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(5.42) (5.43) (5.44) (5.45)

where A , B and C are 32-bit words, A is the AND operation, V is the OR operation, @ is the XOR, and 1A is the complement of A. The MD5 algorithm pads the message using the same rnethod as MD4. As in the MD4 attack, the padding is not important for the attack we discuss here. And, as with MD4, the MD5 hash operates on 512-bit blocks of data, with the 128-bit output of one block being used as the initial value for the next block. The IV used in MD5 is the same as that used in MD4, which appears in (5.7) in Section 5 . 3 . The MD5 algorithm is given in Table 5.7 and the four MD5 round functions are given in Table 5.8. Here, we number the steps consecutively from 0 to 63, with the i t h output denoted by Q i . These Q values correspond t o the A , B , C and D values in [122]. Each step of MD5 has its own additive constant. We denote the constant for step i as Ki. Although these constants play no role in the attack, for completeness, the I, are given in the Appendix in Table A-1. The shift for ( step i is denoted si and the values of si are listed in Table 5.9. In Table 5.7, the permutation applied to the input blocks is denoted by a, that is, Wi = X,,(i). The values of ~ ( i for i = 0 , 1 , 2 , . . . 63, are given in ), Table 5.10. The significant differences between MD4 and MD5 are the following [122]:

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122 122 123 124 127 128 128 130 130 131 132

(3.3)

Consequently, the MD5 compression function includes 64 steps, whereas the MD4 compression function has 48 steps.

2. Each step of MD5 has a unique additive constant, whereas each round of MD4 uses a fixed constant. 3 . The function G in the second round of MD5 is less symmetric than the G function in MD4. 4. Each step of MD5 adds the result of the previous step, which is not the case with MD4. The stated purpose of this modification is to produce a faster avalanche effect. 5. In MD5, the order in which input words are accessed in the second and third rounds is less similar t o each other than is the case in MD4.

5.4 11105

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where Zijp is the activation value of input unit Zi, and vji is the weight between input Zi and hidden unit yj. An alternative to the above formulation of the net input signal for PUs is to include a "distortion" factor within the product, such as

Figure 11: Encryption and decryption not know any of the underlying plaintext A basic assumption is that the ciphertext is always available to an attacker After all if the ciphertext is not available to the attacker, why bother to encrypt In a known plaintext attack, Trudy has the ciphertext as well as some of the corresponding plaintext This might give the attacker some advantage over the ciphertext only scenario-certainly the attacker is no worse off with known plaintext If Trudy knows all of the plaintext, there is probably not much point in bothering to attack the system, so the implicit assumption is that the amount of known plaintext is relatively limited As the name implies, in a chosen plaintext attack, an adversary can choose the plaintext and then obtain the corresponding ciphertext This can only help the attacker, as compared to a known plaintext scenario.

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