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http://andreasnaive.blogspot.com/Thursday, June 07, 2007
CPS-3 (6)
As he said at the end of the previous entrance, the being able to reconstruct the cycles of x' partially has allowed me, as well, to study and (at the moment solely for Jojo).
The first of which you occurred account is of which an operation XOR with the high part of the direction was being carried out (what it caused that the bits showed to cycles of 2^15 masks in ahead); once you applied the same mask to obtain the previous values, you found that the bits showed smaller cycles now, although no longer always with the characteristic of which second half of the cycle was just as first but invested. In addition, although the size of the cycles seemed ordered according to the order of the bits, the 4 first had the same length that last 4 and three of the bits (the number # 1, #4 # 5) showed a property (initially) amazing: in them was clear the effect of an operation XOR with certain bit of the direction (not the same one in the three cases).
In that state of things, the possibility existed of trying to reconstruct better the bits of x' as large as and and using the new knowledge the cycles; nevertheless, I chose to study the structure before of and, under the supposition of which, since we hoped that and were, in a certain sense, "more simple" that x', could more easily be attackable.
After studying a little the data, I realized of which (except for the 4 first bits) the cycles showed one of their stuffed halves with cilos of smaller size 2^4 times; along with other indications, this seemed to indicate that the own one and was generated by means of an operation of type rotate_left(a, 4) XOR (to AND b) where, in this case, b was the low part of the direction operated by means of XOR with a certain fixed number.
With this new knowledge, I reconstructed the cycles of a partially and tried to study its structure. These cycles yes that showed the property of which his second half was exactly like his first but invested, which, next to a visual inspection of such, already made think that they were generated of relatively simple form.
I tested some with more or less satisfactory results and, to little, those 3 bits that showed the surprising behavior that mentioned before finished giving the idea me of how they were being generated exactly (one of those ideas that arises just waked up like result of the work of the subconscious mind during the night): basically, an operation rotate_left(c, 2) + c was being used, where c, as well, was the low part of the direction operated by means of XOR with a fixed number.
After more work of analysis (quite tedious) and many simulations, I have concluded that the following scheme produces the values and that we were looking for:
x? ((A&0xffff)^C1)
x? rotate_left(x, 2)+x
x? rotate_left(x, 4) ^ (x & ((A&0xffff)^C2))
x? x ^ ((A>>16)^C3)
The values of C1, C2 and C3 that produce the result that we looked for are unique and, of fact, C2 is, in Jojo, the same number that already had appeared before in these notes like the value that was being applied by means of a final operation XOR al del fact algorithm (, is becoming the same thing: x? x ^ ((A&0xffff)^C2).
Now, once reconstructed (supposedly, at least) and, we can try to use the first table of CPS-3 (5) to reconstruct with more fidelity x', later to study its structure. According to my initial expectations, x' must have one more a structure more complex than and, but we will have to hope to it to have studied to draw conclusions...
θεος συγχωρεστο το dreamcast....αιωνια η μνημη του


