BOOL froot(_MIPD_ flash x,int n,flash w)
{ /* extract nth root of x - w=x^(1/n) using Newtons method */
BOOL minus,rn,rm,hack;
int nm,dn,s,op[5];
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
copy(x,w);
if (mr_mip->ERNUM || n==1) return TRUE;
if (n==(-1))
{
frecip(_MIPP_ w,w);
return TRUE;
}
MR_IN(52)
minus=FALSE;
if (n<0)
{
minus=TRUE;
n=(-n);
}
s=exsign(w);
if (n%2==0 && s==MINUS)
{
mr_berror(_MIPP_ MR_ERR_NEG_ROOT);
MR_OUT
return FALSE;
}
BOOL zzn2_qr(_MIPD_ zzn2 *u)
{
int j;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return FALSE;
if (zzn2_iszero(u)) return TRUE;
if (size(u->b)==0) return TRUE;
if (mr_mip->qnr==-1 && size(u->a)==0) return TRUE;
MR_IN(203)
nres_modmult(_MIPP_ u->b,u->b,mr_mip->w1);
if (mr_mip->qnr==-2) nres_modadd(_MIPP_ mr_mip->w1,mr_mip->w1,mr_mip->w1);
nres_modmult(_MIPP_ u->a,u->a,mr_mip->w2);
nres_modadd(_MIPP_ mr_mip->w1,mr_mip->w2,mr_mip->w1);
redc(_MIPP_ mr_mip->w1,mr_mip->w1);
j=jack(_MIPP_ mr_mip->w1,mr_mip->modulus);
MR_OUT
if (j==1) return TRUE;
return FALSE;
}
void strong_bigrand(_MIPD_ csprng *rng,big w,big x)
{
int i, m;
mr_small r;
unsigned int ran;
unsigned int ch;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(20)
m = 0;
zero(mr_mip->w1);
do
{
m++;
mr_mip->w1->len=m;
for (r = 0, i = 0; i < sizeof(mr_small); i++) {
ch=(unsigned char)strong_rng(rng);
ran=ch;
r = (r << 8) ^ ran;
}
if (mr_mip->base==0) mr_mip->w1->w[m-1]=r;
else mr_mip->w1->w[m-1]=MR_REMAIN(r,mr_mip->base);
} while (mr_compare(mr_mip->w1,w)<0);
mr_lzero(mr_mip->w1);
divide(_MIPP_ mr_mip->w1,w,w);
copy(mr_mip->w1,x);
MR_OUT
}
void fexp(_MIPD_ flash x,flash y)
{ /* calculates y=exp(x) */
int i,n,nsq,m,sqrn,op[5];
BOOL minus,rem;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
if (size(x)==0)
{
convert(_MIPP_ 1,y);
return;
}
copy(x,y);
MR_IN(54)
minus=FALSE;
if (size(y)<0)
{
minus=TRUE;
negate(y,y);
}
ftrunc(_MIPP_ y,y,mr_mip->w9);
n=size(y);
if (n==MR_TOOBIG)
{
mr_berror(_MIPP_ MR_ERR_FLASH_OVERFLOW);
MR_OUT
return;
}
void zzn3_div2(_MIPD_ zzn3 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(188)
copy(w->a,mr_mip->w1);
if (remain(_MIPP_ mr_mip->w1,2)!=0)
add(_MIPP_ mr_mip->w1,mr_mip->modulus,mr_mip->w1);
subdiv(_MIPP_ mr_mip->w1,2,mr_mip->w1);
copy(mr_mip->w1,w->a);
copy(w->b,mr_mip->w1);
if (remain(_MIPP_ mr_mip->w1,2)!=0)
add(_MIPP_ mr_mip->w1,mr_mip->modulus,mr_mip->w1);
subdiv(_MIPP_ mr_mip->w1,2,mr_mip->w1);
copy(mr_mip->w1,w->b);
copy(w->c,mr_mip->w1);
if (remain(_MIPP_ mr_mip->w1,2)!=0)
add(_MIPP_ mr_mip->w1,mr_mip->modulus,mr_mip->w1);
subdiv(_MIPP_ mr_mip->w1,2,mr_mip->w1);
copy(mr_mip->w1,w->c);
MR_OUT
}
void frand(_MIPD_ flash x)
{ /* generates random flash number 0<x<1 */
int i;
#ifdef MR_FP
mr_small dres;
#endif
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(46)
zero(mr_mip->w6);
mr_mip->w6->len=mr_mip->nib;
for (i=0;i<mr_mip->nib;i++)
{ /* generate a full width random number */
if (mr_mip->base==0) mr_mip->w6->w[i]=brand(_MIPPO_ );
else mr_mip->w6->w[i]=MR_REMAIN(brand(_MIPPO_ ),mr_mip->base);
}
mr_mip->check=OFF;
bigrand(_MIPP_ mr_mip->w6,mr_mip->w5);
mr_mip->check=ON;
mround(_MIPP_ mr_mip->w5,mr_mip->w6,x);
MR_OUT
}
void zzn4_inv(_MIPD_ zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
zzn2 t1,t2;
if (mr_mip->ERNUM) return;
if (w->unitary)
{
zzn4_conj(_MIPP_ w,w);
return;
