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However, the one-time work is significantly larger than an exhaustive key search, so unless the attack is conducted many times, an exhaustive key search is more efficient Hellman s TMTO attack achieves a middle ground between the exhaustive key search and the massive pre-computation (and sorting) of all possible ciphertexts for a given plaintext The TMTO attack requires some one-time work to generate a table of results (the memory part of the TMTO) that.

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TMTO) each time the attack is executed. Suppose that, Trudy wants t o attack a block cipher where the block size is n = 64 bits and key is k = 64 bits. Since the key is 64 bits, t,here are 264 distinct keys. Trudy first chooses a fixed plaintext P and she obtains the corresponding ciphertext C = E ( P ,K ) . Trudy wants t o recover the unknown key K . Trudy first randomly select a 64-bit starting point, denoted S P . She then constructs a chain, of encryptions beginning from S P as follows. Trudy

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Sometimes a company will have income from events that are not a normal or ongoing part of its business, such as the sale of an asset. These items may be shown as other revenue and expenses to give readers a clearer picture of the company s performance. When a rm is organized as a corporation, income tax liability is also shown on the Pro t and Loss Statement. The following is the standard format for a basic Income Statement:

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where El = Kt-1 is the ending point of the chain of encryptions of length t . Note that Trudy uses the ciphertext generated at one step as the key for the next step. Since the block size and the key size are identical, this works. Figure 4.4 illustrates this the process of generating a chain of encryptions from S P to E P . To construct such a chain requires no knowledge of the inner workings of the block cipher. The only fact we have used here is that the block size and the key size are the same, but the process is easily modified if this is not the casc.


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Less: Cost of Goods Sold = Gross Profit Less Expenses = Net Ordinary Income Add Other Income/Expense = Net Income

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Figure 4.4: A chain of encryptions. Another view of an encryption chain is given in Figure 4.5. Here, we have illustrated the chain as a path in the keyspace of the given block cipher. Continuing with the example above, Trudy will generate m encryption chains, each of length t . Now suppose that Trudy computes m = 232 encryption chains, each of length t = 232, and none of the resulting chains overlap. This is unrealistic, since the chains essentially select elements o f t>hekeyspace

To calculate the grand partition function we recall that the derivation of aplau. Hence, in analogy with (7.75), we have in the present case lim - log 2 ( z, V) v ..... OO V where

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at random, but this assumption allows us to easily illustrate the concept behind Hellman s TMTO (below we consider a more realistic scenario). Then each of the 264 keys lies within one exactly one chain. This idealized situation is illustrated in Figure 4.6.

The pro t or loss at the end of each year is summarized in the retained earnings account. The process of reducing the income and expense accounts to a zero balance and determining the net income or loss is sometimes called closing the books. This can be a complicated process. QuickBooks, unlike many other accounting programs, does not require a series of confusing procedures to close your books at the end of an accounting period. QuickBooks automatically updates data as you enter it and allows you to obtain a report at any time within an

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Figure 4.6: Trudy s ideal scenario. Only the starting points and ending points of the chains are savec., that is, Trudy stores



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