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Then in the secondary phase, we guess the control and index rotor settings, and again use the known plaintext, this time to whittle down the number of possible keys to a very small number of candidates Suppose that we have a Sigaba-encrypted ciphertext message, where the first several letters of the corresponding plaintext are known Our goal in the primary phase is to recover the cipher rotors, their order, orientations and initial settings Collectively, we refer to these cipher rotor initializations as the cipher rotor settings In the primary phase, we strive to reduce the number of cipher rotor settings to a small number--ideally just one We refer to an incorrect choice of cipher rotor settings as a random setting, while the correct setting is said to be causal For each cipher rotor setting that survives the primary phase, a secondary phase is required.

Figure 10-3 Normal probability plot of the arsenic concentration data from Example 10-6.

5 1 0

This secondary phase consists of trying all possible control and index rotor settings to determine which are consistent with the known plaintext In this way, the random primary survivors are eliminated and, in the causal case, we determine the key Primary Phase We are assuming that ten different cipher rotors are available Also, each cipher rotor has two possible orientations and 26 possible initial positions Therefore the number of ways to select and initialize the five cipher rotors is.

3. H1: 1 2 4. 0.05 (say) 5. The test statistic is t* 0

2 s1

2 s2

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For each of these choices, we determine whether the setting is consistent with t,he known plaintext as follows. Recall that for each letter typed, from one to four of the cipher rotor rotates. This implies that once we specify the cipher rotors, their orientations and their initial settings, the number of possible new permutations at any

6. The degrees of freedom on t* are found from Equation 10-16 as 0 s2 1 an s2 2 2 n2 b 17.632 2 10 2 3 17.632 104 2 9 c 115.32 2 2 d 10 3 115.32 2 104 2 9

1s2 1

If you have done much traveling, you know that it is almost impossible to see everything, and if you try, you are bound to regret it. It is usually far more productive to avoid the tourist death march and instead focus on a few specific interesting locations. We will take a similar approach here as we peruse selected classic crypto topics, stopping at a few points of interest, but making no attempt to cover every possible topic along the way. Since our focus in the remainder of the book is cryptanalysis, we emphasize attacks on the classic ciphers that we cover.

Therefore, using 0.05, we would reject H0: t* t0.025,13 2.160 0 7. Computations: Using the sample data we nd t* 0 B n1 x1 s2 1 x2 s2 2 n2

if t* 0

Since ancient times, cryptography has been used for military and diplomatic purposes. In the remainder of this chapter we consider a few specific examples of classic ciphers. These ciphers have been carefully selected to illustrate important topics that arise in the study of modern ciphers presented in subsequent chapters. The history of crypto is itself a fascinating topic, but it is not our focus here. For more crypto history, a good crypto timeline can be found at [lo41 and there is always Kahn s book [74]. For a more in-depth technical look at classic ciphers, see Bauer s fine book [8].

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t0.025,13

12.5 27.5 115.32 2 17.632 2 10 B 10

8. Conclusions: Because t* 2.77 t0.025,13 2.160, we reject the null hypoth0 esis. Therefore, there is evidence to conclude that mean arsenic concentration in the drinking water in rural Arizona is different from the mean arsenic concentration in metropolitan Phoenix drinking water. Furthermore, the mean arsenic concentration is higher in rural Arizona communities. The P-value for this test is approximately P 0.016.

Transposition ciphers jumble the letters of the message in a way that is designed to confuse the attacker, but can be unjumbled by the intended recipient. The concept of transposition is an important one and is widely used in the design of modern ciphers, as will be seen in subsequent chapters. Note that the key must provide sufficient information to unscramble the ciphertext.

The Minitab output for this example follows:

Two-Sample T-Test and CI: PHX, RuralAZ Two-sample T for PHX vs RuralAZ N Mean StDev SE Mean PHX 10 12.50 7.63 2.4 RuralAZ 10 27.5 15.3 4.9 Difference mu PHX mu RuralAZ Estimate for difference: 15.00 95% CI for difference: ( 26.71, 3.29) T-Test of difference 0 (vs not ): T-Value 2.77 P-Value

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