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浮點數(shù)比較分支的混淆方法研究

耿普,  祝躍飛

耿普, 祝躍飛. 浮點數(shù)比較分支的混淆方法研究[J]. 電子與信息學(xué)報, 2020, 42(12): 2857-2864. doi: 10.11999/JEIT190743
引用本文: 耿普, 祝躍飛. 浮點數(shù)比較分支的混淆方法研究[J]. 電子與信息學(xué)報, 2020, 42(12): 2857-2864. doi: 10.11999/JEIT190743
Pu GENG, Yuefei ZHU. An Branch Obfuscation Research on Path Branch Which Formed by Floating-point Comparison[J]. Journal of Electronics & Information Technology, 2020, 42(12): 2857-2864. doi: 10.11999/JEIT190743
Citation: Pu GENG, Yuefei ZHU. An Branch Obfuscation Research on Path Branch Which Formed by Floating-point Comparison[J]. Journal of Electronics & Information Technology, 2020, 42(12): 2857-2864. doi: 10.11999/JEIT190743

浮點數(shù)比較分支的混淆方法研究

doi: 10.11999/JEIT190743

  • 信息工程大學(xué) 鄭州 450002

基金項目: 國家重點研發(fā)計劃(2016YFB0801601, 2016YFB0801505)
詳細(xì)信息
    作者簡介:

    耿普：男，1982年生，博士生，研究方向為信息安全

    祝躍飛：男，1962年生，教授、博士生導(dǎo)師，研究方向為網(wǎng)絡(luò)空間安全

    通訊作者:

    耿普　23015636@qq.com

  • 中圖分類號: TP311

An Branch Obfuscation Research on Path Branch Which Formed by Floating-point Comparison

  • Information Engineering University, Zhengzhou 450002, China

Funds: The National Key R&D Program of China (2016YFB0801601, 2016YFB0801505)
  • 摘要:

    針對當(dāng)前分支混淆方法僅對整數(shù)比較分支有效的缺陷，該文分析浮點數(shù)二進(jìn)制表示與大小比較的關(guān)系，證明了浮點數(shù)二進(jìn)制區(qū)間的前綴集合與浮點數(shù)區(qū)間內(nèi)數(shù)據(jù)之間具有前綴匹配關(guān)系。使用哈希函數(shù)對前綴集合進(jìn)行保護(hù)，利用哈希函數(shù)的單向性實現(xiàn)對抗符號執(zhí)行，通過哈希值比對替換浮點數(shù)比較，提出一種基于前綴哈希值比較的分支條件混淆技術(shù)，實現(xiàn)了一種在符號執(zhí)行對抗和混淆還原對抗上具有較強對抗性的混淆方法。最后，通過實驗證和分析，證實了該文提出的混淆方法有消耗小、能夠有效對抗符號執(zhí)行和混淆還原的優(yōu)點，具備較好的實用性。

    Abstract:

    For the faultiness that the recent branch obfuscation method is only efficient on branch condition formed by integer comparison. The relations between the binary representation and big or small comparison of floats are analyzed. The idea that the floats in float interval has prefix matching relation with the prefix set which comes from the binary representation interval of the floats is proved. By protecting the prefix set with Hash function, and based on the comparison of prefix-Hash, a new branch obfuscation method which works well on the branch formed by float number comparison is proposed. The new obfuscation method is powerful on symbolic execution combating and obfuscation recovery combating. At last, the obfuscation proposed in this paper is confirmed to be practical, and is useful to be against symbolic execution and obfuscation recovery.

