题记：
少见使用基于DLP(Discrete Logarithm Problem,离散对数问题)的Elgamal公钥算法来作为注册验证机制
的程序，谨以此例作为对其的研究。
关于Elgamal可以参考：
http://www.cacr.math.uwaterloo.ca/hac/about/chap8.pdf
另外本站的教学也有http://www.pediy.com/tutorial/chap6/Chap6-3-3.htm
以及<<加密与解密（第二版）>>
关于FGInt请参考：
http://triade.studentenweb.org/GInt/gint.html
简单的说是用于Delphi的一种实现了大数运算及几种公钥算法的库。
软件说明：
Official Site:http://www.solid-programs.com/
Introduction:Solid Encryption's One-Time Pad (OTP) encryption a.k.a. infinite key cryptography is absolutely unbreakable if used correctly.
This encryption algorithm is well known and has been used for a long time by various intelligence agencies. W
hen no mistakes were made it has survived unbroken even when the resources off great world powers have been employed to break it.
Unlike most encryption schemes today, not only can you be certain that your communications will not be decoded this year,
but that your secrets are safe for eternity.
用PEiD查无壳，Delphi所写，Krypto ANALyzer识别出RIPEMD-160散列算法和FGInt ElgmalVerify函数，使我们对程序中所
有的算法有个大概的了解。有人说kanal插件有时候会不准，有的算法查不出来，但是这只是个辅助工具。
我平时习惯拿到一个程序后，如果没有加壳就用此插件看一看，有哪些算法，甚至有些加密算法库它都可以
识别出来，如miracl,FGInt.那么这样至少自己心里大概有个数，程序中有哪些算法，虽然这些算法并不一定
用于注册的验证。
接着，用DeDe反编译一下主程序看看，在DeDe的单元信息中可以看到程序的确使用了FGInt和FGIntElGamal
另外还使用了DCP,这是一个在Delphi程序中使用相当广泛的加密算法库。
可以找到RegForm，其中有个RegButtonClick事件，看了一下，注册验证就在其中。将从DeDe导出的map文件导入OD.
可以有两种以上的办法找到注册验证的地方，一种是在DeDe中就可以看到事件处理的地址，另一种就是在
OD中搜索参考字符串，找到与注册有关的字符串。在本例中，这两种方法都可以使用。
另外，还可以在下载FGInt并且编译FGInt后，做出其sig,然后在IDA中apply一下就可以识别FGInt中的一些函数了。
代码:
0047D2BC <>/. 55 push ebp ; <-TRegForm@RegButtonClick
0047D2BD |. 8BEC mov ebp,esp
0047D2BF |. 33C9 xor ecx,ecx
0047D2C1 |. 51 push ecx
0047D2C2 |. 51 push ecx
0047D2C3 |. 51 push ecx
0047D2C4 |. 51 push ecx
0047D2C5 |. 51 push ecx
0047D2C6 |. 51 push ecx
0047D2C7 |. 51 push ecx
0047D2C8 |. 53 push ebx
0047D2C9 |. 56 push esi
0047D2CA |. 8BD8 mov ebx,eax
0047D2CC |. BE 684D4800 mov esi,OTP.00484D68
0047D2D1 |. 33C0 xor eax,eax
0047D2D3 |. 55 push ebp
0047D2D4 |. 68 C5D34700 push <OTP.->System.@HandleFinally;>
0047D2D9 |. 64:FF30 push dword ptr fs:[eax]
0047D2DC |. 64:8920 mov dword ptr fs:[eax],esp
0047D2DF |. 8BC3 mov eax,ebx
0047D2E1 <>|. E8 16FEFFFF call <OTP.<-TRegForm@WriteCodeIni> ; ->:TRegForm.WriteCodeIni()
0047D2E6 |. 8BC3 mov eax,ebx ;这里是将注册信息写入code.ini中,无关紧要
0047D2E8 |. E8 33060000 call OTP.0047D920
0047D2ED |. 8D55 FC lea edx,dword ptr ss:[ebp-4]
0047D2F0 |. 8B06 mov eax,dword ptr ds:[esi]
0047D2F2 <>|. 8B80 1C0300>mov eax,dword ptr ds:[eax+31C] ; *EditSerial:TEdit
0047D2F8 <>|. E8 CF84FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D2FD |. 8B45 FC mov eax,dword ptr ss:[ebp-4]
0047D300 |. 50 push eax
