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#include "gp.h"
void
init_gp(void) /* void */
{
pari_sp ltop = avma;
avma = ltop;
return;
}
/* Finds random point of order n on curve e of order o.
* @returns [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param n desired point order
*/
GEN
find_point(GEN e, GEN o, GEN n) /* vec */
{
pari_sp ltop = avma;
GEN h = gen_0, P = gen_0;
GEN p1 = gen_0; /* vec */
h = gdivent(o, n);
{
pari_sp btop = avma;
do
{
P = genrand(e);
if (gc_needed(btop, 1))
P = gerepilecopy(btop, P);
} while(gequal0(ellmul(e, P, n)));
}
p1 = cgetg(4, t_VEC);
gel(p1, 1) = gcopy(P);
gel(p1, 2) = gcopy(n);
gel(p1, 3) = gcopy(h);
p1 = gerepilecopy(ltop, p1);
return p1;
}
/* Finds random points of orders given by vector p.
* @returns vector of points in format [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param p vector of point orders
*/
GEN
find_points(GEN e, GEN o, GEN p) /* vec */
{
pari_sp ltop = avma;
long l1;
GEN p2 = gen_0; /* vec */
l1 = glength(p);
{
long X;
p2 = cgetg(l1+1, t_VEC);
for (X = 1; X <= l1; ++X)
gel(p2, X) = find_point(e, o, gel(p, X));
}
p2 = gerepilecopy(ltop, p2);
return p2;
}
/*####################################################################*/
GEN
maxprime_order(GEN e, GEN o)
{
pari_sp ltop = avma;
if (!gequal0(gisprime(o, 0)))
{
o = gerepilecopy(ltop, o);
return o;
}
else
{
GEN p1 = gen_0;
p1 = vecmax(factor(o));
p1 = gerepilecopy(ltop, p1);
return p1;
}
avma = ltop;
return gen_0;
}
GEN
minprime_order(GEN e, GEN o)
{
pari_sp ltop = avma;
if (!gequal0(gisprime(o, 0)))
{
o = gerepilecopy(ltop, o);
return o;
}
else
{
GEN p1 = gen_0;
p1 = gcopy(gcoeff(factor(o), 1, 1));
p1 = gerepilecopy(ltop, p1);
return p1;
}
avma = ltop;
return gen_0;
}
GEN
max_order(GEN e, GEN o)
{
pari_sp ltop = avma;
o = gerepilecopy(ltop, o);
return o;
}
/* Finds a random point of order given by f(o).
* @returns [[P.x, P.y], n, h]
* with P being the point with order f(o).
* @param e curve
* @param o curve order
* @param f function returning the point order, \in maxprime_order,
* minprime_order, max_order
*/
GEN
get_point(GEN e, GEN o, GEN f) /* vec */
{
pari_sp ltop = avma;
GEN p1 = gen_0; /* vec */
p1 = find_point(e, o, closure_callgen1(f, o));
p1 = gerepilecopy(ltop, p1);
return p1;
}
/*####################################################################*/
GEN
prime_orders(GEN e, GEN o)
{
pari_sp ltop = avma;
GEN f = gen_0;
if (!gequal0(gisprime(o, 0)))
{
GEN p1 = gen_0; /* vec */
p1 = cgetg(2, t_VEC);
gel(p1, 1) = gcopy(o);
p1 = gerepilecopy(ltop, p1);
return p1;
}
else
{
long l2;
GEN p3 = gen_0; /* vec */
f = factor(o);
l2 = glength(f);
{
long X;
p3 = cgetg(l2+1, t_VEC);
for (X = 1; X <= l2; ++X)
gel(p3, X) = gcopy(gcoeff(f, X, 1));
}
p3 = gerepilecopy(ltop, p3);
return p3;
}
avma = ltop;
return gen_0;
}
/* Finds random points of orders given by f(o).
