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One of the many features on the PowerShot G11 to improve your pictures of people, setting Blink Detection On alerts you to the possibility that one of your subjects may have blinked during the exposure. This gives you the opportunity to retake a picture with all eyes open. Blink Detection displays a face icon with greater-than and less-than symbols for eyes when it notices closed eyes in your photo. This feature is helpful for group shots in low light where you can t see everyone to make sure they are looking in the direction of the camera.

x2 2.069,

The results in Table 2.7 show that we can eliminate the vast majority of random cases using a small amount of known plaintext. Combined with the causal results in Table 2.8, we can further reduce the number of random cases by saving only those cases that are, say, above the expected mean in the corresponding causal case. Of course, this latter refinement implies that we will sometimes discard the causal case, with the probability depending on the selected threshold. This approach provides a method for further reducing the number of primary phase survivors, at the expense of a lower probability of success. Unfortunately, Tables 2.7 arid 2.8 indicate that the variance is high, so a significant number of random cases will remain for any reasonable probability of success. The work for this part of the attack is on the order of 243.4, since most random paths do not survive the first known plaintext test (see Problem 23

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1 n2

or upon substituting the sample values and using t0.025,23 90.0 87.0 2.06914.42 1 15

1 B 10

for a slightly more precise estimate). We would like to minimize the amount of known plaintext required, but we need to reduce the number of primary phase survivors as much as possible. Using the approach outlined here, it appears impractical to reduce the number of primary phase survivors by more than factor of about 220, which leaves a large number of survivors (more than 2 ) that must be tested in the secondary phase (set: Problem 3 2 ) . However, Problem 33 gives a more effective method for reducing the number of primary survivors. The paper [28] contains more information on this attack, including several further refinements.

1 15

Notice that the 95% con dence interval includes zero; therefore, at this level of con dence we cannot conclude that there is a difference in the means. Put another way, there is no evidence that doping the cement with lead affected the mean weight percent of calcium; therefore, we cannot claim that the presence of lead affects this aspect of the hydration mechanism at the 95% level of con dence.

For each of the cipher rotor settings that survived the primary phase, a secondary test is required. This secondary test will determine whether the cipher rotor sctting is consistent with any setting of the control and index rotors. In the process, we eliminate random survivors from the primary phase and for the causal survivor we determine the rotor settings and thereby recover the key. For the secondary test, we choose the order and initial positions of the index rotors and the order, orientation and initial positions of the control rotors- -given the putative cipher rotor settings from the primary phase. The number of settings for the index and control rotors appears to be

2 Case 2: 2 1 2 2 In many situations it is not reasonable to assume that 2 1 2. When this assumption is unwarranted, we may still nd a 100(1 )% con dence interval on 1 2 using the fact 2 that T * 3X1 X2 1 1 S2 n2 is distributed approximately as t with 2 2 2 4 2S1 n1 degrees of freedom v given by Equation 10-16. The CI expression follows.

De nition If x1, x2, s2, and s 2 are the means and variances of two random samples of sizes n1 and 1 2 n2, respectively, from two independent normal populations with unknown and unequal variances, an approximate 100(1 )% con dence interval on the difference in means 1 2 is

Howevcr, as noted above, there arc only about 21 .8 distinct index perniutations. which reduces the overall work factor to

(10-20)

EXERCISES FOR SECTION 10-3

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