0047D301 |. 8D55 F4 lea edx,dword ptr ss:[ebp-C]
0047D304 |. 8B06 mov eax,dword ptr ds:[esi]
0047D306 <>|. 8B80 080300>mov eax,dword ptr ds:[eax+308] ; *EditName:TEdit
0047D30C <>|. E8 BB84FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D311 |. FF75 F4 push dword ptr ss:[ebp-C]
0047D314 |. 8D55 F0 lea edx,dword ptr ss:[ebp-10]
0047D317 |. 8B06 mov eax,dword ptr ds:[esi]
0047D319 <>|. 8B80 0C0300>mov eax,dword ptr ds:[eax+30C] ; *EditAdr1:TEdit
0047D31F <>|. E8 A884FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D324 |. FF75 F0 push dword ptr ss:[ebp-10]
0047D327 |. 8D55 EC lea edx,dword ptr ss:[ebp-14]
0047D32A |. 8B06 mov eax,dword ptr ds:[esi]
0047D32C <>|. 8B80 100300>mov eax,dword ptr ds:[eax+310] ; *EditAdr2:TEdit
0047D332 <>|. E8 9584FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D337 |. FF75 EC push dword ptr ss:[ebp-14]
0047D33A |. 6A 00 push 0
0047D33C |. 8D55 E8 lea edx,dword ptr ss:[ebp-18]
0047D33F |. 8B06 mov eax,dword ptr ds:[esi]
0047D341 <>|. 8B80 140300>mov eax,dword ptr ds:[eax+314] ; *EditCountry:TEdit
0047D347 <>|. E8 8084FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D34C |. FF75 E8 push dword ptr ss:[ebp-18]
0047D34F |. 8D55 E4 lea edx,dword ptr ss:[ebp-1C]
0047D352 |. 8B06 mov eax,dword ptr ds:[esi]
0047D354 <>|. 8B80 180300>mov eax,dword ptr ds:[eax+318] ; *EditEmail:TEdit
0047D35A <>|. E8 6D84FCFF call OTP.004457CC ; ->Controls.TControl.GetText(TControl):TCaption;
0047D35F |. FF75 E4 push dword ptr ss:[ebp-1C]
0047D362 |. 8D45 F8 lea eax,dword ptr ss:[ebp-8]
0047D365 |. BA 06000000 mov edx,6
0047D36A <>|. E8 9574F8FF call OTP.00404804 ; ->System.@LStrCatN;
-----------------------------------------------------------------------
将输入的信息连结起来
在后面可以看到，这是将要被signature的信息
将其记为str_M
-----------------------------------------------------------------------
代码:
0047D36F |. 8B55 F8 mov edx,dword ptr ss:[ebp-8] ;
0047D372 |. 8BC3 mov eax,ebx ;
0047D374 |. 59 pop ecx
0047D375 |. E8 C6020000 call OTP.0047D640 ;这儿就是验证的地方
0047D37A |. 84C0 test al,al
0047D37C |. 74 17 je short OTP.0047D395
0047D37E |. A1 E4314800 mov eax,dword ptr ds:[4831E4]
0047D383 |. 8B00 mov eax,dword ptr ds:[eax]
0047D385 |. B2 01 mov dl,1
0047D387 |. 8B08 mov ecx,dword ptr ds:[eax]
0047D389 |. FF51 64 call dword ptr ds:[ecx+64]
0047D38C |. 8BC3 mov eax,ebx
0047D38E <>|. E8 694DFEFF call OTP.004620FC ; ->Forms.TCustomForm.Close(TCustomForm);
0047D393 |. EB 15 jmp short OTP.0047D3AA
0047D395 |> 6A 00 push 0 ; /Arg1 = 00000000
0047D397 |. 66:8B0D D4D>mov cx,word ptr ds:[47D3D4] ; |
0047D39E |. B2 01 mov dl,1 ; |
0047D3A0 |. B8 E0D34700 mov eax,OTP.0047D3E0 ; |ASCII "Incorrect registration, please try again."
