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This principle states that the strength of a cryptosystem depends only on the key and, in particular, the security does not depend on keeping the encryption algorithm secret This principle is generally construed even more broadly to imply that the attacker knows the protocols and overall system in which a cryptosystem is used Adherence to Kerckhoffs Principle should ensure that the security of a cryptosystem does not depend on the much-dreaded security by obscurity , since the security does not depend on a secret algorithm Unfortunately, there are many real-world pressures that can lead to violations of Kerckhoffs Principle, usually with disastrous consequences..

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k 2 0

6. Reject H0 if 2 0 7. Computations:

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Why do we insist on Kerckhoffs Principle After all, the attacker s job certainly must be more difficult if the crypto algorithm is unknown. In part, the answer is that Kerckhoffs Principle is just a codification of realityalgorithms never remain secret for long so it is far better to find flaws beforehand, rather than after an algorithm is embedded in millions of applications dispersed across the globe. It also happens to be true that designing a secure cipher is not easy, and it is made all the more difficult when efficiency is an issue, which is usually the case. An extensive peer review process is essential before any algorithm can be considered sufficiently secure for use. We will see several real-world examples that illustrate the wisdom of Kerckhoffs in upcoming chapters. Suppose that Alice encrypts a message and sends the ciphertext to Bob. Figure 1.2 illustrates what information is available to Alice, Bob and the attacker, Trudy. At a minimum we assume that Trudy has access to the ciphertext and, by Kerckhoffs Principle, she also knows how the crypto algorithm works. In some cases, Trudy may have additional information, such as known plaintext, chosen plaintext, etc.

2 0.05,1

3.84. 115 113

.~..................................................

28.322 2 28.32

21.242 2 21.24

10.442 2 10.44

, ..........................

2 2 3.84, we are unable to reject the null hypothesis 8. Conclusions: Since 0 2.94 0.05,1 that the distribution of defects in printed circuit boards is Poisson. The P-value for the test is P 0.0864. (This value was computed using an HP-48 calculator.)

EXAMPLE 9-13

In the next section we highlight a few selected classic crypto topics. We also discuss some important cryptanalytic principles arid we provide details on a few specific ciphers that are relevant to later chapters.

A Continuous Distribution A manufacturing engineer is testing a power supply used in a notebook computer and, using 0.05, wishes to determine whether output voltage is adequately described by a normal distribution. Sample estimates of the mean and standard deviation of x 5.04 V and s 0.08 V are obtained from a random sample of n 100 units. A common practice in constructing the class intervals for the frequency distribution used in the chi-square goodness-of- t test is to choose the cell boundaries so that the expected frequencies Ei npi are equal for all cells. To use this method, we want to choose the cell boundaries a0, a1, p , ak for the k cells so that all the probabilities pi P1ai X ai 2

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are equal. Suppose we decide to use k 8 cells. For the standard normal distribution, the intervals that divide the scale into eight equally likely segments are [0, 0.32), [0.32, 0.675) [0.675, 1.15), [1.15, ) and their four mirror image intervals on the other side of zero. For each interval pi 1 8 0.125, so the expected cell frequencies are Ei npi 100(0.125) 12.5. The complete table of observed and expected frequencies is as follows:

Class Interval 4.948 4.986 5.014 5.040 5.066 5.094 5.132 Totals x x x x x x x x 4.948 4.986 5.014 5.040 5.066 5.094 5.132

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