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6-1. Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004. Calculate the sample mean and sample standard deviation, construct a dot diagram, and comment on the data. 6-2. In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating uid between electrodes at 34 kV. The times, in minutes, are as follows: 0.19, 0.78, 0.96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85, 6.50, 7.35, 8.01, 8.27, 12.06, 31.75, 32.52, 33.91, 36.71, and 72.89. Calculate the sample mean and sample standard deviation. 6-3. The January 1990 issue of Arizona Trend contains a supplement describing the 12 best golf courses in the state. The yardages (lengths) of these courses are as follows: 6981, 7099, 6930, 6992, 7518, 7100, 6935, 7518, 7013, 6800, 7041, and 6890. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data. 6-4. An article in the Journal of Structural Engineering (Vol. 115, 1989) describes an experiment to test the yield strength of circular tubes with caps welded to the ends. The rst yields (in kN) are 96, 96, 102, 102, 102, 104, 104, 108, 126, 126, 128, 128, 140, 156, 160, 160, 164, and 170. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data. 6-5. An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 39.30, and 49.71. Calculate the sample mean and sample standard deviation. Construct a dot diagram of the data.

In an effort to decrease the number of rounds required, some recent block cipher designs (such as the AES) differ significantly from the standard Feistel approach Next, we turn our attention to Hellman s time-memory trade-off attack This is an interesting attack method that can be applied to any block cipher Then for the remainder of this chapter, we focus on the cryptanalysis of three specific block ciphers, namely, CMEA, Akelarre and FEAL These three ciphers are each weak enough to be broken with a relatively small amount of work, and each attack has some interesting and noteworthy aspects The CMEA cipher is extremely simple, at least by block cipher standards We discuss a chosen plaintext attack on CMEA, as well as a more realistic known plaintext attack The known plaintext attack is particularly interesting, since it lends itself well to several algorithmic techniques that significantly improve the attack.

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EXERCISES FOR SECTION 12-2

12-13 Consider the regression model fit to the soil shear strength data in Exercise 12-1 (a) Test for significance of regression using 005 What is the P-value for this test (b) Construct the t-test on each regression coefficient What are your conclusions, using 005 12-14 Consider the absorption index data in Exercise 12-2 The total sum of squares for y is SST 74200 (a) Test for significance of regression using 001 What is the P-value for this test (b) Test the hypothesis H0: 1 0 versus H1: 1 0 using 001 What is the P-value for this test What conclusion can you draw about the usefulness of x1 as a regressor in this model 12-15 Consider the NFL data in Exercise 12-4 (a) Test for significance of regression using 005.

What is the P-value for this test (b) Conduct the t-test for each regression coefficient 2, 7, and 8 Using 005, what conclusions can you draw about the variables in this model 12-16 Reconsider the NFL data in Exercise 12-4 (a) Find the amount by which the regressor x8 (opponents yards rushing) increases the regression sum of squares (b) Use the results from part (a) above and Exercise 12-14 to conduct an F-test for H0: 8 0 versus H1: 8 0 using 005 What is the P-value for this test What conclusions can you draw 12-17 Consider the gasoline mileage data in Exercise 12-5 (a) Test for significance of regression using 005 What conclusions can you draw (b) Find the t-test statistic for both regressors Using 005, what conclusions can you draw Do both regressors contribute to the model 12-18.

Akelarre combines important features from two different highly-regarded Mock ciphers In spite of these two rights, Akelarre is a wrong [82],since it is very weak FEAL is a seriously flawed cipher that, nevertheless, proved extremely important in the development of modern cryptanalysis While there are many versions of FEAL, in this chapter we only consider the original version, now known as FEAL-4 We discuss both linear and differential cryptanalytic attacks on FEAL-4 In fact, differential cryptanalysis was originally developed to attack FEAL, and it later proved its true worth when applied to t,he cryptanalysis of the Data Encryption Standard (DES) In a sense, linear and differential cryptanalysis form the foundation on which modern block ciphers are constructed, since all block ciphers are designed to withstand attacks based on these two powerful techniques Generally, these techniques arc only of theoretical interest, but in the case of FEAL they yield practical attacks.

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