0047D3A5 |. E8 4213FCFF call OTP.0043E6EC ; \OTP.0043E6EC
0047D3AA |> 33C0 xor eax,eax ; 注册不正确的提示
0047D3AC |. 5A pop edx
0047D3AD |. 59 pop ecx
0047D3AE |. 59 pop ecx
0047D3AF |. 64:8910 mov dword ptr fs:[eax],edx
0047D3B2 |. 68 CCD34700 push OTP.0047D3CC
0047D3B7 |> 8D45 E4 lea eax,dword ptr ss:[ebp-1C]
0047D3BA |. BA 07000000 mov edx,7
0047D3BF <>|. E8 EC70F8FF call OTP.004044B0 ; ->System.@LStrArrayClr(void;void;Integer);
0047D3C4 \. C3 retn
下面来看看call OTP.0047D640中的代码:
代码:
0047D640 /$ 55 push ebp
0047D641 |. 8BEC mov ebp,esp
0047D643 |. 83C4 C4 add esp,-3C
0047D646 |. 53 push ebx
0047D647 |. 56 push esi
0047D648 |. 33DB xor ebx,ebx
0047D64A |. 895D C4 mov dword ptr ss:[ebp-3C],ebx
0047D64D |. 895D C8 mov dword ptr ss:[ebp-38],ebx
0047D650 |. 895D CC mov dword ptr ss:[ebp-34],ebx
0047D653 |. 895D D0 mov dword ptr ss:[ebp-30],ebx
0047D656 |. 895D D4 mov dword ptr ss:[ebp-2C],ebx
0047D659 |. 895D DC mov dword ptr ss:[ebp-24],ebx
0047D65C |. 895D D8 mov dword ptr ss:[ebp-28],ebx
0047D65F |. 894D F8 mov dword ptr ss:[ebp-8],ecx
0047D662 |. 8955 FC mov dword ptr ss:[ebp-4],edx
0047D665 |. 8BF0 mov esi,eax
0047D667 |. 8B45 FC mov eax,dword ptr ss:[ebp-4]
0047D66A |. E8 BD72F8FF call OTP.0040492C
0047D66F |. 8B45 F8 mov eax,dword ptr ss:[ebp-8]
0047D672 |. E8 B572F8FF call OTP.0040492C
0047D677 |. 8D45 F0 lea eax,dword ptr ss:[ebp-10]
0047D67A |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047D680 |. E8 2F78F8FF call OTP.00404EB4
0047D685 |. 8D45 E8 lea eax,dword ptr ss:[ebp-18]
0047D688 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047D68E |. E8 2178F8FF call OTP.00404EB4
0047D693 |. 8D45 E0 lea eax,dword ptr ss:[ebp-20]
0047D696 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047D69C |. E8 1378F8FF call OTP.00404EB4
0047D6A1 |. 33C0 xor eax,eax
0047D6A3 |. 55 push ebp
0047D6A4 |. 68 C5D74700 push OTP.0047D7C5
0047D6A9 |. 64:FF30 push dword ptr fs:[eax]
0047D6AC |. 64:8920 mov dword ptr fs:[eax],esp
0047D6AF |. 8B45 F8 mov eax,dword ptr ss:[ebp-8]
0047D6B2 |. E8 8D70F8FF call OTP.00404744
0047D6B7 |. 83F8 05 cmp eax,5 ;注册码长度要大于5
0047D6BA |. 7D 07 jge short OTP.0047D6C3
0047D6BC |. 33DB xor ebx,ebx
0047D6BE |. E9 C7000000 jmp OTP.0047D78A
0047D6C3 |> 8D4D D4 lea ecx,dword ptr ss:[ebp-2C]
0047D6C6 |. BA DCD74700 mov edx,OTP.0047D7DC ; ASCII "CECDCECCCAC6CDCBCDCCCECFCF"
0047D6CB |. 8BC6 mov eax,esi
------------------------------------------------------------------
