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99.9 99 Cumulative normal probability 95 80 50 20 5 1 0.1 1.9 0.9 0.1 Residuals 1.1 2.1 Residuals 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 87

Figure 11-10 Normal probability plot of residuals, Example 11-7.

Then-without knowing the key-she can change the destination IP address to an IP address of her choosing (for example, her own IP address), and change the CRC integrity check so that her tanipering goes undetected WEP traffic is only encrypted from the host to the wireless access point (and vice-versa) Therefore, when the altered packet arrives at the access point, it will be decrypted and forwarded to Trudy s preferred IP address Note that this attack is made possible by the lack of any real integrity check Below, we discuss a cryptanalytic attack on the RC4 stream cipher as it is used in WEP This attack succeeds due to the specific way that W E P creates the session key from an initialization vector IV and the long-term key, not.

Figure 11-11 Plot of residuals versus predicted oxygen purity y, Example 11-7.

0.9

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due to any inherent weakness in the RC4 algorithm i t ~ e l f . ~ attack has a The small work factor, and it will succeed provided that a sufficient number of IVs are observed. This clever attack, which can be considered a type of related key attack, is due to Fluhrer, Mantin, and Shamir [51].

Figure 11-12 Plot of residuals versus hydrocarbon level x, Example 11-8.

1,9

RC4 is simplicity itself. At any given time, the state of the cipher consists of a lookup table S containing a permutation of all byte values, 0 , 1 , 2 , .. . ,255, along with two indices i and j . When the cipher is initialized, the permutation is scrambled using a key which can be of any length from 0 to 256 bytes. In the initialization routine, the lookup table S is modified (based on the key) in such a way that S always contains a permutation of the the byte values. The RC4 initialization algorithm appears in Table 3.9. Table 3.9: RC4 Initialization

the analysis of variance identity in Equations 11-24 and 11-25, 0 R2 1 We often refer loosely to R2 as the amount of variability in the data explained or accounted for by the regression model For the oxygen purity regression model, we have R2 SSR SST 15213 17338 0877; that is, the model accounts for 877% of the variability in the data The statistic R2 should be used with caution, because it is always possible to make R2 unity by simply adding enough terms to the model For example, we can obtain a perfect t to n data points with a polynomial of degree n 1 In addition, R2 will always increase if we add a variable to the model, but this does not necessarily imply that the new model is superior to the old one.

Unless the error sum of squares in the new model is reduced by an amount equal to the original error mean square, the new model will have a larger error mean square than the old one, because of the loss of one error degree of freedom Thus, the new model will actually be worse than the old one There are several misconceptions about R2 In general, R2 does not measure the magnitude of the slope of the regression line A large value of R2 does not imply a steep slope Furthermore, R2 does not measure the appropriateness of the model, since it can be arti cially in ated by adding higher order polynomial terms in x to the model Even if y and x are related in a nonlinear fashion, R2 will often be large For example, R2 for the regression equation in Fig.

11-6(b) will be relatively large, even though the linear approximation is poor Finally, even though R2 is large, this does not necessarily imply that the regression model will provide accurate predictions of future observations..

Ki = key[i (mod N ) ]

1600x1200

11-8.3

Lack-of-Fit Test (CD Only)

The RC4 keystream is generated one byte at a time. An index is determined based on the current contents of and the indexed byte is selected as the keystream byte. Similar to the initialization routine, at each step the permutation S is modified so that S always contains a permutation of {0,1,2,. . . ,255). The keystream generation algorithm appears in Table 3.10.

EXERCISES FOR SECTION 11-8

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