Author Topic: Big math help!  (Read 2721 times)

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Offline Newby

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Big math help!
« on: February 09, 2008, 03:53:49 pm »
Ok, so I'm reversing a function (we'll call this function functionA) and here's what it generally looks like:

Code: [Select]
; introBlock
mov     eax, RegCode
lea     ecx, [eax+11h]
imul    ecx, eax

; bblock1
mov     eax, 85D858Bh
imul    ecx
sar     edx, 0Ah
mov     eax, edx
shr     eax, 1Fh
add     eax, edx
imul    eax, 7A69h
sub     ecx, eax
imul    ecx, 1ACFh

; bblock2
mov     eax, 85DCB87Dh
imul    ecx
add     edx, ecx
sar     edx, 0Eh
mov     eax, edx
shr     eax, 1Fh
add     eax, edx
imul    eax, 7A65h
sub     ecx, eax
imul    ecx, 1AD7h

And my C code:

Code: [Select]
/* Necessary stuff so it makes sense. */
typedef unsigned long long int QWORD;
typedef unsigned long int DWORD;

#define HIDWORD(x) ((DWORD)((x) >> 32))

int functionA(int ArgumentOne)
{
        /* introBlock */
QWORD ecx = 0; DWORD edx = 0; DWORD eax = 0;
ecx = (ArgumentOne + 0x11) * ArgumentOne;

        /* bblock1 */
edx = HIDWORD(0x85D858B * ecx) >> 0x0A;
eax = ((edx >> 0x1F) + edx) * 0x7A69;
ecx -= eax;
ecx *= 0x1ACF;

        /* bblock2 */
edx = (HIDWORD(0x85DCB87D * ecx) + ecx) >> 0x0E;
eax = ((edx >> 0x1F) + edx) * 0x7A65;
ecx -= eax;
ecx *= 0x1AD7;
//      ...
}

I've taken the liberty of splitting the assembly/C into their respective blocks, which I will label introBlock, bblock1, and bblock2.

Side-by-side, introBlock and bblock1 are identical in output. When we get to bblock2...

Code: [Select]
edx = (HIDWORD(0x85DCB87D * ecx) + ecx) >> 0x0E;
...it does not have the same output as this:

Code: [Select]
mov     eax, 85DCB87Dh
imul    ecx
add     edx, ecx
sar     edx, 0Eh

I narrowed the problem down to the imul line. The value the assembly puts on register edx when it does edx:eax = eax * ecx is not the same as what I get when I try to do the same with C. I can get the exact same lower dword, but the upper dword isn't the same.

Anybody care to poke at my work and tell me where I went wrong?

Oh, and if anyone would care to explain the concept behind signed and unsigned arithmetic (not just variables, but like, imul and mul are different -- how?) as I can't wrap my mind around their differences. Thanks sidoh!
« Last Edit: February 09, 2008, 04:15:47 pm by Newby »
- Newby
http://www.x86labs.org

Quote
[17:32:45] * xar sets mode: -oooooooooo algorithm ban chris cipher newby stdio TehUser tnarongi|away vursed warz
[17:32:54] * xar sets mode: +o newby
[17:32:58] <xar> new rule
[17:33:02] <xar> me and newby rule all

I'd bet that you're currently bloated like a water ballon on a hot summer's day.

That analogy doesn't even make sense.  Why would a water balloon be especially bloated on a hot summer's day? For your sake, I hope there wasn't too much logic testing on your LSAT. 

Offline Camel

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Re: Big math help!
« Reply #1 on: February 10, 2008, 02:25:28 pm »
You seem to have already solved this, but it's still worth pointing out that your macro is mangled.

<Camel> i said what what
<Blaze> in the butt
<Camel> you want to do it in my butt?
<Blaze> in my butt
<Camel> let's do it in the butt
<Blaze> Okay!

Offline Newby

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Re: Big math help!
« Reply #2 on: February 10, 2008, 06:07:55 pm »
You seem to have already solved this, but it's still worth pointing out that your macro is mangled.

I have not solved the issue (I simply did inline assembly), and can you point out how?
- Newby
http://www.x86labs.org

Quote
[17:32:45] * xar sets mode: -oooooooooo algorithm ban chris cipher newby stdio TehUser tnarongi|away vursed warz
[17:32:54] * xar sets mode: +o newby
[17:32:58] <xar> new rule
[17:33:02] <xar> me and newby rule all

I'd bet that you're currently bloated like a water ballon on a hot summer's day.

That analogy doesn't even make sense.  Why would a water balloon be especially bloated on a hot summer's day? For your sake, I hope there wasn't too much logic testing on your LSAT. 

Offline Camel

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Re: Big math help!
« Reply #3 on: February 11, 2008, 03:55:49 pm »
Nevermind, I miscounted.

<Camel> i said what what
<Blaze> in the butt
<Camel> you want to do it in my butt?
<Blaze> in my butt
<Camel> let's do it in the butt
<Blaze> Okay!