0047D6CD |. E8 46040000 call OTP.0047DB18
这个call跟进去看非常像FGInt中的ConvertHexStringToBase256String这个过程,
但是细看却发现不完全一样
代码:
0047DB18 /$ 55 push ebp
0047DB19 |. 8BEC mov ebp,esp
0047DB1B |. 83C4 F8 add esp,-8
0047DB1E |. 53 push ebx
0047DB1F |. 56 push esi
0047DB20 |. 57 push edi
0047DB21 |. 33DB xor ebx,ebx
0047DB23 |. 895D F8 mov dword ptr ss:[ebp-8],ebx
0047DB26 |. 8BF9 mov edi,ecx
0047DB28 |. 8955 FC mov dword ptr ss:[ebp-4],edx
0047DB2B |. 8B45 FC mov eax,dword ptr ss:[ebp-4]
0047DB2E |. E8 F96DF8FF call OTP.0040492C
0047DB33 |. 33C0 xor eax,eax
0047DB35 |. 55 push ebp
0047DB36 |. 68 E7DB4700 push OTP.0047DBE7
0047DB3B |. 64:FF30 push dword ptr fs:[eax]
0047DB3E |. 64:8920 mov dword ptr fs:[eax],esp
0047DB41 |. 8BC7 mov eax,edi
0047DB43 |. E8 4469F8FF call OTP.0040448C ; LStrClr
0047DB48 |. BB 01000000 mov ebx,1
0047DB4D |> 8B45 FC /mov eax,dword ptr ss:[ebp-4]
0047DB50 |. 8A4418 FF |mov al,byte ptr ds:[eax+ebx-1]
0047DB54 |. 3C 39 |cmp al,39
0047DB56 |. 76 15 |jbe short OTP.0047DB6D
0047DB58 |. 8B55 FC |mov edx,dword ptr ss:[ebp-4]
0047DB5B |. 25 FF000000 |and eax,0FF
0047DB60 |. 83E8 41 |sub eax,41
0047DB63 |. 83C0 0A |add eax,0A
0047DB66 |. 8BF0 |mov esi,eax
0047DB68 |. C1E6 04 |shl esi,4
0047DB6B |. EB 10 |jmp short OTP.0047DB7D
0047DB6D |> 8B55 FC |mov edx,dword ptr ss:[ebp-4]
0047DB70 |. 25 FF000000 |and eax,0FF
0047DB75 |. 83E8 30 |sub eax,30
0047DB78 |. 8BF0 |mov esi,eax
0047DB7A |. C1E6 04 |shl esi,4
0047DB7D |> 43 |inc ebx
0047DB7E |. 8B45 FC |mov eax,dword ptr ss:[ebp-4]
0047DB81 |. 8A4418 FF |mov al,byte ptr ds:[eax+ebx-1]
0047DB85 |. 3C 39 |cmp al,39
0047DB87 |. 76 12 |jbe short OTP.0047DB9B
0047DB89 |. 8B55 FC |mov edx,dword ptr ss:[ebp-4]
0047DB8C |. 25 FF000000 |and eax,0FF
0047DB91 |. 03F0 |add esi,eax
0047DB93 |. 83EE 41 |sub esi,41
0047DB96 |. 83C6 0A |add esi,0A
0047DB99 |. EB 0D |jmp short OTP.0047DBA8
0047DB9B |> 8B55 FC |mov edx,dword ptr ss:[ebp-4]
0047DB9E |. 25 FF000000 |and eax,0FF
0047DBA3 |. 03F0 |add esi,eax
0047DBA5 |. 83EE 30 |sub esi,30
0047DBA8 |> 43 |inc ebx
0047DBA9 |. 8D45 F8 |lea eax,dword ptr ss:[ebp-8]
0047DBAC |. 8BD6 |mov edx,esi
0047DBAE |. 80F2 FF |xor dl,0FF
;
-------------------------------------------------------------------------
主要是上面这个地方不同，多了一个xor,因此在做注册机的时候也要多一个xor才对
-------------------------------------------------------------------------
代码:
0047DBB1 |. E8 B66AF8FF |call OTP.0040466C ; LStrFromChar
