數(shù)據(jù)結(jié)構(gòu)與算法uestc08暑假集訓3.數(shù)學miller

1、Miller-Rabin 算法if n is prime and (a,n) equals one ,then a(n-1) = 1 (mod Carmichael 數(shù)是非常少的。Miller-Rabin 算法if n is prime and (a,n) equals one ,then a(n-1) = 1 (mod Carmichael 數(shù)是非常少的。0、先計算出m、j，使得n-1=m*2j，m，j2、計算 v=bm mod n7、v=v2mod 8、循環(huán)到 5#include #include #include #includetypedef 64MAX_COUNT6;/測試 , vo

2、idfFindFactor(constlltype&num);/主函數(shù)(numlltypepollard_rho(constlltype&c,constlltypeboolmiller_rabin(constlltypeboolfWitNess(constlltype&a,constlltype&n,chart,constlltypelltypemodular_exp(constlltype&a,lltypeb,constlltype&n);/d=ab(modn) lltype fMultiModular(const lltype &a, lltype b, const lltype &n);

3、/(a*b)%numlltype(lltypea,lltypevoidfFindFactor(constlltypeif(miller_rabin(num,MAX_COUNT)=trueallFactor+nFactorif(miller_rabin(num,MAX_COUNT)=trueallFactor+nFactor=lltypefactor=pollard_rho(rand()%(num-1)+1,while(factor=num f(%I64d ,factor); lltypepollard_rho(constlltype&c,constlltypei=1,lltypex=rand(

4、)%num; lltype y = x, comDiv;if(x =fMultiModular(x,x,num)-c)1&comDiv numreturnif (i =k y = k =while(truereturn /miller-rabin法測試素數(shù)count boolmiller_rabin(constlltypeif (n =1 return if (n =2 lltype a, u;char /為了謹慎起見lltype a, u;char /為了謹慎起見用了 lltype, 而沒有/n-1=for (u= n-1;!(u& 0 x1);for i=1;i 0 if (b& 0 x1 dfMultiModular(ddTempn);/不直接 d*dTemp dTemp=fMultiModular(dTemp,dTemp,n); b = 1;return/back =(n 0 ifwhile (b 0 if (b& 0 x1 if(back=back+temp)n) back -= n;if(tempn) temp -=