}
MR_IN(FUNC_BASE+10)
t1.a=mr_mip->w8;
t1.b=mr_mip->w9;
t2.a=mr_mip->w10;
t2.b=mr_mip->w11;
zzn2_mul(_MIPP_ &(w->a),&(w->a),&t1);
zzn2_mul(_MIPP_ &(w->b),&(w->b),&t2);
zzn2_txx(_MIPP_ &t2);
zzn2_sub(_MIPP_ &t1,&t2,&t1);
zzn2_inv(_MIPP_ &t1);
zzn2_mul(_MIPP_ &(w->a),&t1,&(w->a));
zzn2_negate(_MIPP_ &t1,&t1);
zzn2_mul(_MIPP_ &(w->b),&t1,&(w->b));
MR_OUT
}
void nres_powltr(_MIPD_ int x,big y,big w)
{ /* calculates w=x^y mod z using Left to Right Method */
/* uses only n^2 modular squarings, because x is small */
/* Note: x is NOT an nresidue */
int i,nb;
#ifndef MR_GENERIC_MT
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
copy(y,mr_mip->w1);
MR_IN(86)
zero(w);
if (x==0)
{
if (size(mr_mip->w1)==0)
{ /* 0^0 = 1 */
convert(_MIPP_ 1,w);
nres(_MIPP_ w,w);
}
MR_OUT
return;
}
convert(_MIPP_ 1,w);
nres(_MIPP_ w,w);
if (size(mr_mip->w1)==0)
{
MR_OUT
return;
}
void zzn4_mul(_MIPD_ zzn4 *x,zzn4 *y,zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
zzn2 t1,t2,t3;
if (mr_mip->ERNUM) return;
if (x==y) {zzn4_sqr(_MIPP_ x,w); return; }
MR_IN(FUNC_BASE+9)
t1.a=mr_mip->w12;
t1.b=mr_mip->w13;
t2.a=mr_mip->w8;
t2.b=mr_mip->w9;
t3.a=mr_mip->w10;
t3.b=mr_mip->w11;
zzn2_copy(&(x->a),&t1);
zzn2_copy(&(x->b),&t2);
zzn2_mul(_MIPP_ &t1,&(y->a),&t1); /* t1= x->a * y->a */
zzn2_mul(_MIPP_ &t2,&(y->b),&t2); /* t2 = x->b * y->b */
zzn2_copy(&(y->a),&t3);
zzn2_add(_MIPP_ &t3,&(y->b),&t3); /* y->a + y->b */
zzn2_add(_MIPP_ &(x->b),&(x->a),&(w->b)); /* x->a + x->b */
zzn2_mul(_MIPP_ &(w->b),&t3,&(w->b)); /* t3= (x->a + x->b)*(y->a + y->b) */
zzn2_sub(_MIPP_ &(w->b),&t1,&(w->b));
zzn2_sub(_MIPP_ &(w->b),&t2,&(w->b)); /* w->b = t3-(t1+t2) */
zzn2_copy(&t1,&(w->a));
zzn2_txx(_MIPP_ &t2);
zzn2_add(_MIPP_ &(w->a),&t2,&(w->a)); /* w->a = t1+tx(t2) */
if (x->unitary && y->unitary) w->unitary=TRUE;
else w->unitary=FALSE;
MR_OUT
}
void sftbit(_MIPD_ big x,int n,big z)
{ /* shift x by n bits */
int m;
mr_small sm;
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
copy(x,z);
if (n==0) return;
MR_IN(47)
m=mr_abs(n);
sm=mr_shiftbits((mr_small)1,m%mr_mip->lg2b);
if (n>0)
{ /* shift left */
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
mr_shift(_MIPP_ z,n/mr_mip->lg2b,z);
mr_pmul(_MIPP_ z,sm,z);
#ifndef MR_ALWAYS_BINARY
}
else
{
expb2(_MIPP_ m,mr_mip->w1);
multiply(_MIPP_ z,mr_mip->w1,z);
}
#endif
}
else
{ /* shift right */
#ifndef MR_ALWAYS_BINARY
if (mr_mip->base==mr_mip->base2)
{
#endif
mr_shift(_MIPP_ z,n/mr_mip->lg2b,z);
#ifdef MR_FP_ROUNDING
mr_sdiv(_MIPP_ z,sm,mr_invert(sm),z);
#else
mr_sdiv(_MIPP_ z,sm,z);
#endif
#ifndef MR_ALWAYS_BINARY
}
else
{
expb2(_MIPP_ m,mr_mip->w1);
divide(_MIPP_ z,mr_mip->w1,z);
}
#endif
}
MR_OUT
}
void zzn3_ssub(_MIPD_ zzn3 *x,big y,zzn3 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(183)
nres_modsub(_MIPP_ x->a,y,w->a);
MR_OUT
}
void zzn2_sadd(_MIPD_ zzn2 *x,big y,zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(169)
nres_modadd(_MIPP_ x->a,y,w->a);
MR_OUT
}
void zzn4_powq(_MIPD_ zzn2 *fr,zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
MR_IN(FUNC_BASE+12)
zzn2_conj(_MIPP_ &(w->a),&(w->a));
zzn2_conj(_MIPP_ &(w->b),&(w->b));
zzn2_mul(_MIPP_ &(w->b),fr,&(w->b));
MR_OUT
}
void zzn4_sadd(_MIPD_ zzn4 *x,zzn2 *y,zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(FUNC_BASE+4)
zzn2_add(_MIPP_ &(x->a),y,&(w->a));
