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In this chapter we considered three of the most famous pre-modern cipher machines It is striking that the vast majority of cipher machines of the World War I 1 era (and earlier) proved to be insecure, and most were shockingly weak, at least by modern standards As mentioned in the introduction to this chapter, this was due in part to a failure to appreciate the differences between machine systems and their predecessors, which consisted largely of codebooks One important difference is that the amount of data that was encrypted with a machine was typically far greater than that which could be processed using a codebook Although by modern standards, the quantity of data generated by these machines was miniscule, it was far greater than was possible using labor intensive manual systems As a result, the cryptanalysts had a.

6. Reject H0 if t0 t0.025,8 2.306 or if t0 t0.025,8 2.306. 7. Computations: The sample average and standard deviation of the differences dj are d 0.2736 and sD 0.1356, so the test statistic is t0 8. d sD 1n 0.2736 0.1356 19 6.05

Conclusions: Since t0 6.05 2.306, we conclude that the strength prediction methods yield different results. Speci cally, the data indicate that the Karlsruhe method produces, on the average, higher strength predictions than does the Lehigh method. The P-value for t0 6.05 is P 0.0002, so the test statistic is well into the critical region.

Paired Versus Unpaired Comparisons In performing a comparative experiment, the investigator can sometimes choose between the paired experiment and the two-sample (or unpaired) experiment. If n measurements are to be made on each population, the two-sample t-statistic is T0 X1 Sp 1 Bn X2 1 n

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relatively large amount of data to analyze, which allowed statistical weaknesses of a cipher to be exploited Of course, there are statistical attacks on codebook ciphers, and these were well understood The protection of a codebook relied first and foremost on ensuring the physical security of the codebook itself Secondarily, the use of additive sequences could extend the useful life of the codebook Whereas the security of a codebook depended primarily on the physical security of the book, the security of a machine system depends almost entirely on its statistical security, that is, it depends on the lack of any useful statistical information leaking to the attacker through the ciphertext This was not well understood during WWII and, in fact, much effort was expended trying to maintain the physical security of cipher machines, and comparatively little was done to probe for potential statistical weaknesses.

This setting tells the G11 to adjust focus when using the optional TC-DC58D TeleConverter lens attachment. Unless doing so, leave this option off.

which would be compared to t2n 2, and of course, the paired t-statistic is T0 which is compared to tn 1. Notice that since D Dj a n j 1

the numerators of both statistics are identical. However, the denominator of the two-sample t-test is based on the assumption that X1 and X2 are independent. In many paired experiments, a strong positive correlation exists between X1 and X2. Then it can be shown that V 1D2 V1X1 V1X1 2 2

Even with the relatively secure Sigaba, it, was considered absolutely essential that the machine not fall into enemy hands For modern cipher design, Kerckhoffs Principle reigns suprenie--at least in principle, if not always in practice Consequently, any respectable cipher must go through an open and cxtensive peer-review process before it can be considered secure, with the theory being that more eyes will lead to more security , particularly if those eyes belong to skilled cryptanalysts It is also.

11 n

2 assuming that both populations X1 and X2 have identical variances 2. Furthermore, SD n estimates the variance of D. Whenever there is positive correlation within the pairs, the denominator for the paired t-test will be smaller than the denominator of the two-sample t-test. This can cause the two-sample t-test to considerably understate the signi cance of the data if it is incorrectly applied to paired samples. Although pairing will often lead to a smaller value of the variance of X1 X2 , it does have a disadvantage namely, the paired t-test leads to a loss of n 1 degrees of freedom in comparison to the two-sample t-test. Generally, we know that increasing the degrees of freedom of a test increases the power against any xed alternative values of the parameter. So how do we decide to conduct the experiment Should we pair the observations or not Although there is no general answer to this question, we can give some guidelines based on the above discussion.

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