int dldp_pgonMakeSafe(dldp_p* dp, randomGeneratorContext* rgc, size_t pbits)
{
/*
* Generate parameters with a safe prime; i.e. p = 2q+1, where q is prime
*/
register size_t psize = MP_BITS_TO_WORDS(pbits + MP_WBITS - 1);
register mpw* temp = (mpw*) malloc((8*psize+2) * sizeof(mpw));
if (temp)
{
/* generate safe p */
mpprndsafe_w(&dp->p, rgc, pbits, mpptrials(pbits), temp);
/* set n */
mpbsubone(&dp->p, temp);
mpbset(&dp->n, psize, temp);
/* set q */
mpcopy(psize, temp, dp->p.modl);
mpdivtwo(psize, temp);
mpbset(&dp->q, psize, temp);
/* set r = 2 */
mpnsetw(&dp->r, 2);
dldp_pgonGenerator_w(dp, rgc, temp);
free(temp);
return 0;
}
return -1;
}
int dldp_pgoqMakeSafe(dldp_p* dp, randomGeneratorContext* rgc, size_t bits)
{
/*
* Generate parameters with a safe prime; p = 2q+1 i.e. r=2
*
*/
register size_t size = MP_BITS_TO_WORDS(bits + MP_WBITS - 1);
register mpw* temp = (mpw*) malloc((8*size+2) * sizeof(mpw));
if (temp)
{
/* generate p */
mpprndsafe_w(&dp->p, rgc, bits, mpptrials(bits), temp);
/* set q */
mpcopy(size, temp, dp->p.modl);
mpdivtwo(size, temp);
mpbset(&dp->q, size, temp);
/* set r = 2 */
mpnsetw(&dp->r, 2);
/* clear n */
mpbzero(&dp->n);
dldp_pgoqGenerator_w(dp, rgc, temp);
free(temp);
return 0;
}
return -1;
}
void mpprndsafe_w(mpbarrett* p, randomGeneratorContext* rc, size_t bits, int t, mpw* wksp)
{
/*
* Initialize with a probable safe prime of 'size' words, with probability factor t
*
* A safe prime p has the property that p = 2q+1, where q is also prime
* Use for ElGamal type schemes, where a generator of order (p-1) is required
*/
size_t size = MP_BITS_TO_WORDS(bits + MP_WBITS - 1);
mpbinit(p, size);
if (p->modl != (mpw*) 0)
{
mpbarrett q;
mpbzero(&q);
mpbinit(&q, size);
while (1)
{
/*
* Generate a random appropriate candidate prime, and test
* it with small prime divisor test BEFORE computing mu
*/
mpprndbits(p, bits, 2, (mpnumber*) 0, (mpnumber*) 0, rc, wksp);
mpcopy(size, q.modl, p->modl);
mpdivtwo(size, q.modl);
/* do a small prime product trial division on q */
if (!mppsppdiv_w(&q, wksp))
continue;
/* do a small prime product trial division on p */
if (!mppsppdiv_w(p, wksp))
continue;
/* candidate prime has passed small prime division test for p and q */
mpbmu_w(&q, wksp);
if (!mppmilrab_w(&q, rc, t, wksp))
continue;
mpbmu_w(p, wksp);
if (!mppmilrab_w(p, rc, t, wksp))
continue;
mpbfree(&q);
return;
}
}
}
static int Zmpbinv_w(const mpbarrett* b, size_t xsize, const mpw* xdata, mpw* result, mpw* wksp)
{
size_t ysize = b->size+1;
size_t ubits, vbits;
int k = 0;
mpw* u = wksp;
mpw* v = u+ysize;
mpw* A = v+ysize;
mpw* B = A+ysize;
mpw* C = B+ysize;
mpw* D = C+ysize;
mpsetx(ysize, u, xsize, xdata);
mpsetx(ysize, v, b->size, b->modl);
mpsetw(ysize, A, 1);
mpzero(ysize, B);
mpzero(ysize, C);
mpsetw(ysize, D, 1);
for (k = 0; mpeven(ysize, u) && mpeven(ysize, v); k++) {
mpdivtwo(ysize, u);
mpdivtwo(ysize, v);
}
if (mpeven(ysize, u))
(void) mpadd(ysize, u, v);
if (_debug < 0)
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
if (_debug < 0)
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
if (_debug < 0)