w->unitary=FALSE;
MR_OUT
}
void zzn4_negate(_MIPD_ zzn4 *x,zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(FUNC_BASE+1)
zzn4_copy(x,w);
zzn2_negate(_MIPP_ &(w->a),&(w->a));
zzn2_negate(_MIPP_ &(w->b),&(w->b));
MR_OUT
}
void zzn3_sub(_MIPD_ zzn3 *x,zzn3 *y,zzn3 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(182)
nres_modsub(_MIPP_ x->a,y->a,w->a);
nres_modsub(_MIPP_ x->b,y->b,w->b);
nres_modsub(_MIPP_ x->c,y->c,w->c);
MR_OUT
}
void zzn3_from_big(_MIPD_ big x, zzn3 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(177)
nres(_MIPP_ x,w->a);
zero(w->b); zero(w->c);
MR_OUT
}
void zzn4_imul(_MIPD_ zzn4 *x,int y,zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(FUNC_BASE+14)
zzn2_imul(_MIPP_ &(x->a),y,&(w->a));
zzn2_imul(_MIPP_ &(x->b),y,&(w->b));
MR_OUT
}
void zzn2_from_bigs(_MIPD_ big x,big y, zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(166)
nres(_MIPP_ x,w->a);
nres(_MIPP_ y,w->b);
MR_OUT
}
int invmodp(_MIPD_ big x,big y,big z)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
int gcd;
MR_IN(213);
gcd=xgcd(_MIPP_ x,y,z,z,z);
MR_OUT
return gcd;
}
void zzn4_from_big(_MIPD_ big x, zzn4 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(FUNC_BASE+16)
zzn2_from_big(_MIPP_ x,&(w->a));
zzn2_zero(&(w->b));
MR_OUT
}
void zzn2_negate(_MIPD_ zzn2 *x,zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(157)
zzn2_copy(x,w);
nres_negate(_MIPP_ w->a,w->a);
nres_negate(_MIPP_ w->b,w->b);
MR_OUT
}
void zzn2_div5(_MIPD_ zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(209)
nres_div5(_MIPP_ w->a,w->a);
nres_div5(_MIPP_ w->b,w->b);
MR_OUT
}
void add(_MIPD_ big x,big y,big z)
{ /* add two signed big numbers together z=x+y */
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(27)
mr_select(_MIPP_ x,PLUS,y,z);
MR_OUT
}
void subtract(_MIPD_ big x,big y,big z)
{ /* subtract two big signed numbers z=x-y */
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(28)
mr_select(_MIPP_ x,MINUS,y,z);
MR_OUT
}
void zzn2_from_int(_MIPD_ int i,zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(156)
convert(_MIPP_ i,mr_mip->w1);
nres(_MIPP_ mr_mip->w1,w->a);
zero(w->b);
MR_OUT
}
void zzn2_sub(_MIPD_ zzn2 *x,zzn2 *y,zzn2 *w)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
#ifdef MR_COUNT_OPS
fpaq++;
#endif
MR_IN(160)
nres_modsub(_MIPP_ x->a,y->a,w->a);
nres_modsub(_MIPP_ x->b,y->b,w->b);
MR_OUT
}
void fmodulo(_MIPD_ flash x,flash y,flash z)
{ /* sets z=x mod y */
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM) return;
MR_IN(89)
fdiv(_MIPP_ x,y,mr_mip->w8);
ftrunc(_MIPP_ mr_mip->w8,mr_mip->w8,mr_mip->w8);
fmul(_MIPP_ mr_mip->w8,y,mr_mip->w8);
fsub(_MIPP_ x,mr_mip->w8,z);
MR_OUT
}
void zzn3_powq(_MIPD_ zzn3 *x,zzn3 *w)
{ /* sru - precalculated sixth root of unity */
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
MR_IN(178)
zzn3_copy(x,w);
nres_modmult(_MIPP_ mr_mip->sru,mr_mip->sru,mr_mip->w1); /* cube root of unity */
nres_modmult(_MIPP_ w->b,mr_mip->w1,w->b);
nres_modmult(_MIPP_ w->c,mr_mip->w1,w->c);
nres_modmult(_MIPP_ w->c,mr_mip->w1,w->c);
MR_OUT
}
BOOL zzn2_isunity(_MIPD_ zzn2 *x)
{
#ifdef MR_OS_THREADS
miracl *mr_mip=get_mip();
#endif
if (mr_mip->ERNUM || size(x->b)!=0) return FALSE;
MR_IN(155)
redc(_MIPP_ x->a,mr_mip->w1);
MR_OUT
if (size(mr_mip->w1)==1) return TRUE;
return FALSE;
}
