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The regression model for the oxygen purity data in Example 11-1 is y 74.283 14.947x. Table 11-4 presents the observed and predicted values of y at each value of x from this data set, along with the corresponding residual. These values were computed using Minitab and show

does not know the key or plaintext-and to the CRC value so that the receiver will not detect the tampering The bottom line is that this supposed integrity check provides no cryptographic integrity whatsoever Perhaps a CRC was used in WEP due to resource limitations, but that is no excuse for promoting the CRC calculation as an integrity check WEP encrypts data with the stream cipher RC4 using a long-term key that seldom (if ever) changes To avoid repeated keystreams, an initialization vector, or IV, is sent in the clear with each message, where each packet is treated as a new message The IV is mixed with the long-term key to produce the message key The upshot is that the attacker, Trudy, gets to see the IVs, and any time an IV repeats, Trudy knows that the same keystream is being used to encrypt the data.

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Table 11-4 Oxygen Purity Data from Example 11-1, Predicted Values, and Residuals Hydrocarbon Level, x 1 2 3 4 5 6 7 8 9 10 0.99 1.02 1.15 1.29 1.46 1.36 0.87 1.23 1.55 1.40 Oxygen Purity, y 90.01 89.05 91.43 93.74 96.73 94.45 87.59 91.77 99.42 93.65 Predicted Value, y 89.069009 89.518136 91.464353 93.560279 96.105332 94.608242 87.272501 92.662025 97.452713 95.207078 Residual e y y 0.940991 0.468136 0.034353 0.179721 0.624668 0.158242 0.317499 0.892025 1.967287 1.557078 11 12 13 14 15 16 17 18 19 20 Hydrocarbon Level, x 1.19 1.15 0.98 1.01 1.11 1.20 1.26 1.32 1.43 0.95 Oxygen Purity, y 93.54 92.52 90.56 89.54 89.85 90.39 93.25 93.41 94.98 87.33 Predicted Value, y 92.063189 91.614062 88.919300 89.368427 90.865517 92.212898 93.111152 94.009406 95.656205 88.470173 Residual y e y 1.476811 0.905938 1.640700 0.171573 1.015517 1.822898 0.138848 0.599406 0.676205 1.140173

the number of decimal places typical of computer output. A normal probability plot of the residuals is shown in Fig. 11-10. Since the residuals fall approximately along a straight line in the gure, we conclude that there is no severe departure from normality. The residuals are also plotted against the predicted value yi in Fig. 11-11 and against the hydrocarbon levels xi in Fig. 11-12. These plots do not indicate any serious model inadequacies.

11-8.2

Since the IV is only 24 bits, repeated IVs will occur relatively often, which implies repeated keystreams Since a stream cipher is used; a repeated keystream is at least as bad as reuse of a one-time pad That is, a repeated keystream provides statistical information to the attacker who could then conceivably liberate the keystream from the ciphertexts However, in WEP, there are several possible shortcuts that make an attacker s life easier For example, if the attacker Trudy can send a message over the wireless link and intercept the ciphertext, then she knows the plaintext and the corresponding ciphertext, which enables her to immediately recover the keystream.

Coef cient of Determination(R2)

The quantity R2 SSR SST 1 SSE SST (11-34)

This same keystream will be used to encrypt any message that bears the same IV, provided the long-term key has not changed-which it seldom does, since a key change is manual, and the key must be shared with all users of a particular wireless access point How realistic is it for Trudy to send a known message over the wireless link As long as she can contact someone on the wireless LAN (for example, by sending an email message), she can potentially accomplish this trick The primary practical difficulty for Trudy is to determine which intercepted message corresponds to her chosen plaintext There are many more WEP security vulnerabilities For example, suppose that Trudy knows (or can guess) the destination IP address of a given WEP-encrypted packet.

The G11 allows you to resize images to any smaller resolution size than the one it was taken in for easier portability when attaching them to e-mails or uploading to Web sites, blogs, or sharing sites on the Internet. To quickly resize images to a lower resolution, follow these steps: 1. Place the camera in Playback mode.

is called the coef cient of determination and is often used to judge the adequacy of a regression model. Subsequently, we will see that in the case where X and Y are jointly distributed random variables, R2 is the square of the correlation coef cient between X and Y. From

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