0047DBB6 |. 8B55 F8 |mov edx,dword ptr ss:[ebp-8]
0047DBB9 |. 8BC7 |mov eax,edi
0047DBBB |. E8 8C6BF8FF |call OTP.0040474C ; LStrCat
0047DBC0 |. 8B45 FC |mov eax,dword ptr ss:[ebp-4]
0047DBC3 |. E8 7C6BF8FF |call OTP.00404744 ; LStrLen
0047DBC8 |. 3BD8 |cmp ebx,eax
0047DBCA |.^ 7E 81 \jle short OTP.0047DB4D
0047DBCC |. 33C0 xor eax,eax
0047DBCE |. 5A pop edx
0047DBCF |. 59 pop ecx
0047DBD0 |. 59 pop ecx
0047DBD1 |. 64:8910 mov dword ptr fs:[eax],edx
0047DBD4 |. 68 EEDB4700 push OTP.0047DBEE
0047DBD9 |> 8D45 F8 lea eax,dword ptr ss:[ebp-8]
0047DBDC |. BA 02000000 mov edx,2
0047DBE1 |. E8 CA68F8FF call OTP.004044B0
0047DBE6 \. C3 retn
-------------------------------------------------------------------
0047D6D2 |. 8B45 D4 mov eax,dword ptr ss:[ebp-2C] ;转换后的Base10String '1213592423100'
0047D6D5 |. 8D55 E0 lea edx,dword ptr ss:[ebp-20] ;这是上面初始化的FGInt
0047D6D8 |. E8 DBD0FFFF call OTP.0047A7B8 ;Base10StringToFGInt,以下相同。
0047D6DD |. 8D4D D0 lea ecx,dword ptr ss:[ebp-30]
0047D6E0 |. BA 00D84700 mov edx,OTP.0047D800 ; ASCII "CEC9CCCBCFC9C7C7CDCBC8CFC6"
0047D6E5 |. 8BC6 mov eax,esi
0047D6E7 |. E8 2C040000 call OTP.0047DB18
0047D6EC |. 8B45 D0 mov eax,dword ptr ss:[ebp-30] ;1634068824709
0047D6EF |. 8D55 F0 lea edx,dword ptr ss:[ebp-10]
0047D6F2 |. E8 C1D0FFFF call OTP.0047A7B8
0047D6F7 |. 8D4D CC lea ecx,dword ptr ss:[ebp-34]
0047D6FA |. BA 24D84700 mov edx,OTP.0047D824 ; ASCII "CAC9CFCDCFCAC9CDCDCDCACBCCCBCECBCBC8C8CEC8CFC9C7C8CDCDCDCDC7CACCCDCDC9CCC8C7CDCDC7CCCDCEC8CDC8C7CEC9C7CCC9CFCACDCBCFCFC7CAC9C7CEC7CDC9CBCFCFCBCCCAC9CDCDCFCBCDCBC9CECBC9CBC9CAC7C8C7CBCECCCECCCDCBC9CFC7C7CCCACACFCE"
0047D6FF |. 8BC6 mov eax,esi
0047D701 |. E8 12040000 call OTP.0047DB18
0047D706 |. 8B45 CC mov eax,dword ptr ss:[ebp-34] ;
---------------------------------------------------------------
这个时候，得到了3个十进制字符串，分别是
1213592423100
1634068824709
5602056222543414477170687222285322637822832172781683605240085681826400435622042461464658784131324608835501
根据后面的分析可知，它们分别对应于Elgamal Signature Scheme的3个参数，
上面的程序可以表示如下：
str_y:='1213592423100';
Base10StringToFGInt(str_y,FGInt_y);
str_p:='1634068824709';
Base10StringToFGInt(str_p,FGInt_p);
str_g:='5602056222543414477170687222285322637822832172781683605240085681826400435622042461464658784131324608835501';
Base10StringToFGInt(str_g,FGInt_g);
实际上对于str_g我们可以用一个简单的运算找到与其等价的大数从而将其缩小
在Elgamal Signature中有如下等式:
Base^Exponent = Power (mod Modulus)
即g^x = y mod p,也可以写成y = g^x mod p
那么如果觉得上面的str_g太冗长的话，
