double mult2_double(int eb,epoint *g)
{
big e1,e2;
int iterations=0;
clock_t start;
double elapsed;
char *mem1;
char *mem2;
epoint *w;
epoint *r1;
epoint *r2;
mem1=(char *)memalloc(2);
mem2=(char *)ecp_memalloc(3);
e1=mirvar_mem(mem1,0);
e2=mirvar_mem(mem1,1);
w=epoint_init_mem(mem2,0);
r1=epoint_init_mem(mem2,1);
r2=epoint_init_mem(mem2,2);
bigbits(eb,e1);
ecurve2_mult(e1,g,r1); /* generate a random point on the curve */
bigbits(eb,e2);
ecurve2_mult(e2,g,r2); /* generate a random point on the curve */
bigbits(eb,e1);
bigbits(eb,e2);
start=clock();
do {
ecurve2_mult2(e1,r1,e2,r2,w);
iterations++;
elapsed=(clock()-start)/(double)CLOCKS_PER_SEC;
} while (elapsed<MIN_TIME || iterations<MIN_ITERS);
elapsed=1000.0*elapsed/iterations;
printf("ED - %8d iterations ",iterations);
printf(" %8.2lf ms per iteration\n",elapsed);
ecp_memkill(mem2,3);
memkill(mem1,2);
return elapsed;
}
double mults2(int eb,epoint *g)
{
big e;
int iterations=0;
clock_t start;
double elapsed;
epoint *w;
epoint *r;
char *mem1;
char *mem2;
mem1=(char *)memalloc(1);
mem2=(char *)ecp_memalloc(2);
e=mirvar_mem(mem1,0);
w=epoint_init_mem(mem2,0);
r=epoint_init_mem(mem2,1);
bigbits(eb,e);
ecurve2_mult(e,g,r); /* generate a random point on the curve */
bigbits(eb,e);
start=clock();
do {
ecurve2_mult(e,r,w);
iterations++;
elapsed=(clock()-start)/(double)CLOCKS_PER_SEC;
} while (elapsed<MIN_TIME || iterations<MIN_ITERS);
elapsed=1000.0*elapsed/iterations;
printf("ER - %8d iterations ",iterations);
printf(" %8.2lf ms per iteration\n",elapsed);
memkill(mem1,1);
ecp_memkill(mem2,2);
return elapsed;
}
int main()
{
#ifdef MR_GENERIC_MT
miracl instance;
#endif
big p,A,B,fr,q,delta,t,T;
zzn2 res,Qx,Qy;
epoint *P;
int i,romptr;
#ifndef MR_STATIC
#ifdef MR_GENERIC_MT
miracl *mr_mip=mirsys(&instance,WORDS*NPW,16);
#else
miracl *mr_mip=mirsys(WORDS*NPW,16);
#endif
char *mem=memalloc(_MIPP_ 14);
char *mem1=ecp_memalloc(_MIPP_ 1);
#else
#ifdef MR_GENERIC_MT
miracl *mr_mip=mirsys(&instance,MR_STATIC*NPW,16);
#else
miracl *mr_mip=mirsys(MR_STATIC*NPW,16);
#endif
char mem[MR_BIG_RESERVE(14)]; /* reserve space on the stack for 14 bigs */
char mem1[MR_ECP_RESERVE(1)]; /* reserve space on stack for 1 curve points */
memset(mem,0,MR_BIG_RESERVE(14)); /* clear this memory */
