/*
* needs workspace of (7*size+2) words
*/
int mpbpprime_w(const mpbarrett* b, randomGeneratorContext* r, int t, mpw* wksp)
{
/*
* This test works for candidate probable primes >= 3, which are also not small primes.
*
* It assumes that b->modl contains the candidate prime
*
*/
size_t size = b->size;
/* first test if modl is odd */
if (mpodd(b->size, b->modl))
{
/*
* Small prime factor test:
*
* Tables in mpspprod contain multi-precision integers with products of small primes
* If the greatest common divisor of this product and the candidate is not one, then
* the candidate has small prime factors, or is a small prime. Neither is acceptable when
* we are looking for large probable primes =)
*
*/
if (size > SMALL_PRIMES_PRODUCT_MAX)
{
mpsetx(size, wksp+size, SMALL_PRIMES_PRODUCT_MAX, mpspprod[SMALL_PRIMES_PRODUCT_MAX-1]);
mpgcd_w(size, b->modl, wksp+size, wksp, wksp+2*size);
}
else
{
mpgcd_w(size, b->modl, mpspprod[size-1], wksp, wksp+2*size);
}
if (mpisone(size, wksp))
{
return mppmilrab_w(b, r, t, wksp);
}
}
return 0;
}
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;
}
