/*
* mpbslide_w
* precomputes the sliding window table for computing powers of x modulo b
* needs workspace (4*size+2)
*/
void mpbslide_w(const mpbarrett* b, size_t xsize, const mpw* xdata, mpw* slide, mpw* wksp)
{
register size_t size = b->size;
mpbsqrmod_w(b, xsize, xdata, slide , wksp); /* x^2 mod b, temp */
mpbmulmod_w(b, xsize, xdata, size, slide , slide+size , wksp); /* x^3 mod b */
mpbmulmod_w(b, size, slide, size, slide+size , slide+2*size, wksp); /* x^5 mod b */
mpbmulmod_w(b, size, slide, size, slide+2*size, slide+3*size, wksp); /* x^7 mod b */
mpbmulmod_w(b, size, slide, size, slide+3*size, slide+4*size, wksp); /* x^9 mod b */
mpbmulmod_w(b, size, slide, size, slide+4*size, slide+5*size, wksp); /* x^11 mod b */
mpbmulmod_w(b, size, slide, size, slide+5*size, slide+6*size, wksp); /* x^13 mod b */
mpbmulmod_w(b, size, slide, size, slide+6*size, slide+7*size, wksp); /* x^15 mod b */
mpsetx(size, slide, xsize, xdata); /* x^1 mod b */
}
/*
* needs workspace of (5*size+2) words
*/
int mppmilraba_w(const mpbarrett* p, const mpw* adata, int s, const mpw* rdata, const mpw* ndata, mpw* wksp)
{
register size_t size = p->size;
register int j = 0;
mpbpowmod_w(p, size, adata, size, rdata, wksp, wksp+size);
while (1)
{
if (mpisone(size, wksp))
return (j == 0);
if (mpeq(size, wksp, ndata))
return 1;
if (++j < s)
mpbsqrmod_w(p, size, wksp, wksp, wksp+size);
else
return 0;
}
}
/*
* mpbtwopowmod_w
* needs workspace of (4*size+2) words
*/
void mpbtwopowmod_w(const mpbarrett* b, size_t psize, const mpw* pdata, mpw* result, mpw* wksp)
{
/*
* Modular exponention, 2^p mod modulus, special optimization
*
* Uses left-to-right exponentiation; needs no extra storage
*
*/
/* this routine calls mpbmod, which needs (size*2+2), this routine needs (size*2) for sdata */
register size_t size = b->size;
register mpw temp = 0;
mpsetw(size, result, 1);
while (psize)
{
if ((temp = *(pdata++))) /* break when first non-zero word found */
break;
psize--;
}
/* if temp is still zero, then we're trying to raise x to power zero, and result stays one */
if (temp)
{
register int count = MP_WBITS;
/* first skip bits until we reach a one */
while (count)
{
if (temp & MP_MSBMASK)
break;
temp <<= 1;
count--;
}
while (psize--)
{
while (count)
{
/* always square */
mpbsqrmod_w(b, size, result, result, wksp);
/* multiply by two if bit is 1 */
if (temp & MP_MSBMASK)
{
if (mpadd(size, result, result) || mpge(size, result, b->modl))
{
/* there was carry, or the result is greater than the modulus, so we need to adjust */
mpsub(size, result, b->modl);
}
}
temp <<= 1;
count--;
}
count = MP_WBITS;
temp = *(pdata++);
}
}
}
void mpbpowmodsld_w(const mpbarrett* b, const mpw* slide, size_t psize, const mpw* pdata, mpw* result, mpw* wksp)
{
/*
* Modular exponentiation with precomputed sliding window table, so no x is required
*
*/
size_t size = b->size;
mpw temp;
mpsetw(size, result, 1);
while (psize)
{
if ((temp = *(pdata++))) /* break when first non-zero word found in power */
break;
psize--;
}
/* if temp is still zero, then we're trying to raise x to power zero, and result stays one */
if (temp)
{
short l = 0, n = 0, count = MP_WBITS;
/* first skip bits until we reach a one */
while (count)
{
if (temp & MP_MSBMASK)
break;
temp <<= 1;
count--;
}
while (psize)
{
while (count)
{
byte bit = (temp & MP_MSBMASK) ? 1 : 0;
n <<= 1;
n += bit;
if (n)
{
if (l)
l++;
else if (bit)
l = 1;
if (l == 4)
{
byte s = mpbslide_presq[n];
while (s--)
mpbsqrmod_w(b, size, result, result, wksp);
mpbmulmod_w(b, size, result, size, slide+mpbslide_mulg[n]*size, result, wksp);
s = mpbslide_postsq[n];
while (s--)
mpbsqrmod_w(b, size, result, result, wksp);
l = n = 0;
}
}
else
mpbsqrmod_w(b, size, result, result, wksp);
temp <<= 1;
count--;
}
if (--psize)
{
count = MP_WBITS;
temp = *(pdata++);
}
}
if (n)
{
byte s = mpbslide_presq[n];
while (s--)
mpbsqrmod_w(b, size, result, result, wksp);
mpbmulmod_w(b, size, result, size, slide+mpbslide_mulg[n]*size, result, wksp);
s = mpbslide_postsq[n];
while (s--)
mpbsqrmod_w(b, size, result, result, wksp);
}
}
}
int dldp_pgonGenerator_w(dldp_p* dp, randomGeneratorContext* rgc, mpw* wksp)
{
register size_t size = dp->p.size;
mpnfree(&dp->g);
mpnsize(&dp->g, size);
while (1)
{
mpbrnd_w(&dp->p, rgc, dp->g.data, wksp);
if (mpistwo(dp->r.size, dp->r.data))
{
/*
* A little math here: the only element in the group which has order 2 is (p-1);
* the two group elements raised to power two which result in 1 (mod p) are thus (p-1) and 1
*
* mpbrnd_w doesn't return 1 or (p-1), so the test where g^2 mod p = 1 can be safely skipped
*/
/* check g^q mod p*/
mpbpowmod_w(&dp->p, size, dp->g.data, dp->q.size, dp->q.modl, wksp, wksp+size);
if (mpisone(size, wksp))
continue;
}
else
{
/* we can either compute g^r, g^2q and g^(qr/2) or
* we first compute s = r/2, and then compute g^2s, g^2q and g^qs
*
* hence we first compute t = g^s
* then compute t^2 mod p, and test if one
* then compute t^q mod p, and test if one
* then compute (g^q mod p)^2 mod p, and test if one
*/
/* compute s = r/2 */
mpsetx(size, wksp, dp->r.size, dp->r.data);
mpdivtwo(size, wksp);
/* compute t = g^s mod p */
mpbpowmod_w(&dp->p, size, dp->g.data, size, wksp, wksp+size, wksp+2*size);
/* compute t^2 mod p = g^2s mod p = g^r mod p*/
mpbsqrmod_w(&dp->p, size, wksp+size, wksp+size, wksp+2*size);
if (mpisone(size, wksp+size))
continue;
/* compute t^q mod p = g^qs mod p */
mpbpowmod_w(&dp->p, size, wksp, dp->q.size, dp->q.modl, wksp+size, wksp+2*size);
if (mpisone(size, wksp+size))
continue;
/* compute g^2q mod p */
mpbpowmod_w(&dp->p, size, dp->g.data, dp->q.size, dp->q.modl, wksp, wksp+size);
mpbsqrmod_w(&dp->p, size, wksp, wksp+size, wksp+2*size);
if (mpisone(size, wksp+size))
continue;
}
return 0;
}
return -1;
}
