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Figure 4.4: A chain of encryptions. Another view of an encryption chain is given in Figure 4.5. Here, we have illustrated the chain as a path in the keyspace of the given block cipher. Continuing with the example above, Trudy will generate m encryption chains, each of length t . Now suppose that Trudy computes m = 232 encryption chains, each of length t = 232, and none of the resulting chains overlap. This is unrealistic, since the chains essentially select elements o f t>hekeyspace

12-4

A regression model can be used to predict new or future observations on the response variable Y corresponding to particular values of the independent variables, say, x01, x02, p , x0k. 31, x01, x02, p , x0k 4 , a point estimate of the future observation Y0 at the point x01, If x 0 x02, p , x0k is

y0

at random, but this assumption allows us to easily illustrate the concept behind Hellman s TMTO (below we consider a more realistic scenario). Then each of the 264 keys lies within one exactly one chain. This idealized situation is illustrated in Figure 4.6.

x 0

(12-39)

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Low Light mode is good for capturing some action photos in low light because of its quick 2.4 frames per second shutter, but there is a trade-off in le size and resolution, limiting your optimal printing choices to smaller prints. The Low Light le size is about one-quarter the Large JPEG image le size. In this mode, the recording pixel resolution is exactly one-half in both the horizontal and vertical directions. Each pixel in the resulting Low Light image appears to be generated from 4 pixels (2 x 2) from the image sensor. You are limited to Auto ISO Speed settings in Low Light mode, meaning you have no control over the ISO, and the AF-assist lamp is on by default and cannot be deactivated.

Figure 4.6: Trudy s ideal scenario. Only the starting points and ending points of the chains are savec., that is, Trudy stores

A 100(1

y0

11 Y0

For m = 232, the storage requirement is 2 m = 233 words, where each word is 64 bits. In general, 2 m words must be stored, where each word is n bits. Generating the starting points and computing the corresponding end points is one-time work. The set of starting points and end points will be used each time Trudy conducts the attack to recover an unknown key K , so the precomputation work can be amortized over the number of times the attack is conducted. Once the pre-computation is completed, the attack is implemented as follows. Trudy chooses the same plaintext P that was used in the precomputation phase, and she obtains the corresponding ciphertext C. To find the key K , Trudy computes an encryption chain beginning with C of

x 1 2 0

y0

and at each step i = 1 , 2 , . . . (up to a maximum of t steps), she compares X i to each of the stored endpoints

x0 2

x 1 2 0

Since C is itself a possible key value, by our idealized assumption, C lies somewhere within exactly one chain. Suppose C is on chain j . Then for some i E (0, l , . .. , t - l}, Trudy will find X i = EP,. This situation is illustrated in Figure 4.7.

x0 2

(12-40)

ISO 320 1/30 F2.8 In Quick Shot mode, you compose and shoot only through the view nder 2 1 0 1 2 0 while the LCD monitor is dedicated to displaying the main exposure controls. Indicated on the Mode dial by a ying camera icon, Quick Shot allows adjust528 ing camera functions from the new Quick Shot screen. Once in Quick Shot 3.7 The new Quick Shot screen of the G11 mode, simply press the Function/Set button, and scroll around the controls and highlight the one that needs changing, then turn the Control dial to cycle through choices for that particular function.

This prediction interval is a generalization of the prediction interval given in Equation 11-33 for a future observation in simple linear regression. If you compare the prediction interval Equation 12-40 with the expression for the confidence interval on the mean, Equation 12-38, you will observe that the prediction interval is always wider than the confidence interval. The confidence interval expresses the error in estimating the mean of a distribution, while the prediction interval expresses the error in predicting a future observation from the distribution at

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