fprintf(stderr, " A: "), mpfprintln(stderr, ysize, A);
if (_debug < 0)
fprintf(stderr, " B: "), mpfprintln(stderr, ysize, B);
if (_debug < 0)
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
if (_debug < 0)
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
ubits = vbits = MP_WORDS_TO_BITS(ysize);
do {
while (mpeven(ysize, v)) {
mpsdivtwo(ysize, v);
vbits -= 1;
if (mpodd(ysize, C)) {
(void) mpaddx(ysize, C, b->size, b->modl);
(void) mpsubx(ysize, D, xsize, xdata);
}
mpsdivtwo(ysize, C);
mpsdivtwo(ysize, D);
if (_debug < 0)
fprintf(stderr, "-->> v: "), mpfprintln(stderr, ysize, v);
}
if (ubits >= vbits) {
mpw* swapu;
size_t swapi;
if (_debug < 0)
fprintf(stderr, "--> (swap u <-> v)\n");
swapu = u; u = v; v = swapu;
swapi = ubits; ubits = vbits; vbits = swapi;
swapu = A; A = C; C = swapu;
swapu = B; B = D; D = swapu;
}
if (!((u[ysize-1] + v[ysize-1]) & 0x3)) {
if (_debug < 0)
fprintf(stderr, "--> (even parity)\n");
mpadd(ysize, v, u);
mpadd(ysize, C, A);
mpadd(ysize, D, B);
} else {
if (_debug < 0)
fprintf(stderr, "--> (odd parity)\n");
mpsub(ysize, v, u);
mpsub(ysize, C, A);
mpsub(ysize, D, B);
}
if (_debug < 0)
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
if (_debug < 0)
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
if (_debug < 0)
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
vbits++;
} while (mpnz(ysize, v));
#ifdef NOTYET
if (!mpisone(ysize, u))
return 0;
#endif
if (result) {
mpsetx(b->size, result, ysize, A);
/*@-usedef@*/
if (*A & 0x80000000)
(void) mpneg(b->size, result);
/*@=usedef@*/
while (--k > 0)
mpadd(b->size, result, result);
}
fprintf(stderr, "=== EXIT: "), mpfprintln(stderr, b->size, result);
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
fprintf(stderr, " A: "), mpfprintln(stderr, ysize, A);
fprintf(stderr, " B: "), mpfprintln(stderr, ysize, B);
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
return 1;
}
/**
* Computes the inverse (modulo b) of x, and returns 1 if x was invertible.
* needs workspace of (6*size+6) words
* @note xdata and result cannot point to the same area
*/
static int Xmpbinv_w(const mpbarrett* b, size_t xsize, const mpw* xdata, mpw* result, mpw* wksp)
{
/*
* Fact: if a element of Zn, then a is invertible if and only if gcd(a,n) = 1
* Hence: if b->modl is even, then x must be odd, otherwise the gcd(x,n) >= 2
*
* The calling routine must guarantee this condition.
*/
size_t ysize = b->size+1;
mpw* u = wksp;
mpw* v = u+ysize;
mpw* A = v+ysize;
mpw* B = A+ysize;
mpw* C = B+ysize;
mpw* D = C+ysize;
mpsetx(ysize, u, b->size, b->modl);
mpsetx(ysize, v, xsize, xdata);
mpsetw(ysize, A, 1);
mpzero(ysize, B);
mpzero(ysize, C);
mpsetw(ysize, D, 1);
if (_debug < 0)
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
if (_debug < 0)
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
if (_debug < 0)
fprintf(stderr, " A: "), mpfprintln(stderr, ysize, A);
if (_debug < 0)
fprintf(stderr, " B: "), mpfprintln(stderr, ysize, B);
if (_debug < 0)
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
if (_debug < 0)
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
