Stevens Implementation of Wang s Attack in .NET

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Stevens Implementation of Wang s Attack
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Stevens [144] gives the algorithm in Table 5.18 for finding a message block n/l, satisfying Wang s differential conditions. This attack is based on the set of output conditions given in Tables A-6 and A-7, which appear in the Appendix. Table 5.18: Efficient Algorithm t o Find h ( f, Find 1 1 = ( X ,X I , .. . , X I S )where all 1110 conditions refers to: 10 , all Table A-7 conditions, all IV conditions for M I (see Table A-8), both ( T 2 1 = 0)14 and ( T J = O),G ~ Find Al repeat Choose Q o ,Q 2 , Q 3 , . . . , Q15 satisfying conditions in Table A-6 Compute X o , X s ,X i , . . . , Xi5 repeat Choose Q ~ satisfying conditions G Compute X I using j = 16 Compute Q1 and X 2 , X : $X4, X s , Compute Q17, Q I ~ QN, Q ~ o , u n t i l QlH, Q 1 7 , . . . , Q 2 0 satisfy conditions in Table A-6 f o r ( Q 8 , Q9) consistent with X I1 Compute X x g , Xio, Xi2, Xi:$ X Compute Q21, Q 2 2 , . . . , Qss i f all A40 conditions arc satisfied then return M end i f next ( Q x , Q g ) u n t i l all 1110 conditions are satisfied end Find Strveris also presents ail efficient algorithm for the second block, All,
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which we give in Table 5.19. This is identical to the algorithm given by Klima in [81]. However, finding MO dominates the overall collision-finding work, so all efforts to improve Wang s attack have been focused on the first message block, Mo. Table 5.19: Efficient Algorithm to Find M 1 Find M1 = (XO, I , ,. . , XIS),where all MI conditions refers to: X all Table A-9 conditions, both (7 21 = 0)14 and (T33 = 0)ls Find M1 repeat Choose Q1, Q 2 , . . . ,6215 satisfying conditions in Table A-8 Compute Xd, Xg , . . . , XI4 repeat Choose Qo satisfying conditions Compute Xo, XI,XZ X 3 , X , , Compute Q16, Qi7, Ql81Q19, Q20 until Q16, Q 1 7 , . . . ,Q 2 0 satisfy conditions in Table A-8 f o r (Q8, Qs) consistent with X11 Compute X8rXS,XlOrX12,X13 Compute Q21, Q22, . . . , Q63 i f all M1 conditions are satisfied then return M
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end i f next ( Q 8 , Q g ) until all M I conditions are satisfied
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end Find M I
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It is sometimes claimed that most hash collision attacks are of little or no practical significance. For the MD5 attack, it is presently not possible to produce arbitrary collisions, so it seems highly improbable that a meaningful collision can be constructed. However, there are cases where an apparently useless collision can be used to create a security vu1nt:rability. Here, we consider one such scenario; see Daum and Lucks [35] for the original description of this clever attack. Suppose that Alice wants to digitally sign the letter of recommendation shown in Figure 5.6, which is in the form of a postscript file, rec.ps. Alice carefully reads the letter, which was created by her new secretary, Trudy, then Alice digitally signs it. As usual, the signature is computed by first hashing
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the file and the resulting hash value is signed. Suppose that the MD5 hash function is used in this signing operation. In this case, Alice computes
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