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Circa 1400, a type of cipher known as a nomenclator was invented and came into widespread use by trading states in Europe and by the Catholic Church. A nomenclator is a book that describes how letters, syllables, and words are converted into ciphertext and vice versa. In effect, this is a hybrid between a simple substitution and a codebook cipher (described below), and it has a larger number of possible keys than a simple substitution cipher. All else being equal (which it never is), this should make the cryptanalyst s job more difficult.

2 c1

Y0

During the Renaissance, the first poly-alphabetic substitution cipher was invented by one Leon Battista Alberti (1404-1472). Such a cipher is essentially a variable simple substitution cipher, that is, a different substitution alphabet is used for different parts of the message. In Alberti s cipher, this was accomplished by use of a device that included an inner and outer cipher wheel with the alphabet written in particular ways on each wheel. The inner wheel freely rotated allowing the two alphabets to be aligned in any fashion, with

x 22

has a t distribution with n 2 degrees of freedom. From this we can develop the following prediction interval de nition. De nition A 100(1 given by

y0

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each alignment generating a different (simple) substitution. As the message was encrypted, differing substitution alphabets could be used, as determined by both parties in advance, or as specified within the message itself. In his book Traict6 des Chaffres, Blaise de Vigenkre (1585) discusses a poly-alphabetic substitution that uses a 26 x 26 rectangular array of letters. The first row of the array is A, B, C, . . . , Z, and each succeeding row is a cyclic left shift of the preceding one. A keyword can then be used to determine which of the cipher alphabets to use at each position in the text. In this way, all shift-by-n simple substitutions are readily available for use. The Vigenkre cipher, and its cryptanalysis, is discussed below.

2 c1

x 22

and so on. These results are tabulated in Table 3.8 along with a set of empirically obtained results. It is interesting that the empirical results match the theoretical results so closely.

y0

2 c1

4. Scroll through your images to 2.19 The G11 automatically recognizes the nd one that requires red-eye eyes that need correction and allows you to apply the correction after the image has correction and press the been taken. Function/Set button again. A Busy icon appears while the G11 makes the correction. If the camera detects a face, a box appears around the eyes that were corrected. If no face is detected, a Cannot modify message appears at the bottom of the LCD. 5. Repeat Step 4 to remove red-eye from any other photos you want. If you feel there s room on the memory card, choose to save the file as a new file rather than overwrite the original. This allows you flexibility to go back to the original file in post-production should you ever need to.

x 22

Expected Fills 65,536 6144 576 54 5 1

(11-33)

x. 1 0

Computed Fills 65,536 6029 551 47 3 1

Notice that the prediction interval is of minimum width at x0 x and widens as 0 x0 x 0 increases. By comparing Equation 11-33 with Equation 11-31, we observe that the prediction interval at the point x0 is always wider than the con dence interval at x0. This results because the prediction interval depends on both the error from the tted model and the error associated with future observations. EXAMPLE 11-6 To illustrate the construction of a prediction interval, suppose we use the data in Example 11-1 and nd a 95% prediction interval on the next observation of oxygen purity at x0 1.00%. Using Equation 11-33 and recalling from Example 11-5 that y0 89.23, we nd that the prediction interval is B 1.18 c 1 11.00 1.19602 2 d 0.68088 Y0 89.23 2.101 B

1 20

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