/* Galbraith & Scott Method */
static void gs(BIG u[4],BIG e)
{
int i,j;
BIG v[4],t,q;
DBIG d;
BIG_rcopy(q,CURVE_Order);
for (i=0;i<4;i++)
{
BIG_rcopy(t,CURVE_WB[i]);
BIG_mul(d,t,e);
BIG_ddiv(v[i],d,q);
BIG_zero(u[i]);
}
BIG_copy(u[0],e);
for (i=0;i<4;i++)
for (j=0;j<4;j++)
{
BIG_rcopy(t,CURVE_BB[j][i]);
BIG_modmul(t,v[j],t,q);
BIG_add(u[i],u[i],q);
BIG_sub(u[i],u[i],t);
BIG_mod(u[i],q);
}
return;
}
/* Galbraith & Scott Method */
static void gs(BIG u[4],BIG e)
{
int i;
#if CHOICE<BLS_CURVES
int j;
BIG v[4],t,q;
DBIG d;
BIG_rcopy(q,CURVE_Order);
for (i=0; i<4; i++)
{
BIG_rcopy(t,CURVE_WB[i]);
//BIG_norm(t); BIG_norm(e);
BIG_mul(d,t,e);
BIG_ddiv(v[i],d,q);
BIG_zero(u[i]);
}
BIG_copy(u[0],e);
for (i=0; i<4; i++)
for (j=0; j<4; j++)
{
BIG_rcopy(t,CURVE_BB[j][i]);
BIG_modmul(t,v[j],t,q);
BIG_add(u[i],u[i],q);
BIG_sub(u[i],u[i],t);
BIG_mod(u[i],q);
}
#else
BIG x,w;
BIG_rcopy(x,CURVE_Bnx);
BIG_copy(w,e);
for (i=0; i<4; i++)
{
BIG_copy(u[i],w);
BIG_mod(u[i],x);
BIG_sdiv(w,x);
}
#endif
return;
}
/* GLV method */
static void glv(BIG u[2],BIG e)
{
#if CHOICE<BLS_CURVES
int i,j;
BIG v[2],t,q;
DBIG d;
BIG_rcopy(q,CURVE_Order);
for (i=0; i<2; i++)
{
BIG_rcopy(t,CURVE_W[i]);
//BIG_norm(t); BIG_norm(e);
BIG_mul(d,t,e);
BIG_ddiv(v[i],d,q);
BIG_zero(u[i]);
}
BIG_copy(u[0],e);
for (i=0; i<2; i++)
for (j=0; j<2; j++)
{
BIG_rcopy(t,CURVE_SB[j][i]);
BIG_modmul(t,v[j],t,q);
BIG_add(u[i],u[i],q);
BIG_sub(u[i],u[i],t);
BIG_mod(u[i],q);
}
#else
// -(x^2).P = (Beta.x,y)
BIG x,x2,q;
BIG_rcopy(x,CURVE_Bnx);
BIG_smul(x2,x,x);
BIG_copy(u[0],e);
BIG_mod(u[0],x2);
BIG_copy(u[1],e);
BIG_sdiv(u[1],x2);
BIG_rcopy(q,CURVE_Order);
BIG_sub(u[1],q,u[1]);
#endif
return;
}
void FP12_pow4(FP12 *p,FP12 *q,BIG u[4])
{
int i,j,a[4],nb,m;
FP12 g[8],c,s[2];
BIG t[4],mt;
sign8 w[NLEN*BASEBITS+1];
for (i=0;i<4;i++)
BIG_copy(t[i],u[i]);
FP12_copy(&g[0],&q[0]); FP12_conj(&s[0],&q[1]); FP12_mul(&g[0],&s[0]); /* P/Q */
FP12_copy(&g[1],&g[0]);
FP12_copy(&g[2],&g[0]);
FP12_copy(&g[3],&g[0]);
FP12_copy(&g[4],&q[0]); FP12_mul(&g[4],&q[1]); /* P*Q */
FP12_copy(&g[5],&g[4]);
FP12_copy(&g[6],&g[4]);
FP12_copy(&g[7],&g[4]);
FP12_copy(&s[1],&q[2]); FP12_conj(&s[0],&q[3]); FP12_mul(&s[1],&s[0]); /* R/S */
FP12_conj(&s[0],&s[1]); FP12_mul(&g[1],&s[0]);
FP12_mul(&g[2],&s[1]);
FP12_mul(&g[5],&s[0]);
FP12_mul(&g[6],&s[1]);
FP12_copy(&s[1],&q[2]); FP12_mul(&s[1],&q[3]); /* R*S */
FP12_conj(&s[0],&s[1]); FP12_mul(&g[0],&s[0]);
FP12_mul(&g[3],&s[1]);
FP12_mul(&g[4],&s[0]);
FP12_mul(&g[7],&s[1]);
/* if power is even add 1 to power, and add q to correction */
FP12_one(&c);
BIG_zero(mt);
for (i=0;i<4;i++)
{
if (BIG_parity(t[i])==0)
{
BIG_inc(t[i],1); BIG_norm(t[i]);
FP12_mul(&c,&q[i]);
}
BIG_add(mt,mt,t[i]); BIG_norm(mt);
}
FP12_conj(&c,&c);
nb=1+BIG_nbits(mt);
/* convert exponent to signed 1-bit window */
for (j=0;j<nb;j++)
{
for (i=0;i<4;i++)
{
a[i]=BIG_lastbits(t[i],2)-2;
BIG_dec(t[i],a[i]); BIG_norm(t[i]);
BIG_fshr(t[i],1);
}
w[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
}
w[nb]=8*BIG_lastbits(t[0],2)+4*BIG_lastbits(t[1],2)+2*BIG_lastbits(t[2],2)+BIG_lastbits(t[3],2);
FP12_copy(p,&g[(w[nb]-1)/2]);
for (i=nb-1;i>=0;i--)
{
m=w[i]>>7;
j=(w[i]^m)-m; /* j=abs(w[i]) */
j=(j-1)/2;
FP12_copy(&s[0],&g[j]);
FP12_conj(&s[1],&g[j]);
FP12_usqr(p,p);
FP12_mul(p,&s[m&1]);
}
FP12_mul(p,&c); /* apply correction */
FP12_reduce(p);
}
