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Martin Hellman describes his namesake cryptanalytic TMTO attack in [65] Hellman s TMTO is a generic attack on a block cipher, but it is particularly effective against the Data Encryption Standard (DES) due to the small key size of 56 bits Hellman s TMTO is a chosen plaintext attack Let P be a specified chosen plaintext block, and let C = E ( P , K ) be the corresponding ciphertext block We assume that whenever Trudy wants to attack this cipher, she can specify the plaintext block P and obtain the corresponding ciphertext block C Trudy s goal is to recover the key K The most obvious way to attempt to break a cipher is an exhaustive key search.

Equation 12-38 is a CI about the regression plane (or hyperplane). It is the multiple regression generalization of Equation 11-31. EXAMPLE 12-7 The engineer in Example 12-1 would like to construct a 95% CI on the mean pull strength for a wire bond with wire length x1 8 and die height x2 275. Therefore, 1 8 275

x0

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If the block cipher key K consists of k bits, then there are 2k keys and via an exhaustive key search, Trudy would expect to find K after trying about half of the keys Then the exhaustive key search attack has a time requirement of about and no memory (pre-computation) requirement Since we are assuming a known plaintext attack is possible, Trudy could instead pre-compute the ciphertext C for every possible key K for her specified chosen plaintext P This attack requires a one-time pre-computation of 2k encryptions and storage of these 2k results Then each time Trudy executes the attack, only a single table lookup is required, provided that the pre-computed list is sorted Neglecting the one-time work, the time per attack is negligible.

2.26379 2754 2.74427 0.01253

2x0 1 2 1

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.

5.2352 31 8 2754 5.2352 10.044442 2.074 10.23266

.214653 .007491 .000340 0.23266

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.007491 .001671 .000019

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

.000340 1 .000019 8 .0000015 275

Therefore, a 95% CI on the mean pull strength at this point is found from Equation 12-38 as 27.66 which reduces to 26.66

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.

2.074 10.23266

Some computer software packages will provide estimates of the mean for a point of interest x0 and the associated CI. Table 12-4 shows the Minitab output for Example 12-7. Both the estimate of the mean and the 95% CI are provided.

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