do {
while (mpeven(ysize, u))
{
mpdivtwo(ysize, u);
if (mpodd(ysize, A) || mpodd(ysize, B))
{
(void) mpaddx(ysize, A, xsize, xdata);
(void) mpsubx(ysize, B, b->size, b->modl);
}
mpsdivtwo(ysize, A);
mpsdivtwo(ysize, B);
}
while (mpeven(ysize, v))
{
mpdivtwo(ysize, v);
if (mpodd(ysize, C) || mpodd(ysize, D))
{
(void) mpaddx(ysize, C, xsize, xdata);
(void) mpsubx(ysize, D, b->size, b->modl);
}
mpsdivtwo(ysize, C);
mpsdivtwo(ysize, D);
}
if (mpge(ysize, u, v))
{
if (_debug < 0)
fprintf(stderr, "--> 5 (u >= v)\n");
(void) mpsub(ysize, u, v);
(void) mpsub(ysize, A, C);
(void) mpsub(ysize, B, D);
if (_debug < 0)
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
if (_debug < 0)
fprintf(stderr, " A: "), mpfprintln(stderr, ysize, A);
if (_debug < 0)
fprintf(stderr, " B: "), mpfprintln(stderr, ysize, B);
}
else
{
if (_debug < 0)
fprintf(stderr, "--> 5 (u < v)\n");
(void) mpsub(ysize, v, u);
(void) mpsub(ysize, C, A);
(void) mpsub(ysize, D, B);
if (_debug < 0)
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
if (_debug < 0)
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
if (_debug < 0)
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
}
} while (mpnz(ysize, u));
if (!mpisone(ysize, v))
return 0;
if (result)
{
mpsetx(b->size, result, ysize, D);
/*@-usedef@*/
if (*D & 0x80000000)
(void) mpadd(b->size, result, b->modl);
/*@=usedef@*/
}
fprintf(stderr, "=== EXIT: "), mpfprintln(stderr, b->size, result);
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
fprintf(stderr, " A: "), mpfprintln(stderr, ysize, A);
fprintf(stderr, " B: "), mpfprintln(stderr, ysize, B);
fprintf(stderr, " C: "), mpfprintln(stderr, ysize, C);
fprintf(stderr, " D: "), mpfprintln(stderr, ysize, D);
return 1;
}
static int Ympbinv_w(const mpbarrett* b, size_t xsize, const mpw* xdata, mpw* result, mpw* wksp)
{
size_t ysize = b->size+1;
int k;
mpw* u1 = wksp;
mpw* u2 = u1+ysize;
mpw* u3 = u2+ysize;
mpw* v1 = u3+ysize;
mpw* v2 = v1+ysize;
mpw* v3 = v2+ysize;
mpw* t1 = v3+ysize;
mpw* t2 = t1+ysize;
mpw* t3 = t2+ysize;
mpw* u = t3+ysize;
mpw* v = u+ysize;
mpsetx(ysize, u, xsize, xdata);
mpsetx(ysize, v, b->size, b->modl);
/* Y1. Find power of 2. */
for (k = 0; mpeven(ysize, u) && mpeven(ysize, v); k++) {
mpdivtwo(ysize, u);
mpdivtwo(ysize, v);
}
if (_debug < 0)
fprintf(stderr, " u: "), mpfprintln(stderr, ysize, u);
if (_debug < 0)
fprintf(stderr, " v: "), mpfprintln(stderr, ysize, v);
/* Y2. Initialize. */
mpsetw(ysize, u1, 1);
if (_debug < 0)
fprintf(stderr, " u1: "), mpfprintln(stderr, ysize, u1);
mpzero(ysize, u2);
if (_debug < 0)
fprintf(stderr, " u2: "), mpfprintln(stderr, ysize, u2);
mpsetx(ysize, u3, ysize, u);
if (_debug < 0)
fprintf(stderr, " u3: "), mpfprintln(stderr, ysize, u3);
mpsetx(ysize, v1, ysize, v);
if (_debug < 0)
fprintf(stderr, " v1: "), mpfprintln(stderr, ysize, v1);
mpsetw(ysize, v2, 1);
(void) mpsub(ysize, v2, u);
if (_debug < 0)
fprintf(stderr, " v2: "), mpfprintln(stderr, ysize, v2);
mpsetx(ysize, v3, ysize, v);
if (_debug < 0)
fprintf(stderr, " v3: "), mpfprintln(stderr, ysize, v3);