memset(mem1,0,MR_ECP_RESERVE(1));
#endif
p=mirvar_mem(_MIPP_ mem,0);
A=mirvar_mem(_MIPP_ mem,1);
B=mirvar_mem(_MIPP_ mem,2);
T=mirvar_mem(_MIPP_ mem,3);
q=mirvar_mem(_MIPP_ mem,4);
fr=mirvar_mem(_MIPP_ mem,5);
delta=mirvar_mem(_MIPP_ mem,6);
res.a=mirvar_mem(_MIPP_ mem,7);
res.b=mirvar_mem(_MIPP_ mem,8);
t=mirvar_mem(_MIPP_ mem,9);
Qx.a=mirvar_mem(_MIPP_ mem,10);
Qx.b=mirvar_mem(_MIPP_ mem,11);
Qy.a=mirvar_mem(_MIPP_ mem,12);
Qy.b=mirvar_mem(_MIPP_ mem,13);
P=epoint_init_mem(_MIPP_ mem1,0);
convert(_MIPP_ -3,A);
romptr=0;
init_big_from_rom(p,WORDS,romp,ROMSZ,&romptr);
init_big_from_rom(B,WORDS,romp,ROMSZ,&romptr);
init_big_from_rom(q,WORDS,romp,ROMSZ,&romptr);
init_big_from_rom(delta,WORDS,romp,ROMSZ,&romptr);
init_big_from_rom(fr,WORDS,romp,ROMSZ,&romptr);
init_big_from_rom(T,WORDS,romp,ROMSZ,&romptr);
#ifndef MR_NO_STANDARD_IO
printf("ROM size= %d\n",sizeof(romp)+sizeof(Prom));
printf("sizeof(miracl)= %d\n",sizeof(miracl));
#endif
ecurve_init(_MIPP_ A,B,p,MR_PROJECTIVE);
romptr=0;
init_point_from_rom(P,WORDS,Prom,PROMSZ,&romptr);
init_big_from_rom(Qx.a,WORDS,Prom,PROMSZ,&romptr);
init_big_from_rom(Qx.b,WORDS,Prom,PROMSZ,&romptr);
init_big_from_rom(Qy.a,WORDS,Prom,PROMSZ,&romptr);
init_big_from_rom(Qy.b,WORDS,Prom,PROMSZ,&romptr);
#ifdef MR_COUNT_OPS
fpa=fpc=fpx=0;
#endif
ecap(_MIPP_ &Qx,&Qy,P,T,fr,delta,&res);
/*
#ifdef MR_COUNT_OPS
printf("fpc= %d\n",fpc);
printf("fpa= %d\n",fpa);
printf("fpx= %d\n",fpx);
fpa=fpc=fpx=0;
#endif
*/
bigbits(_MIPP_ 160,t);
zzn2_powl(_MIPP_ &res,t,&res);
#ifndef MR_NO_STANDARD_IO
zzn2_out(_MIPP_ "res= ",&res);
#endif
ecurve_mult(_MIPP_ t,P,P);
ecap(_MIPP_ &Qx,&Qy,P,T,fr,delta,&res);
#ifndef MR_NO_STANDARD_IO
zzn2_out(_MIPP_ "res= ",&res);
#endif
#ifndef MR_STATIC
memkill(_MIPP_ mem,14);
ecp_memkill(_MIPP_ mem1,1);
#else
memset(mem,0,MR_BIG_RESERVE(14)); /* clear this stack memory */
memset(mem1,0,MR_ECP_RESERVE(1));
#endif
return 0;
}
int main()
{
big a2,a6,bx,r;
big res[4];
epoint *P,*Q;
int i,romptr;
miracl instance; /* sizeof(miracl)= 2000 bytes from the stack */
#ifndef MR_STATIC
#ifdef MR_GENERIC_MT
miracl *mr_mip=mirsys(WORDS*NPW,16);
#else
miracl *mr_mip=mirsys(WORDS*NPW,16);
#endif
char *mem=(char *)memalloc(_MIPP_ 8);
char *mem1=(char *)ecp_memalloc(_MIPP_ 2);
#else
#ifdef MR_GENERIC_MT
