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In this case, Trudy can replace M with M and the resulting keyed hash value would not need to be altered. Again, this defeats the purpose of the keyed hash. Although this second attack is perhaps less serious than the first -since a collision must be found, in which case we consider the hash broken-both attacks are easily prevented by computing a hashed message authentication code, which is mercifully shortened t o HMAC. In effect, the HMAC more thoroughly mixes the key into the hash value. HMAC is defined in RFC 2104 [86] as follows. Let B be the number of bytes in a hash block. For most popular hash functions, B = 64. Define ipad and opad

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Figure 15.4 Results of other multiconvolution kernels. (a) Canny with sigma = 0 8; (b) Laplacian with brightness enhancement; (c) Prewitt; (d) Kirsch.

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Most developers choose for loops over while loops for most situations. You should certainly know about both and choose the one that makes the most sense for each situation. If you re not sure, just stick with for loops. Either can be used for most situations. for statements express a lot more information about the loop in a single line, and are less likely to result in an in nite loop because they tend to count toward a well-de ned upper (or lower) limit. Furthermore, although I ve shown a basic for loop that increments a single loop variable up to its limit, lots of interesting variations are possible. The three loop control expressions can really be anything. If you want to get tricky, you can use a comma operator in the loop initialization expression or the loop counter expression to initialize and operate on multiple loop variables at once.

If any loop is allowed to continue running unchecked, you are likely to encounter an in nite loop. An in nite loop can occur when the loop variables fail to change or when the loop termination condition is poorly designed so that it never occurs. In nite loops should always be avoided as they cause the Flash Player to hang. The following is a simple example of an in nite loop.

Then the HMAC of the message M is HMAC(M, K ) = h ( K @ opad, h ( K C ipad, M ) ) , where h is a cryptographic hash function For the HMAC, two hashes are computed, but the outer hash is only computed over a small input, not the entire message M (which could be extremely large) An HMAC can be used to provide message integrity, as can a MAC or a digital signature However, an HMAC has many other nifty uses as well Note that an HMAC can be used to detect errors that occur in transmission However, as with any cryptographic integrity protection scheme, the HMAC provides much more than any error detection method (such as a cyclic redundancy check, or CRC) can provide.

while (true) { trace("desu"); }

In nite loops don t have to be as obvious as while(true) either. Any loop structure can be in nite if there s a mistake in its logic, for example:

By using a cryptographic hash, the HMAC is resistant to attack by an intelligent adversary, whereas any error detection scheme can be defeated by such an adversary See Section 34 and [142] for examples of the perils of using an error detection scheme when a cryptographic integrity check (such as HMAC) is required We note in passing that a symmetric cipher can be used as a hash function and vice versa However, there are certain subtle issues that arise For example, a block cipher that is used as a hash function must resist certain attacks that are not relevant when it is used as a cipher; see Problem 2 In the next two sections we consider the cryptanalysis of the hash functions MD4 and MD5.

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