[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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posted on 2012-05-15 22:13 tilltheendwjx 阅读(7173) 评论(0) 编辑 收藏 举报