miracl *mr_mip=mirsys(&instance,MR_STATIC*NPW,16); /* size of bigs is fixed */
#else
miracl *mr_mip=mirsys(&instance,MR_STATIC*NPW,16);
#endif
char mem[MR_BIG_RESERVE(8)]; /* reserve space on the stack for 8 bigs */
char mem1[MR_ECP_RESERVE(2)]; /* reserve space on stack for 2 curve points */
memset(mem,0,MR_BIG_RESERVE(8)); /* clear this memory */
memset(mem1,0,MR_ECP_RESERVE(2)); /* ~668 bytes in all */
#endif
/* Initialise bigs */
a2=mirvar_mem(_MIPP_ mem,0);
a6=mirvar_mem(_MIPP_ mem,1);
bx=mirvar_mem(_MIPP_ mem,2);
for (i=0;i<4;i++)
res[i]=mirvar_mem(_MIPP_ mem,3+i);
r=mirvar_mem(_MIPP_ mem,7);
/* printf("ROM size= %d\n",sizeof(rom)+sizeof(prom)); */
#ifndef MR_NO_STANDARD_IO
#ifdef MR_STATIC
printf("n Bigs require n*%d+%d bytes\n",MR_SIZE,MR_SL);
printf("n Points require n*%d+%d bytes\n",MR_ESIZE,MR_SL);
printf("sizeof(miracl)= %d\n",sizeof(miracl));
#endif
#endif
/* Initialise Elliptic curve points */
P=epoint_init_mem(_MIPP_ mem1,0);
Q=epoint_init_mem(_MIPP_ mem1,1);
/* Initialise supersingular curve */
convert(_MIPP_ 1,a2);
convert(_MIPP_ B,a6);
/* The -M tells MIRACL that this is a supersingular curve */
if (!ecurve2_init(_MIPP_ -M,T,U,V,a2,a6,FALSE,MR_PROJECTIVE))
{
#ifndef MR_NO_STANDARD_IO
printf("Problem with the curve\n");
#endif
return 0;
}
/* Get P and Q from ROM */
/* These should have been multiplied by the cofactor 487805 = 5*97561 */
/* 487805 is a cofactor of the group order 2^271+2^136+1 */
romptr=0;
init_point_from_rom(P,WORDS,rom,ROMSZ,&romptr);
init_point_from_rom(Q,WORDS,rom,ROMSZ,&romptr);
#ifndef MR_NO_STANDARD_IO
printf( "P= \n");
otnum(_MIPP_ P->X,stdout);
otnum(_MIPP_ P->Y,stdout);
printf( "Q= \n");
otnum(_MIPP_ Q->X,stdout);
otnum(_MIPP_ Q->Y,stdout);
#endif
bigbits(_MIPP_ 160,r);
/* Simple bilinearity test */
tate(_MIPP_ P,Q,res);
/* this could break the 4k stack, 2060+668+2996 >4K */
/* so we cannot afford much precomputation in power4 */
power4(_MIPP_ res,r,res); /* res=res^{sr} */
#ifndef MR_NO_STANDARD_IO
printf( "\ne(P,Q)^r= \n");
for (i=0;i<4;i++)
{
otnum(_MIPP_ res[i],stdout);
zero(res[i]);
}
#endif
ecurve2_mult(_MIPP_ r,Q,Q); /* Q=rQ */
epoint2_norm(_MIPP_ Q);
tate(_MIPP_ P,Q,res); /* Now invert is taken out of Tate, and the stack should be OK */
#ifndef MR_NO_STANDARD_IO
printf( "\ne(P,rQ)= \n");