我们可以做如下的运算
FGIntMod(FGInt_g,FGInt_p,FGInt_base),我们得到FGInt_base=456996142523
也就是说用FGInt_g先去模FGInt_p得到小于FGInt_p的FGInt_base
根据模运算的性质，我们可以知道FGInt_base与FGInt_g是等价的。
---------------------------------------------------------------
代码:
0047D709 |. 8D55 E8 lea edx,dword ptr ss:[ebp-18]
0047D70C |. E8 A7D0FFFF call OTP.0047A7B8
0047D711 |. 8D45 DC lea eax,dword ptr ss:[ebp-24]
0047D714 |. E8 736DF8FF call OTP.0040448C
0047D719 |. BB 01000000 mov ebx,1
0047D71E |> 8D45 C8 /lea eax,dword ptr ss:[ebp-38]
0047D721 |. 8B55 F8 |mov edx,dword ptr ss:[ebp-8]
0047D724 |. 8A541A FF |mov dl,byte ptr ds:[edx+ebx-1]
0047D728 |. E8 3F6FF8FF |call OTP.0040466C ;LStrFromChar
0047D72D |. 8B55 C8 |mov edx,dword ptr ss:[ebp-38]
0047D730 |. 8D45 DC |lea eax,dword ptr ss:[ebp-24]
0047D733 |. E8 1470F8FF |call OTP.0040474C ;LStrCat
0047D738 |. 43 |inc ebx
0047D739 |. 8B45 F8 |mov eax,dword ptr ss:[ebp-8]
0047D73C |. 807C18 FF 2>|cmp byte ptr ds:[eax+ebx-1],2D
0047D741 |.^ 75 DB \jnz short OTP.0047D71E ;取'-'前面的字符串
0047D743 |. 43 inc ebx
0047D744 |> 8D45 C4 /lea eax,dword ptr ss:[ebp-3C]
0047D747 |. 8B55 F8 |mov edx,dword ptr ss:[ebp-8]
0047D74A |. 8A541A FF |mov dl,byte ptr ds:[edx+ebx-1]
0047D74E |. E8 196FF8FF |call OTP.0040466C
0047D753 |. 8B55 C4 |mov edx,dword ptr ss:[ebp-3C]
0047D756 |. 8D45 D8 |lea eax,dword ptr ss:[ebp-28]
0047D759 |. E8 EE6FF8FF |call OTP.0040474C
0047D75E |. 43 |inc ebx
0047D75F |. 8B45 F8 |mov eax,dword ptr ss:[ebp-8]
0047D762 |. E8 DD6FF8FF |call OTP.00404744
0047D767 |. 3BD8 |cmp ebx,eax
0047D769 |.^ 7E D9 \jle short OTP.0047D744 ;取剩下的字符串
0047D76B |. 8D45 F0 lea eax,dword ptr ss:[ebp-10] ; FGInt_p
------------------------------------------------------------------
[ebp-10]所指向的是刚刚初始化后的大数,在这里不妨总结一下FGInt的大数格式，并与其它几种
大数库的格式进行一些简单的比较。
在内存中[ebp-10]的数据是这样的。
0012F5E0 01 54 E4 00 B4 73 E5 00 T?磗?萞?_X
注意到第一个byte是01,这是FGInt的符号位，后面一个dword是00E573B4
这是指向真正的大数数据地址的pointer
跟到00E573B4处看看
00E573B4 02 00 00 00 00 00 00 00 85 82 17 76 00 00 00 00 .......厒v....
00E573C4 F8 02 00 00 00 00 00 00 ?......(
其中的02 00 00 00即00000002,这是大数的长度，FGInt是用2^31进制（即2的31次方)来表示大数的,而
miracl是用2^32进制，freelip是用2^30进制,在相互转换的时候要注意了.
可以看看FGInt的Delphi定义:
TSign = (negative, positive);
TFGInt = Record
Sign : TSign;
Number : Array Of LongWord;
呵呵，与我们的判断正好相符。
兄弟们可能会注意到在两个数据中间会有一个值为0的dword,可能这是在老版本的FGInt中的
在使用主页的最新FGInt在Delphi7下编译后，这中间是没有值为0的dword的，即是如下
格式
00D53FE4 02 00 00 00 85 82 17 76 F8 02 00 00 00 00 00 00 ...厒v?......
