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At the price of $276,495 Alf Blowfish sells his house to Ann Bonidea ... Figure 5.4: MD4 collision [42].
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MD5 attack, we give an example that shows how a meaningless collision can be used to break security in a very meaningful way.
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Message Digest 5, or MD5, is a strengthened version of MD4. Like MD4, the MD5 hash was invented by Rivest [122]. Also, MD5 was obviously used as the model for SHA-1, since they share many common features. It is undoubtedly the case that MD5 and SHA-1 are the two most widely used hash algorithms today, but use of MD5 will certainly decline over time, since it is now considered broken. At the time of this writing, it appears certain that SHA-1 will soon share the same fate as MD5.
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MD5 is similar to MD4 and in this section, we often refer to our previous discussion of MD4. It is important to read Section 5.3 carefully before attempting this section, since both the operation of MD4 and various aspects of the MD4 attack will be referenced here.
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226 Define the four functions
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F ( A ,B, ) = ( AA B ) V ( 1 AA C ) C G ( A ,B, ) = ( AA C ) V ( B A -C) C H(A,B,C) A @ B @ C = I ( A ,B, C) = B @ ( AV -C)
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(5.42) (5.43) (5.44) (5.45)
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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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1. MD5 has four rounds, whereas MD4 has only three.
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Consequently, the MD5 compression function includes 64 steps, whereas the MD4 compression function has 48 steps.
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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.
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