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result in a table, digest another message, compare it to the first one, and save the result in the table, and then digest another message, compare it to all previously saved values, and so on. Figure 5-4 illustrates these properties with a challenge: Find the message, or any message, and produce the given digest.

The average cost method is best used by rms that buy large amounts of goods that are similar in nature and stored in a common place. Grain, gasoline, and coal are good examples of products that could logically be costed under weighted average. There are some limitations that should be noted in this valuation pro cedure. Unit cost cannot be related to any physical purchase and does not represent any price changes. In those industries that are greatly affected by price and style change, this method will not yield speci c cost deter mination. Also, the time needed to assemble the data is greater under this method then for FIFO or LIFO, if there are many purchases of a variety of different items bought.

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Figure 5-4 Can you find the message we used to produce this digest (or any message that will produce it) If so, you will have found a collision in SHA-1

NOTE:

By the way, you probably already know this, but for the sake of completeness, let s say it. A message is not necessarily a communication between two people. Any data you give to a digest algorithm is a message, even if it s not in human-readable form. Each byte of input is simply a byte of input, whether or not the byte is an ASCII character.

4

When an algorithm violates one of the last two properties discussed in the preceding section, the result is a collision, the technical term to describe a situation in which two messages produce the same digest. A collision occurs when a second message produces the same digest as a previous message, or when two messages any two messages produce the same digest whatever that digest is. If two messages collide, they meet at the digest. Although the number of possible messages is virtually infinite, the number of possible digests is finite. With SHA-1, the number of possible digests is 2160. Clearly, there will be many messages that produce any one digest. To show that, let s use the time-honored mathematical tool known as the pigeonhole principle. Suppose you had a cabinet of pigeonholes (see Figure 5-5). Each pigeonhole corresponds to a digest. The zeroth pigeonhole is for the digest 00 00 . . . 00, the first is for 00 00 . . . 01, and so on, until you reach the last pigeonhole, the place for FF FF . . . FF. Now you start digesting messages. After you digest a message, place the message into the pigeonhole of the digest it produces. For example, the digest of the 1-byte message 00 is

The three methods for costing inven tory are: rst-in, rst-out (FIFO), lastin, rst-out (LIFO), and weighted av erage cost valuation system.

Message 01 goes into pigeonhole BF 8B . . . F7. Suppose you keep digesting messages, the next message being the preceding message plus 1. The sequence of messages is 00, 01, 02, . . ., FF, 01 00, 01 01, . . ., FF FF, 01 00 00, and so on. Suppose you did this for 2160 messages. The last message in the sequence would be

Figure 5-5

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