for (i=0;i<4;i++)
otnum(_MIPP_ res[i],stdout);
#endif
/* all done */
#ifndef MR_STATIC
memkill(_MIPP_ mem,8);
ecp_memkill(_MIPP_ mem1,2);
#else
memset(mem,0,MR_BIG_RESERVE(8)); /* clear this stack memory */
memset(mem1,0,MR_ECP_RESERVE(2));
#endif
mirexit(_MIPPO_ ); /* clears workspace memory */
return 0;
}
void fast_tate_pairing(_MIPD_ epoint *P,zzn3 *Qx,zzn3 *Qy,big q,big cf,zzn6 *w,zzn6* res)
{
int i,j,n,nb,nbw,nzs;
epoint *t[4],*A,*P2;
zzn6 zn[4];
big work[4];
#ifndef MR_STATIC
char *mem=memalloc(_MIPP_ 28);
char *mem1=ecp_memalloc(_MIPP_ 6);
#else
char mem[MR_BIG_RESERVE(28)];
char mem1[MR_ECP_RESERVE(6)];
memset(mem,0,MR_BIG_RESERVE(28));
memset(mem1,0,MR_ECP_RESERVE(6));
#endif
for (i=0;i<4;i++)
t[i]=epoint_init_mem(_MIPP_ mem1,i);
A=epoint_init_mem(_MIPP_ mem1,4);
P2=epoint_init_mem(_MIPP_ mem1,5);
for (j=i=0;i<4;i++)
{
work[i]=mirvar_mem(_MIPP_ mem,j++);
zn[i].x.a=mirvar_mem(_MIPP_ mem,j++);
zn[i].x.b=mirvar_mem(_MIPP_ mem,j++);
zn[i].x.c=mirvar_mem(_MIPP_ mem,j++);
zn[i].y.a=mirvar_mem(_MIPP_ mem,j++);
zn[i].y.b=mirvar_mem(_MIPP_ mem,j++);
zn[i].y.c=mirvar_mem(_MIPP_ mem,j++);
zn[i].unitary=FALSE;
}
zzn6_from_int(_MIPP_ 1,&zn[0]);
epoint_copy(P,A);
epoint_copy(P,P2);
epoint_copy(P,t[0]);
g(_MIPP_ P2,P2,Qx,Qy,res);
epoint_norm(_MIPP_ P2);
for (i=1;i<4;i++)
{
g(_MIPP_ A,P2,Qx,Qy,w);
epoint_copy(A,t[i]);
zzn6_mul(_MIPP_ &zn[i-1],w,&zn[i]);
zzn6_mul(_MIPP_ &zn[i],res,&zn[i]);
}
epoint_multi_norm(_MIPP_ 4,work,t);
epoint_copy(P,A);
zzn6_from_int(_MIPP_ 1,res);
nb=logb2(_MIPP_ q);
for (i=nb-2;i>=0;i-=(nbw+nzs))
{
n=mr_window(_MIPP_ q,i,&nbw,&nzs,3);
for (j=0;j<nbw;j++)
{
zzn6_mul(_MIPP_ res,res,res);
g(_MIPP_ A,A,Qx,Qy,w);
zzn6_mul(_MIPP_ res,w,res);
}
if (n>0)
{
zzn6_mul(_MIPP_ res,&zn[n/2],res);
g(_MIPP_ A,t[n/2],Qx,Qy,w);
zzn6_mul(_MIPP_ res,w,res);
}
for (j=0;j<nzs;j++)
{
zzn6_mul(_MIPP_ res,res,res);
g(_MIPP_ A,A,Qx,Qy,w);
zzn6_mul(_MIPP_ res,w,res);
}
}
zzn6_copy(res,w);
zzn6_powq(_MIPP_ w);
zzn6_mul(_MIPP_ res,w,res);
zzn6_copy(res,w);
zzn6_powq(_MIPP_ w);
zzn6_powq(_MIPP_ w);
zzn6_powq(_MIPP_ w);
zzn6_inv(_MIPP_ res);
zzn6_mul(_MIPP_ res,w,res);
res->unitary=TRUE;
#ifndef MR_STATIC
memkill(_MIPP_ mem,28);
ecp_memkill(_MIPP_ mem1,6);
#else
memset(mem,0,MR_BIG_RESERVE(28));
memset(mem1,0,MR_ECP_RESERVE(6));
#endif
}