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Note that for the attack in Table 3.15, the maximum number of ( X ,Y, 2)lists generated is 238, so that the expected number of lists generated before the solution is found is 237. The price we pay for this simplification is that we cannot implement the duplicate-reduction step which reduces the number of putative 2-lists, and thereby reduces the overall work factor. If more than 13 bytes of known plaintext is available, the simplified attack given here will have a higher work factor than the nonsimplified attack discussed above, provided

(12-14)

The last item on the Function menu is le quality, and here you re offered ve options of JPEG, a Wide panoramic-style capture, RAW, or you can shoot and combine RAW and JPEG in separate les You turn the 4-Way Controller to select the image quality If you choose the JPEG format, you can then choose between different image and le sizes: L Large JPEG at 10MB (3648 pixels by 2736 pixels) M1 Medium JPEG at 6MB (2816 pixels by 2112 pixels) M2 Medium JPEG at 4MB (2272 pixels by 1704 pixels) M3 Medium JPEG at 2MB (1600 pixels by 1200 pixels) S Small JPEG at 0.

The difference between the observation yi and the fitted value yi is a residual, say, i. The (n 1) vector of residuals is denoted by ei yi y

(12-15)

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An ajJine cipher is a simple substitution where ci = api + b (mod 26). Here, the constants a and b are integers in the range 0 to 25 (as are p , and ci). To decrypt uniquely--always a nice feature for a cipher system--we must have gcd(a, 26) = 1. Consequently, there are 26.4(26) = 312 affine ciphers for the English language, where 4 is the Euler-phi function (see the Appendix for a definition of the 4 function). The decryption function for the affine cipher is pi = aP1(ci - b ) (mod 26), where aa-l = 1 (mod 26), that is, u p 1 is the multiplicative inverse of a,modulo 26. Affine ciphers are weak for several reasons, but the most obvious problem is that they have a small keyspace. A ciphertext only attack can be performed by conducting a brute force search of all 312 possible key pairs ( a , b). This attack is trivial, provided we can recognize the plaintext when we see it (or, better yet, automatically test for it).

EXAMPLE 12-2

0 1 x1

Trying all possible keys is known as an exhaustive key search, and this attack is always an option for Trudy. If there are N possible keys, then Trudy will, on average, need to try about half of these, that is; N/2 of the keys, before she can expect to find the correct key. Therefore, the first rule of cryptography is that any cipher must have a large enough keyspace so that an exhaustive search is impractical. However, a large keyspace does not ensure that a cipher is secure. To see that this is the case, we next consider an attack that will work against any simple substitution cipher and, in the general case, requires far less work than an exhaustive key search. This attack relies on the fact that statistical information that is present in the plaintext language leaks through a simple substitution. Suppose we have a reasonably large ciphertext message generated by a simple substitution, and we know that the underlying plaintext is English. Consider the English letter frequency information in Table 1.3, which was

2 x2

where y is the observed pull strength for a wire bond, x1 is the wire length, and x2 is the die height. The 25 observations are in Table 12-2. We will now use the matrix approach

compiled from a 7834-letter sample of written English. By simply computing letter frequency counts on our ciphertext, we can make educated guesses as to which plaintext letters correspond to some of the ciphertext letters. For example, the most common ciphertext letter probably corresponds to plaintext E. We can obtain additional statistical information by making use of digraphs (pairs of letters) and common trigraphs (triples). This type of statistical attack on a simple substitution, is very effective. After a few letters have been guessed correctly, partial words will start to appear and the cipher should then quickly unravel. Table 1.3: English Letter Frequencies as Percentages Relative

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