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Consider the wire bond pull strength data in Example 12-1. We will investigate the contribution of the variable x2 (die height) to the model using the partial F-test approach. That is, we wish to test H0: H1:

20 1, 0 2

of plaintext using this IV and the key K . She saves only the final ciphertext block Ce, which is the MAC. Alice can then send Ce, the IV and her plaintext message to Bob. Upon receiving the message, Bob uses the IV and the shared key K to CBC encrypt the received data. He compares the final ciphertext block with the received MAC, and if they agree he can be virtually certain that the data he has received is the data that Alice sent (see Problem 2 ) . The MAC computation works because any change to a plaintext block will almost certainly propagate through the CBC encryption, resulting in a different final ciphertext block. Note that this is in stark contrast to CBC decryption, where changes do not propagate, as discussed above. There are, in fact, many other block cipher modes. One of the most useful modes is counter mode, or CTR mode (see Problem 3), which allows a block cipher to be used like a stream cipher [142].

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1, 2, 0 2 1, 2 0

1, 2 0 02

Before we dive into the cryptanalysis of specific block ciphers, we briefly consider one popular block cipher design strategy, due to Horst Feistel [70]. In a Feistel Cipher the plaintext block P is split into a left half LOand a right half Ro, that is, p = (Lo,Ro). Then for each round i are computed as

20 1, 0 2 10 02

This is the increase in the regression sum of squares due to adding x2 to a model already containing x1. To test H0: 2 0, calculate the test statistic f0 SSR 1

20 1, 0 2

where Ki is the subkey for round i, and F is the round function. The subkey Ki is derived from the key K , via a key schedule algorithm. The ciphertext C is the output of the final round, that is,

104.9191 1 5.2352

Note that the MSE from the full model, using both x1 and x2, is used in the denominator of the test statistic. Since f0.05,1,22 4.30, we reject H0: 2 0 and conclude that the regressor die height (x2) contributes significantly to the model. Table 12-4 shows the Minitab regression output for the wire bond pull strength data. Just below the analysis of variance summary in this table the quantity labeled Seq SS shows the sum of squares obtained by fitting x1 alone (5885.9) and the sum of squares obtained by fitting x2 after x1. Notationally, these are referred to above as SSR 1 1 0 0 2 and SSR 1 2 0 1, 0 2 . Since the partial F-test in the above example involves a single variable, it is equivalent to the t-test. To see this, recall from Example 12-5 that the t-test on H0: 2 0 resulted in the test statistic t0 4.4767. Furthermore, the square of a t-random variable with degrees of freedom is an F-random variable with one and degrees of freedom, and we note that t 2 0 (4.4767)2 20.04 f0.

To decrypt, we can simply solve for Li-1 and Ri-1 and run the Feistel process backwards from n to 1. More precisely, starting with C = (L n ,Rn), for i = n, n - 1,.. . ,I,we computc

12-2.3

3.5 Manual mode is great for action shots, like this one of sailing enthusiast Ray Slabicki, where I know in advance what settings I want to use. The G11 was in a waterproof case and set to Manual mode at ISO 100, f/4, 1/500 second with a 6.1mm lens setting.

More About the Extra Sum of Squares Method (CD Only)

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