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KGC_TEST/KGCAPP/3rdparty/miracl/source/mrjack.c

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/***************************************************************************
*
Copyright 2013 CertiVox UK Ltd. *
*
This file is part of CertiVox MIRACL Crypto SDK. *
*
The CertiVox MIRACL Crypto SDK provides developers with an *
extensive and efficient set of cryptographic functions. *
For further information about its features and functionalities please *
refer to http://www.certivox.com *
*
* The CertiVox MIRACL Crypto SDK is free software: you can *
redistribute it and/or modify it under the terms of the *
GNU Affero General Public License as published by the *
Free Software Foundation, either version 3 of the License, *
or (at your option) any later version. *
*
* The CertiVox MIRACL Crypto SDK is distributed in the hope *
that it will be useful, but WITHOUT ANY WARRANTY; without even the *
implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
See the GNU Affero General Public License for more details. *
*
* You should have received a copy of the GNU Affero General Public *
License along with CertiVox MIRACL Crypto SDK. *
If not, see <http://www.gnu.org/licenses/>. *
*
You can be released from the requirements of the license by purchasing *
a commercial license. Buying such a license is mandatory as soon as you *
develop commercial activities involving the CertiVox MIRACL Crypto SDK *
without disclosing the source code of your own applications, or shipping *
the CertiVox MIRACL Crypto SDK with a closed source product. *
*
***************************************************************************/
/*
* MIRACL Jacobi symbol routine
* mrjack.c
*
* See "A binary algorithm for the Jacobi symbol"
* Shallit and Sorenson
*/
#include <stdlib.h>
#include "miracl.h"
int jack(_MIPD_ big a,big n)
{ /* find jacobi symbol (a/n), for positive odd n */
big w;
int nm8,onm8,t;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM || size(a)==0 || size(n) <1) return 0;
MR_IN(3)
t=1;
copy(n,mr_mip->w2);
nm8=remain(_MIPP_ mr_mip->w2,8);
if (nm8%2==0)
{
MR_OUT
return 0;
}
if (size(a)<0)
{
if (nm8%4==3) t=-1;
negify(a,mr_mip->w1);
}
else copy(a,mr_mip->w1);
while (size(mr_mip->w1)!=0)
{
while (remain(_MIPP_ mr_mip->w1,2)==0)
{
subdiv(_MIPP_ mr_mip->w1,2,mr_mip->w1);
if (nm8==3 || nm8==5) t=-t;
}
if (mr_compare(mr_mip->w1,mr_mip->w2)<0)
{
onm8=nm8;
w=mr_mip->w1; mr_mip->w1=mr_mip->w2; mr_mip->w2=w;
nm8=remain(_MIPP_ mr_mip->w2,8);
if (onm8%4==3 && nm8%4==3) t=-t;
}
mr_psub(_MIPP_ mr_mip->w1,mr_mip->w2,mr_mip->w1);
subdiv(_MIPP_ mr_mip->w1,2,mr_mip->w1);
if (nm8==3 || nm8==5) t=-t;
}
MR_OUT
if (size(mr_mip->w2)==1) return t;
return 0;
}
/*
* See "Efficient Algorithms for Computing the Jacobi Symbol"
* Eikenberry & Sorenson
*
* Its turns out this is slower than the binary method above for reasonable sizes
* of parameters (and takes up a lot more space!)
#ifdef MR_FP
#include <math.h>
#endif
static void rfind(mr_small u,mr_small v,mr_small k,mr_small sk,mr_utype *a,mr_utype *b)
{
mr_utype x2,y2,r;
mr_small w,q,x1,y1,sr;
#ifdef MR_FP
mr_small dres;
#endif
w=invers(v,k);
w=smul(u,w,k);
x1=k; x2=0;
y1=w; y2=1;
// NOTE: x1 and y1 are always +ve. x2 and y2 are always small
while (y1>=sk)
{
#ifndef MR_NOFULLWIDTH
if (x1==0) q=muldvm((mr_small)1,(mr_small)0,y1,&sr);
else
#endif
q=MR_DIV(x1,y1);
r= x1-q*y1; x1=y1; y1=r;
sr=x2-q*y2; x2=y2; y2=sr;
}
if (y2>=0) { *a=y2; *b=0-y1; }
else { *a=-y2; *b=y1; }
}
int jack(_MIPD_ big U,big V)
{ // find jacobi symbol for U wrt V. Only defined for
// positive V, V odd. Otherwise returns 0
int i,e,r,m,t,v8,u4;
mr_utype a,b;