if (mpodd(ysize, u)) {
mpzero(ysize, t1);
if (_debug < 0)
fprintf(stderr, " t1: "), mpfprintln(stderr, ysize, t1);
mpzero(ysize, t2);
mpsubw(ysize, t2, 1);
if (_debug < 0)
fprintf(stderr, " t2: "), mpfprintln(stderr, ysize, t2);
mpzero(ysize, t3);
mpsub(ysize, t3, v);
if (_debug < 0)
fprintf(stderr, " t3: "), mpfprintln(stderr, ysize, t3);
goto Y4;
} else {
mpsetw(ysize, t1, 1);
if (_debug < 0)
fprintf(stderr, " t1: "), mpfprintln(stderr, ysize, t1);
mpzero(ysize, t2);
if (_debug < 0)
fprintf(stderr, " t2: "), mpfprintln(stderr, ysize, t2);
mpsetx(ysize, t3, ysize, u);
if (_debug < 0)
fprintf(stderr, " t3: "), mpfprintln(stderr, ysize, t3);
}
do {
do {
if (mpodd(ysize, t1) || mpodd(ysize, t2)) {
mpadd(ysize, t1, v);
mpsub(ysize, t2, u);
}
mpsdivtwo(ysize, t1);
mpsdivtwo(ysize, t2);
mpsdivtwo(ysize, t3);
Y4:
if (_debug < 0)
fprintf(stderr, " Y4 t3: "), mpfprintln(stderr, ysize, t3);
} while (mpeven(ysize, t3));
/* Y5. Reset max(u3,v3). */
if (!(*t3 & 0x80000000)) {
if (_debug < 0)
fprintf(stderr, "--> Y5 (t3 > 0)\n");
mpsetx(ysize, u1, ysize, t1);
if (_debug < 0)
fprintf(stderr, " u1: "), mpfprintln(stderr, ysize, u1);
mpsetx(ysize, u2, ysize, t2);
if (_debug < 0)
fprintf(stderr, " u2: "), mpfprintln(stderr, ysize, u2);
mpsetx(ysize, u3, ysize, t3);
if (_debug < 0)
fprintf(stderr, " u3: "), mpfprintln(stderr, ysize, u3);
} else {
if (_debug < 0)
fprintf(stderr, "--> Y5 (t3 <= 0)\n");
mpsetx(ysize, v1, ysize, v);
mpsub(ysize, v1, t1);
if (_debug < 0)
fprintf(stderr, " v1: "), mpfprintln(stderr, ysize, v1);
mpsetx(ysize, v2, ysize, u);
mpneg(ysize, v2);
mpsub(ysize, v2, t2);
if (_debug < 0)
fprintf(stderr, " v2: "), mpfprintln(stderr, ysize, v2);
mpzero(ysize, v3);
mpsub(ysize, v3, t3);
if (_debug < 0)
fprintf(stderr, " v3: "), mpfprintln(stderr, ysize, v3);
}
/* Y6. Subtract. */
mpsetx(ysize, t1, ysize, u1);
mpsub(ysize, t1, v1);
mpsetx(ysize, t2, ysize, u2);
mpsub(ysize, t2, v2);
mpsetx(ysize, t3, ysize, u3);
mpsub(ysize, t3, v3);
if (*t1 & 0x80000000) {
mpadd(ysize, t1, v);
mpsub(ysize, t2, u);
}
if (_debug < 0)
fprintf(stderr, "-->Y6 t1: "), mpfprintln(stderr, ysize, t1);
if (_debug < 0)
fprintf(stderr, " t2: "), mpfprintln(stderr, ysize, t2);
if (_debug < 0)
fprintf(stderr, " t3: "), mpfprintln(stderr, ysize, t3);
} while (mpnz(ysize, t3));
if (!(mpisone(ysize, u3) && mpisone(ysize, v3)))
return 0;
if (result) {
while (--k > 0)
mpadd(ysize, u1, u1);
mpsetx(b->size, result, ysize, u1);
}
fprintf(stderr, "=== EXIT: "), mpfprintln(stderr, b->size, result);
fprintf(stderr, " u1: "), mpfprintln(stderr, ysize, u1);
fprintf(stderr, " u2: "), mpfprintln(stderr, ysize, u2);
fprintf(stderr, " u3: "), mpfprintln(stderr, ysize, u3);
fprintf(stderr, " v1: "), mpfprintln(stderr, ysize, v1);
fprintf(stderr, " v2: "), mpfprintln(stderr, ysize, v2);
fprintf(stderr, " v3: "), mpfprintln(stderr, ysize, v3);
fprintf(stderr, " t1: "), mpfprintln(stderr, ysize, t1);
fprintf(stderr, " t2: "), mpfprintln(stderr, ysize, t2);
fprintf(stderr, " t3: "), mpfprintln(stderr, ysize, t3);
return 1;
}
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;
}