在上面，程序取了'-'前面的字符串，分别作为Elgamal签名的字符串，即str_a,str_b
至此，我们得到了用于ElGamalVerify的全部参数
Procedure ElGamalVerify(Var g, y, p : TFGInt; a, b, M : String; Var ok : Boolean);
--------------------------------------------------------------------------
代码:
0047D76E |. 50 push eax
0047D76F |. 8B45 DC mov eax,dword ptr ss:[ebp-24] ;str_a
0047D772 |. 50 push eax
0047D773 |. 8B45 D8 mov eax,dword ptr ss:[ebp-28] ;str_b
0047D776 |. 50 push eax
0047D777 |. 8B45 FC mov eax,dword ptr ss:[ebp-4] ; str_M
0047D77A |. 50 push eax
0047D77B |. 8D4D E0 lea ecx,dword ptr ss:[ebp-20] ; FGInt_y
0047D77E |. 8D55 E8 lea edx,dword ptr ss:[ebp-18] ; FGInt_g
0047D781 |. 8BC6 mov eax,esi
0047D783 |. E8 70040000 call OTP.0047DBF8
-------------------------------------------------------
0047DBF8 /$ 55 push ebp
0047DBF9 |. 8BEC mov ebp,esp
0047DBFB |. 83C4 DC add esp,-24
0047DBFE |. 53 push ebx
0047DBFF |. 56 push esi
0047DC00 |. 57 push edi
0047DC01 |. 33DB xor ebx,ebx
0047DC03 |. 895D E0 mov dword ptr ss:[ebp-20],ebx
0047DC06 |. 895D DC mov dword ptr ss:[ebp-24],ebx
0047DC09 |. 8B75 14 mov esi,dword ptr ss:[ebp+14]
0047DC0C |. 8D7D E8 lea edi,dword ptr ss:[ebp-18]
0047DC0F |. A5 movs dword ptr es:[edi],dword ptr >
0047DC10 |. A5 movs dword ptr es:[edi],dword ptr >
0047DC11 |. 8BF1 mov esi,ecx
0047DC13 |. 8D7D F0 lea edi,dword ptr ss:[ebp-10]
0047DC16 |. A5 movs dword ptr es:[edi],dword ptr >
0047DC17 |. A5 movs dword ptr es:[edi],dword ptr >
0047DC18 |. 8BF2 mov esi,edx
0047DC1A |. 8D7D F8 lea edi,dword ptr ss:[ebp-8]
0047DC1D |. A5 movs dword ptr es:[edi],dword ptr >
0047DC1E |. A5 movs dword ptr es:[edi],dword ptr >
0047DC1F |. 8BD8 mov ebx,eax
0047DC21 |. 8D45 F8 lea eax,dword ptr ss:[ebp-8]
0047DC24 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047DC2A |. E8 8174F8FF call OTP.004050B0
0047DC2F |. 8D45 F0 lea eax,dword ptr ss:[ebp-10]
0047DC32 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047DC38 |. E8 7374F8FF call OTP.004050B0
0047DC3D |. 8D45 E8 lea eax,dword ptr ss:[ebp-18]
0047DC40 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047DC46 |. E8 6574F8FF call OTP.004050B0
0047DC4B |. 8B45 10 mov eax,dword ptr ss:[ebp+10]
0047DC4E |. E8 D96CF8FF call OTP.0040492C
0047DC53 |. 8B45 0C mov eax,dword ptr ss:[ebp+C]
0047DC56 |. E8 D16CF8FF call OTP.0040492C
0047DC5B |. 8B45 08 mov eax,dword ptr ss:[ebp+8]
0047DC5E |. E8 C96CF8FF call OTP.0040492C
0047DC63 |. 33C0 xor eax,eax
0047DC65 |. 55 push ebp
0047DC66 |. 68 E7DC4700 push OTP.0047DCE7
0047DC6B |. 64:FF30 push dword ptr fs:[eax]
0047DC6E |. 64:8920 mov dword ptr fs:[eax],esp
0047DC71 |. 8D4D E0 lea ecx,dword ptr ss:[ebp-20]
0047DC74 |. 8B55 10 mov edx,dword ptr ss:[ebp+10]
0047DC77 |. 8BC3 mov eax,ebx
0047DC79 |. E8 9AFEFFFF call OTP.0047DB18
0047DC7E |. 8D4D DC lea ecx,dword ptr ss:[ebp-24]
0047DC81 |. 8B55 0C mov edx,dword ptr ss:[ebp+C]
0047DC84 |. 8BC3 mov eax,ebx
0047DC86 |. E8 8DFEFFFF call OTP.0047DB18
0047DC8B |. 8B45 E0 mov eax,dword ptr ss:[ebp-20] ; str_a
0047DC8E |. 50 push eax
