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2 includes a differential phase, but the attack is primarily based on a clever equation solving technique In the differential phase of Dobbertin s attack, the input modular difference is specified, but the output differences are not highly constrained This is crucial since the continuous approximation technique (the equation solving phase) makes heavy use of the fact that the output values can be altered In contrast, Wang s MD5 attack is more of a pure differential attack Wang s attack completely specifies the input differences In addition, Wang places significant constraints on the output differences--in fact, the output differences are much more tightly constrained than the input differences, since the signed difference is applied to the outputs At a high level, Wang s attack can be viewed as consisting of two phases First, appropriate input and output differential patterns must be found.

0.4

0.6 0.4 0.8 1.2 y 1.6 2.0 2.4

11-5

Then the computational part of the attack consists of finding messages that satisfy the given patterns These two phases can be further broken down as follows:.

2 0.0557 and F0 The summary statistics for this model are R 2 0.8745, MSE 160.26 (the P value is 0.0001). A plot of the residuals versus yi is shown in Figure S11-3. This residual plot indicates model inadequacy and implies that the linear relationship has not captured all of the information in the wind speed variable. Note that the curvature that was apparent in the scatter diagram of Figure S11-2 is greatly ampli ed in the residual plots. Clearly some other model form must be considered. We might initially consider using a quadratic model such as

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to account for the apparent curvature. However, the scatter diagram Figure S11-2 suggests that as wind speed increases, DC output approaches an upper limit of approximately 2.5. This is also consistent with the theory of windmill operation. Since the quadratic model will eventually bend downward as wind speed increases, it would not be appropriate for these data. A more reasonable model for the windmill data that incorporates an upper asymptote would be y

1. Specify an input differential pattern that behaves nicely in the later rounds. Here, the modular difference is used.

Table S11-2 Observed Values yi and Regressor Variable xi for Example S11-2 Observation Number, i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Wind Velocity (mph), xi 5.00 6.00 3.40 2.70 10.00 9.70 9.55 3.05 8.15 6.20 2.90 6.35 4.60 5.80 7.40 3.60 7.85 8.80 7.00 5.45 9.10 10.20 4.10 3.95 2.45 DC Output, yi 1.582 1.822 1.057 0.500 2.236 2.386 2.294 0.558 2.166 1.866 0.653 1.930 1.562 1.737 2.088 1.137 2.179 2.112 1.800 1.501 2.303 2.310 1.194 1.144 0.123

When you advance your images using the left and right areas of the 4-Way Controller while in Playback mode, Transition effects provide several options for how those images move on the LCD screen. Choose from: Off. Provides no effect. Fade. One image fades out before the next image fades in. Scroll. Images appear to move diagonally as they transition. Slide. A new image appears to move in front of the previous image.

11-6

2. Specify an output differential pattern that is easily satisfied in the early rounds. For the output differential, the more restrictive signed differWang s approach has also been described as intuitive and done by hand by other baffled authors.

Figure S11-4 is a scatter diagram with the transformed variable x 1 x. This plot appears linear, indicating that the reciprocal transformation is appropriate. The tted regression model is

6.9345 x

2 The summary statistics for this model are R2 0.9800, MSE 0.0089, and F0 1128.43 (the P value is 0.0001). A plot of the residuals from the transformed model versus y is shown in Figure S11-5. This plot does not reveal any serious problem with inequality of variance. The normal probability plot, shown in Figure S11-6, gives a mild indication that the errors come from a distribution with heavier tails than the normal (notice the slight upward and downward curve at the extremes). This normal probability plot has the z-score value plotted on the horizontal axis. Since there is no strong signal of model inadequacy, we conclude that the transformed model is satisfactory.

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