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assumed that the crypto algorithm is known to the attacker. Furthermore, a cipher must be resistant to a variety of attacks, including known plaintext, chosen plaintext, adaptively chosen plaintext, and so on, even if these attacks do not seem particularly realistic in a specific application. This is all in stark contrast to the situation in WWII, where a secret design was considered essential. The bottom line is that the machine ciphers of WWII were often viewed as little more than glorified codebook ciphers, which obscured the fundamental distinctions between manual and machine cryptanalysis. In fairness to WWII cipher designers, cryptology was not entirely scientific at the time, in part due to the lack of any solid foundation for the field. That situation began to change during WWII, and with the publication of Shannon s classic 1949 paper [133], cryptography finally emerged from the realm of black art into a genuine scientific discipline.

If the experimental units are relatively homogeneous (small ) and the correlation within pairs is small, the gain in precision attributable to pairing will be offset by the loss of degrees of freedom, so an independent-sample experiment should be used. 2. If the experimental units are relatively heterogeneous (large ) and there is large positive correlation within pairs, the paired experiment should be used. Typically, this case occurs when the experimental units are the same for both treatments; as in Example 10-9, the same girders were used to test the two methods.

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Implementing the rules still requires judgment, because and are never known precisely. Furthermore, if the number of degrees of freedom is large (say, 40 or 50), the loss of n 1 of them for pairing may not be serious. However, if the number of degrees of freedom is small (say, 10 or 20), losing half of them is potentially serious if not compensated for by increased precision from pairing. A Con dence Interval for D To construct the con dence interval for T D D SD 1n

follows a t distribution with n 1 degrees of freedom. Then, since P( t 2,n 1 T t 2,n 1) 1 , we can substitute for T in the above expression and perform the necessary steps to isolate D )% 1 2 between the inequalities. This leads to the following 100(1 con dence interval on 1 2.

1. Consider a rotor with permutation P of { 0 , 1 , 2 , . . . , n - l}. Suppose that P permutes i to pi. Let di be the displacement of p i , that is, di = p i - i (mod n). Find a formula for the elements of permutation 4, the kth rotor shift of P, where the shift is in the same direction as the rotors described in Section 2.2.3. Your formula must be in terms of pi and d i .

De nition If d and sD are the sample mean and standard deviation of the difference of n random pairs of normally distributed measurements, a 100(1 )% con dence interval on the difference in means D is 1 2 d where t /2,n freedom.

Table 10-3 Time in Seconds to Parallel Park Two Automobiles Automobile Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1(x1j) 37.0 25.8 16.2 24.2 22.0 33.4 23.8 58.2 33.6 24.4 23.4 21.2 36.2 29.8 2(x2j) 17.8 20.2 16.8 41.4 21.4 38.4 16.8 32.2 27.8 23.2 29.6 20.6 32.2 53.8 Difference (dj) 19.2 5.6 0.6 17.2 0.6 5.0 7.0 26.0 5.8 1.2 6.2 0.6 4.0 24.0

2. Let F ( p ) , for p = 0 , 1 , 2 , . . . ,13, be the number of ways to plug p cables into the Enigma stecker. Show that

Popular for snapshots in the 1980s, this control adds date or date and time information directly to the image le so that it appears in the lower-right corner of the image when shot in either vertical or horizontal mode. Useful for environmental or construction projects, this mode displays a date icon on the live LCD while shooting to alert you this feature is on. Be sure the date and time are set correctly before using this feature because once inserted into the image they cannot be removed by the camera. This feature does not work when shooting in RAW capture mode.

2 2 2 This con dence interval is also valid for the case where 2 1 2 , because sD estimates D V(X1 X2). Also, for large samples (say, n 30 pairs), the explicit assumption of normality is unnecessary because of the central limit theorem.

EXAMPLE 10-10

F(p) =

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