[原]有限域的多项式乘法逆元求解

题目：

求解算法，扩展的欧几里得算法

/*
@author tilltheendwjx
@blog http://blog.csdn.net/wjh200821或者http://www.cnblogs.com/tilltheendwjx/ 
*/ 
#include<iostream>
using namespace std;
int indexofmax1(int value)
{
    int tmp=1;
    int count=0;
    for(int i=0;i<sizeof(int)*8;++i)
    {
          if((value&tmp))
             count=i;
          tmp=tmp*2;
    }
    return count;
}
void polynomialtostring(int value)
{
    int tmp=1;
    int flag=0;
    int c=indexofmax1(value);
    for(int i=0;i<sizeof(int)*8;++i)
    {
          if((value&tmp))
          {
             if(i==0)
             {
               cout<<"1";
             }else if(i==1)
             {
               cout<<"x";
             }else
             {
               cout<<"x^"<<i;
             }
             flag=1;
             if(i<c)
               cout<<"+";
          }   
          tmp=tmp*2;
    }
    if(flag==0)
      cout<<"0";
}
int powofvalue(int value)
{
    return 1<<(value);
}
int divide(int m,int b,int &remainvalue)
{
    int mindex=indexofmax1(m);
    int vindex=indexofmax1(b);
    if(mindex<vindex)
    {
        remainvalue=m;
        return 0;
    }
    int c=mindex-vindex;
    int tmp=b;
    tmp=tmp<<c;
    m=m^tmp;
    return powofvalue(c)|divide(m,b,remainvalue);
}
int Tx(int ax,int q,int bx)
{
    //cout<<endl;
    //cout<<ax<<"\t"<<bx<<"\t";
    int tmp=1;
    int value=0;
    for(int i=0;i<sizeof(int)*8;++i)
    {
          if((q&tmp))
          {
             value=value^((bx<<i));   
          }   
          tmp=tmp*2;
    }
    //cout<<ax<<"\t"<<value<<"\t";
    //cout<<endl;
    return ax^(value);
}
int extent_gcd(int m,int b,int &x,int &y)
{
   int a1=1,a2=0,a3=m;
   int b1=0,b2=1,b3=b;
   int remainvalue=0;
   while(1)
   {
           polynomialtostring(a1);
           cout<<"    ";
           polynomialtostring(a2);
           cout<<"    ";
           polynomialtostring(a3);
           cout<<"    ";
           polynomialtostring(b1);
           cout<<"    ";
           polynomialtostring(b2);
           cout<<"    ";
           polynomialtostring(b3);
           cout<<"    ";
          if(b3==0)
              return a3;
          if(b3==1)
               return b3;
          int q=divide(a3,b3,remainvalue);
          int t1=Tx(a1,q,b1);
          int t2=Tx(a2,q,b2);
          int t3=remainvalue;
          cout<<t1<<endl;
          cout<<t2<<endl;
          a1=b1;a2=b2;a3=b3;
          b1=t1;b2=t2;b3=t3;
          x=b2;y=b3;
          polynomialtostring(q);
          cout<<endl;
   } 
}
int main(void)
{
int m=283,b=83,x=0,y=0;
cout<<"中间结果如下:"<<endl; 
cout<<"a1   a2    a3    b1    b2    b3    q"<<endl;
int reault=extent_gcd(m,b,x,y);
cout<<endl;
cout<<"多项式(";polynomialtostring(b);cout<<")mod(";polynomialtostring(m);cout<<")的乘法逆元是(";polynomialtostring(x);cout<<")"<<endl;
system("pause"); 
return 0;
}

运行结果如下图

作者：wjh200821 发表于2012-5-15 22:13:00 原文链接

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