0047DC8F |. 8B45 DC mov eax,dword ptr ss:[ebp-24] ; str_b
0047DC92 |. 50 push eax
0047DC93 |. 8B45 08 mov eax,dword ptr ss:[ebp+8] ; str_M
0047DC96 |. 50 push eax
0047DC97 |. 8D45 E7 lea eax,dword ptr ss:[ebp-19] ; flag
0047DC9A |. 50 push eax
0047DC9B |. 8D4D E8 lea ecx,dword ptr ss:[ebp-18] ; FGInt_p
0047DC9E |. 8D55 F0 lea edx,dword ptr ss:[ebp-10] ; FGInt_y
0047DCA1 |. 8D45 F8 lea eax,dword ptr ss:[ebp-8] ; FGInt_g
0047DCA4 |. E8 F3EFFFFF call OTP.0047CC9C ; ElGamalVerify
0047DCA9 |. 8A5D E7 mov bl,byte ptr ss:[ebp-19] ; 这个是flag
-----------------------------------------------------------------------
0047D788 |. 8BD8 mov ebx,eax
0047D78A |> 33C0 xor eax,eax
0047D78C |. 5A pop edx
0047D78D |. 59 pop ecx
0047D78E |. 59 pop ecx
0047D78F |. 64:8910 mov dword ptr fs:[eax],edx
0047D792 |. 68 CCD74700 push OTP.0047D7CC
0047D797 |> 8D45 C4 lea eax,dword ptr ss:[ebp-3C]
0047D79A |. BA 07000000 mov edx,7
0047D79F |. E8 0C6DF8FF call OTP.004044B0
0047D7A4 |. 8D45 E0 lea eax,dword ptr ss:[ebp-20]
0047D7A7 |. 8B15 94A447>mov edx,dword ptr ds:[47A494] ; OTP.0047A498
0047D7AD |. B9 03000000 mov ecx,3
0047D7B2 |. E8 0178F8FF call OTP.00404FB8
0047D7B7 |. 8D45 F8 lea eax,dword ptr ss:[ebp-8]
0047D7BA |. BA 02000000 mov edx,2
0047D7BF |. E8 EC6CF8FF call OTP.004044B0
0047D7C4 \. C3 retn
到现在验证的流程清楚了
即 ElgamalVerify(FGInt_g,FGInt_y,FGInt_p,str_a,str_b,str_M,flag);
对于ElGamal，任务就是要求出Base^Exponent = Power (mod Modulus)中的
Exponent，即y = g^x mod p中的x,现在base,power和modulus都已经知道了
而且还可以用上面求出的FGInt_base来代替p.
这是一个DLP(Discrete Logarithm Problem,离散对数问题)，可以使用DLPTool
来求出x.
DLPTool可以在这里下载http://www.pediy.com/tools/Cryptography.htm
另外，还可以使用在线Discrete logarithm calculator(离散对数计算器)
即http://www.alpertron.com.ar/DILOG.HTM,在这里我们使用
Discrete Logarithm calculator,其中
Base即可以输入5602056222543414477170687222285322637822832172781683605240085681826400435622042461464658784131324608835501
也可以输入456996142523，显然第二个更小一些
Power输入str_y,即1213592423100
Mod输入str_p,即1634068824709
然后点击Find Discrete Logarithm,秒杀，呵呵
我们得到Exp=586292948503,即所求的x
ElGamal在签名的时候,要生成一个随机数k,使其与p-1互素，
p-1=1634068824708,将其分解得到其素数因子
PRIME FACTOR: 2
PRIME FACTOR: 2
PRIME FACTOR: 3
PRIME FACTOR: 29
PRIME FACTOR: 41
PRIME FACTOR: 114526831
因此在生成随机数的时候不要选择这几个数的任何一个或几个的乘积就可以了，比如2x2=4,那么4也不能作为k的值
在这里我们选择1，方便些.
现在可以做注册机了，代码如下:
代码:
Base10StringToFGInt('1',FGInt_k);
str_x:='586292948503';
Base10StringToFGInt(str_x,FGInt_x);
str_y:='1213592423100';
Base10StringToFGInt(str_y,FGInt_y);
str_p:='1634068824709';
Base10StringToFGInt(str_p,FGInt_p);
str_base:='456996142523';
Base10StringToFGInt(str_base,FGInt_base);
ElGamalSign(str_M,FGInt_p,FGInt_base,FGInt_x,FGInt_k,str256_a,str256_b);
For i:=1 To length(str256_a) Do
str_a[i]:=chr(ord(str256_a[i]) xor $FF);
For i:=1 To length(str256_b) Do
str_b[i]:=chr(ord(str256_b[i]) xor $FF);
ConvertBase256StringToHexString(str256_a,strhex_a);
ConvertBase256StringToHexString(str256_b,strhex_b);
str_sn:=strhex_a+'-'+strhex_b;
This is the end. That's all.
cnbragon [iPB][RCT]