    • HTML全文

  • 圖  1  浮點數(shù)IEEE 754標(biāo)準(zhǔn)存儲示意圖

    圖  2  浮點數(shù)比較分支的混淆示意圖

    　算法1 前綴算法
    　輸入：a1a2···an//起始值a的二進(jìn)制表示
    　　　　b1b2···bn//結(jié)束值b的二進(jìn)制表示
    　輸出：PrefixSet//區(qū)間的前綴集合
    　PrefixSet Get_Prefix(a1a2···an，b1b2···bn)
    　{
    　　for (int k=1; (k<=n) && (ak==bk); k++)
    　　{
    　　　if (k==(n+1))
    　　　　return { a1a2···an};
    　　}
    　　if ((akak+1···an == 00···0) && (bkbk+1···bn == 11···1))
    　　{
    　　　if (k== 1)
    　　　　return {*};
    　　　else
    　　　　return {a1a2···ak-1};
    　　}
    　　PrefixSet1 = Get_Prefix(ak+1ak+2···an, 11···1);
    　　PrefixSet2 = Get_Prefix(00···0, bk+1bk+2···bn);
    　　Return {a1a2···ak-10+PrefixSet1, a1a2···ak－11+PrefixSet2};
    　}
    下載: 導(dǎo)出CSV
    　算法2：isMatch(x, HS) //判斷輸入為x時，分支條件的取值，算
    　法返回值為true或者false
    　輸入：浮點數(shù)x，浮點數(shù)區(qū)間[a, b]對應(yīng)二進(jìn)制前綴集合的sha1集
    　合HS1和HS2
    　輸出：x是否屬于浮點數(shù)區(qū)間[a,b]
    　bool isMatch(x,HS1,HS2)
    　{ char tmp[32] = {‘*’,‘*’,···,‘*’};
    　　　int Ix= *((int *)&x); char sha1out[32][24];
    　　　char sign = (Ix>>(31-i))&1; tmp[0] = sign;
    　　　for(int i=1; i<32; i++){
    　　　　tmp[i]=(Ix>>(31-i))&1; sha1out[i]=sha1(tmp,32);
    　　　　char sign = tmp[0];
    　　　　if(sign == 0)
    　　　　{for(int j=0; j<hashNumofHS1;j++)
    　　　　{ if(sha1out[i]==HS1[j]) return true; }
    　　　　}
    　　　　else if(sign == 1)
    　　　　{for(int j=0; j<hashNumofHS2;j++)
    　　　　　{ if(sha1out[i]==HS2[j]) return true; }
    　　　　}
    　　　}
    　　　return false;}
    下載: 導(dǎo)出CSV

    表  1  單分支混淆的消耗數(shù)據(jù)表

    分支條件空間消耗(Byte)時間消耗(ms)
    解密后前綴數(shù)據(jù)空間Sha1算法代碼空間isMatch算法代碼空間
    if(1.0≤x ≤10.0)混淆后變?yōu)椋篿f(isMatch(x, HS1))4×20=8026844680.033
    if((x ≤1.0)||((y>10.0)&&(1.0≤z ≤10.0))) 混淆后變?yōu)椋篿f(isMatch(x,HS2)||(isMatch (y,HS3) && isMatch(z,HS4)))(9+8+4)×20=44026844680.102
    注釋：(1) 空間消耗中，只有前綴數(shù)據(jù)占用空間是每個分支混淆需要獨占的，其余空間是所有分支混淆共享的空間。(2) HS1, HS2, HS3和HS4表示前綴數(shù)據(jù)的哈希值集合。
    下載: 導(dǎo)出CSV

    表  2  分支混淆前后程序占用空間和執(zhí)行時間數(shù)據(jù)表

    混淆前的數(shù)據(jù)處理程序混淆后的數(shù)據(jù)處理程序
    占用空間(Byte)3737641472
    執(zhí)行時間(ms)235.6
    被混淆分支數(shù)(個)1
    分支執(zhí)行次數(shù)(次)1000
    下載: 導(dǎo)出CSV

    表  3  混淆方法執(zhí)行效率比較

    混淆方法單分支單次執(zhí)行平均時間消耗(ms)單分支混淆空間消耗(Byte)實驗主機分支類型
    本文方法0.0334×103CPU為Intel I5的主機浮點數(shù)比較
    王志方法0.0314×103CPU為Intel I5的主機整數(shù)大小比較
    王志方法(11312-1442.7)/(3×10000)=0.3294×103CPU為Intel Core2 Q9400的主機整數(shù)大小比較
    陳喆方法2209.8×104CPU為Intel Core2 Q9400的主機整數(shù)大小比較
    Ma方法7507×103CPU為Intel Core2 Q9400的主機整數(shù)大小比較
    下載: 導(dǎo)出CSV

    表  4  混淆分支的符號執(zhí)行測試結(jié)果

    利用符號執(zhí)行的程序分析工具執(zhí)行時間(min)結(jié)果
    Angr80求解出使得isMatch返回值為真的分支輸入值的解個數(shù)為0
    KLEE360共執(zhí)行593906條指令和 118個分支執(zhí)行，但求解出使得isMatch返回值為真的分支輸入值的解個數(shù)為0
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2019-09-27
  • 修回日期:  2020-05-23
  • 網(wǎng)絡(luò)出版日期:  2020-07-09
  • 刊出日期:  2020-12-08

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