrinsic permeability of concrete and x compressive strength. Find a 95% con dence interval on each of the following: (a) Slope (b) Intercept (c) Mean permeability when x 2.5 (d) Find a 95% prediction interval on permeability when x 2.5. Explain why this interval is wider than the interval in part (c). 11-32. Exercise 11-2 presented data on roadway surface temperature x and pavement de ection y. Find a 99% con dence interval on each of the following: (a) Slope (b) Intercept (c) Mean de ection when temperature x 85 F (d) Find a 99% prediction interval on pavement de ection when the temperature is 90 F . 11-33. Exercise 11-4 presented data on the number of games won by NFL teams in 1976. Find a 95% con dence interval on each of the following: (a) Slope (b) Intercept (c) Mean number of games won when opponents rushing yardage is limited to x 1800 (d) Find a 95% prediction interval on the number of games won when opponents rushing yards is 1800. 11-34. Refer to the data on y house selling price and x taxes paid in Exercise 11-5. Find a 95% con dence interval on each of the following: (a) 1 (b) 0 (c) Mean selling price when the taxes paid are x 7.50 (d) Compute the 95% prediction interval for selling price when the taxes paid are x 7.50. 11-35. Exercise 11-6 presented data on y steam usage and x monthly average temperature. (a) Find a 99% con dence interval for 1. (b) Find a 99% con dence interval for 0. (c) Find a 95% con dence interval on mean steam usage when the average temperature is 55 F .

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