mr_small u,v,d,g,k,sk,s;
#ifdef MR_FP
mr_small dres;
#endif
big w;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
#ifdef MR_FP_ROUNDING
mr_large ik,id;
#endif
if (mr_mip->ERNUM || size(U)==0 || size(V) <1) return 0;
copy(U,mr_mip->w1);
copy(V,mr_mip->w2);
a=0;
MR_IN(3)
if (remain(_MIPP_ mr_mip->w2,2)==0)
{ // V is even
MR_OUT
return 0;
}
if (mr_mip->base!=0)
{
k=1;
for (m=1;;m++)
{
k*=2;
if (k==MAXBASE) break;
}
if (m%2==1) {m--; k=MR_DIV(k,2);}
#ifdef MR_FP_ROUNDING
ik=mr_invert(k);
#endif
}
else
{
m=MIRACL;
k=0;
}
r=m/2;
sk=1;
for (i=0;i<r;i++) sk*=2;
t=1;
v8=remain(_MIPP_ mr_mip->w2,8);
while (!mr_mip->ERNUM && size(mr_mip->w1)!=0)
{
if (size(mr_mip->w1)<0)
{
negify(mr_mip->w1,mr_mip->w1);
if (v8%4==3) t=-t;
}
do { // oddify
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
if (mr_mip->base==k) u=mr_mip->w1->w[0];
else u=MR_REMAIN(mr_mip->w1->w[0],k);
#ifndef MR_ALWAYS_BINARY
}
#ifdef MR_FP_ROUNDING
else u=mr_sdiv(_MIPP_ mr_mip->w1,k,ik,mr_mip->w3);
#else
else u=mr_sdiv(_MIPP_ mr_mip->w1,k,mr_mip->w3);
#endif
#endif
if (u==0) {s=k; e=0;}
else
{
s=1; e=0;
while (MR_REMAIN(u,2)==0) {s*=2; e++; u=MR_DIV(u,2);}
}
if (s==mr_mip->base) mr_shift(_MIPP_ mr_mip->w1,-1,mr_mip->w1);
#ifdef MR_FP_ROUNDING
else if (s>1)
{
mr_sdiv(_MIPP_ mr_mip->w1,s,mr_invert(s),mr_mip->w1);
}
#else
else if (s>1) mr_sdiv(_MIPP_ mr_mip->w1,s,mr_mip->w1);
#endif
} while (u==0);
if (e%2!=0 && (v8==3 || v8==5)) t=-t;
if (mr_compare(mr_mip->w1,mr_mip->w2)<0)
{
if (mr_mip->base==mr_mip->base2) u4=(int)MR_REMAIN(mr_mip->w1->w[0],4);
else u4=remain(_MIPP_ mr_mip->w1,4);
if (v8%4==3 && u4==3) t=-t;
w=mr_mip->w1; mr_mip->w1=mr_mip->w2; mr_mip->w2=w;
}
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
if (k==mr_mip->base)
{
u=mr_mip->w1->w[0];
v=mr_mip->w2->w[0];
}
else
{
u=MR_REMAIN(mr_mip->w1->w[0],k);
v=MR_REMAIN(mr_mip->w2->w[0],k);
}
#ifndef MR_ALWAYS_BINARY
}
else
{
#ifdef MR_FP_ROUNDING
u=mr_sdiv(_MIPP_ mr_mip->w1,k,ik,mr_mip->w3);
v=mr_sdiv(_MIPP_ mr_mip->w2,k,ik,mr_mip->w3);
#else
u=mr_sdiv(_MIPP_ mr_mip->w1,k,mr_mip->w3);
v=mr_sdiv(_MIPP_ mr_mip->w2,k,mr_mip->w3);
#endif
}
#endif
rfind(u,v,k,sk,&a,&b);
if (a>1)
{
#ifdef MR_FP_ROUNDING
d=mr_sdiv(_MIPP_ mr_mip->w2,a,mr_invert(a),mr_mip->w3);
#else
d=mr_sdiv(_MIPP_ mr_mip->w2,a,mr_mip->w3);
#endif
d=sgcd(d,a);
a=MR_DIV(a,d);
}
else d=1;
if (d>1)
{
#ifdef MR_FP_ROUNDING
id=mr_invert(d);
mr_sdiv(_MIPP_ mr_mip->w2,d,id,mr_mip->w2);
u=mr_sdiv(_MIPP_ mr_mip->w1,d,id,mr_mip->w3);
#else
mr_sdiv(_MIPP_ mr_mip->w2,d,mr_mip->w2);
u=mr_sdiv(_MIPP_ mr_mip->w1,d,mr_mip->w3);
#endif
}
else u=0;
g=a;
if (mr_mip->base==mr_mip->base2) v8=(int)MR_REMAIN(mr_mip->w2->w[0],8);
else v8=remain(_MIPP_ mr_mip->w2,8);
while (MR_REMAIN(g,2)==0)
{
g=MR_DIV(g,2);
if (v8==3 || v8==5) t=-t;
}
if (MR_REMAIN(g,4)==3 && v8%4==3) t=-t;
#ifdef MR_FP_ROUNDING
v=mr_sdiv(_MIPP_ mr_mip->w2,g,mr_invert(g),mr_mip->w3);
#else
v=mr_sdiv(_MIPP_ mr_mip->w2,g,mr_mip->w3);
#endif
t*=jac(v,g)*jac(u,d);
if (t==0)
{
MR_OUT
return 0;
}
// printf("a= %I64d b=%I64d %d\n",a,b,(int)b);
if (a>1) mr_pmul(_MIPP_ mr_mip->w1,a,mr_mip->w1);
if (b>=0)
mr_pmul(_MIPP_ mr_mip->w2,b,mr_mip->w3);
else
{
b=-b;
mr_pmul(_MIPP_ mr_mip->w2,b,mr_mip->w3);
negify(mr_mip->w3,mr_mip->w3);
}
// premult(_MIPP_ mr_mip->w2,(int)b,mr_mip->w3); <- nasty bug - potential loss of precision in b
add(_MIPP_ mr_mip->w1,mr_mip->w3,mr_mip->w1);
if (k==mr_mip->base) mr_shift(_MIPP_ mr_mip->w1,-1,mr_mip->w1);
#ifdef MR_FP_ROUNDING
else mr_sdiv(_MIPP_ mr_mip->w1,k,ik,mr_mip->w1);
#else
else mr_sdiv(_MIPP_ mr_mip->w1,k,mr_mip->w1);
#endif
}
MR_OUT
if (size(mr_mip->w2)==1) return t;
return 0;
}
*/
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