* @returns vector of points in format [[P.x, P.y], n, h]
* @param e curve
* @param o curve order
* @param f function returning a vector of point orders
*/
GEN
get_points(GEN e, GEN o, GEN f) /* vec */
{
pari_sp ltop = avma;
GEN p1 = gen_0; /* vec */
p1 = find_points(e, o, closure_callgen1(f, o));
p1 = gerepilecopy(ltop, p1);
return p1;
}
/* E(Fp): y^2 = x^3 + ax + b mod p
* @returns [p, a, b, [G.x, G.y], n, h]
* @param p
* @param a
* @param b
*/
GEN
largest_prime(GEN p, GEN a, GEN b, long prec)
{
pari_sp ltop = avma;
GEN e = gen_0, o = gen_0, G = gen_0;
GEN p1 = gen_0, p2 = gen_0; /* vec */
p1 = cgetg(3, t_VEC);
gel(p1, 1) = gcopy(a);
gel(p1, 2) = gcopy(b);
e = ellinit(p1, p, prec);
o = ellsea(e, 0);
if (gequal0(o))
{
avma = ltop;
return gen_0;
}
G = find_point(e, o, maxprime_order(o, gen_0));
p2 = cgetg(8, t_VEC);
gel(p2, 1) = gcopy(p);
gel(p2, 2) = gcopy(a);
gel(p2, 3) = gcopy(b);
gel(p2, 4) = lift(gel(gel(G, 1), 1));
gel(p2, 5) = lift(gel(gel(G, 1), 2));
gel(p2, 6) = gcopy(gel(G, 2));
gel(p2, 7) = gcopy(gel(G, 3));
p2 = gerepilecopy(ltop, p2);
return p2;
}
/* E(Fp): y^2 = x^3 + ax + b mod p
* @returns [p, a, b, G, n, h]
* @param p
* @param a
* @param b
*/
GEN
smallest_prime(GEN p, GEN a, GEN b, long prec)
{
pari_sp ltop = avma;
GEN e = gen_0, o = gen_0, G = gen_0;
GEN p1 = gen_0, p2 = gen_0; /* vec */
p1 = cgetg(3, t_VEC);
gel(p1, 1) = gcopy(a);
gel(p1, 2) = gcopy(b);
e = ellinit(p1, p, prec);
o = ellsea(e, 0);
if (gequal0(o))
{
avma = ltop;
return gen_0;
}
G = find_point(e, o, minprime_order(o, gen_0));
p2 = cgetg(8, t_VEC);
gel(p2, 1) = gcopy(p);
gel(p2, 2) = gcopy(a);
gel(p2, 3) = gcopy(b);
gel(p2, 4) = lift(gel(gel(G, 1), 1));
gel(p2, 5) = lift(gel(gel(G, 1), 2));
gel(p2, 6) = gcopy(gel(G, 2));
gel(p2, 7) = gcopy(gel(G, 3));
p2 = gerepilecopy(ltop, p2);
return p2;
}
/* E(Fp): y^2 = x^3 + ax + b mod p
* @returns vector of domain parameters [p, a, b, G, n, h] points of all prime orders
* @param p
* @param a
* @param b
*/
GEN
all_prime(GEN p, GEN a, GEN b, long prec)
{
pari_sp ltop = avma;
GEN e = gen_0, o = gen_0, G = gen_0;
GEN p1 = gen_0; /* vec */
long l2;
GEN p3 = gen_0; /* vec */
p1 = cgetg(3, t_VEC);
gel(p1, 1) = gcopy(a);
gel(p1, 2) = gcopy(b);
e = ellinit(p1, p, prec);
o = ellsea(e, 0);
if (gequal0(o))
{
avma = ltop;
return gen_0;
}
G = find_points(e, o, prime_orders(o, gen_0));
l2 = glength(G);
{
long X;
p3 = cgetg(l2+1, t_VEC);
for (X = 1; X <= l2; ++X)
{
GEN p4 = gen_0; /* vec */
p4 = cgetg(8, t_VEC);
gel(p4, 1) = gcopy(p);
gel(p4, 2) = gcopy(a);
gel(p4, 3) = gcopy(b);
gel(p4, 4) = lift(gel(gel(gel(G, X), 1), 1));
gel(p4, 5) = lift(gel(gel(gel(G, X), 1), 2));
gel(p4, 6) = gcopy(gel(gel(G, X), 2));
gel(p4, 7) = gcopy(gel(gel(G, X), 3));
gel(p3, X) = p4;
}
}
p3 = gerepilecopy(ltop, p3);
return p3;
}
/*####################################################################*/
/* E(Fp): y^2 = x^3 + ax + b mod p
* @returns [p, a, b, G.x, G.y, r, k, P.x, P.y, n]
*/
GEN
small_pubkey(GEN p, GEN a, GEN b, long prec)
{
pari_sp ltop = avma;
GEN e = gen_0, o = gen_0, f = gen_0, G = gen_0, n = gen_0, h = gen_0, r = gen_0, P = gen_0;
GEN p1 = gen_0, p2 = gen_0; /* vec */
p1 = cgetg(3, t_VEC);
gel(p1, 1) = gcopy(a);
gel(p1, 2) = gcopy(b);
e = ellinit(p1, p, prec);
o = ellsea(e, 0);
if (gequal0(o))
{
avma = ltop;
return gen_0;
}
if (!gequal0(gisprime(o, 0)))
{
G = genrand(e);
n = o;
h = gen_1;
P = genrand(e);
}
else
{
f = factor(o);
f = vecsort0(f, NULL, 0);
n = gcopy(gcoeff(f, 1, 2));
h = gdivent(o, n);
/*printf("%s %u %u\n", f, n, h); */
{
pari_sp btop = avma;
do
{
G = genrand(e);
r = ellorder(e, G, NULL);
if (gc_needed(btop, 1))
gerepileall(btop, 2, &G, &r);
} while(!gequal0(gmod(r, n)));
}
/*printf("%s %s\n", G, r); */
P = ellmul(e, G, gdivent(r, n));
}
p2 = cgetg(11, t_VEC);
gel(p2, 1) = gcopy(p);
gel(p2, 2) = gcopy(a);
gel(p2, 3) = gcopy(b);
gel(p2, 4) = lift(gel(G, 1));
gel(p2, 5) = lift(gel(G, 2));
gel(p2, 6) = gcopy(r);
gel(p2, 7) = gdivent(o, r);
gel(p2, 8) = lift(gel(P, 1));
gel(p2, 9) = lift(gel(P, 2));
gel(p2, 10) = gcopy(n);
p2 = gerepilecopy(ltop, p2);
return p2;
}
void
print_params(GEN curve) /* void */
{
pari_sp ltop = avma;
printf0("%x,%x,%x,%x,%x,%x,%x\n", mkvecn(7, gel(curve, 1), gel(curve, 2), gel(curve, 3), gel(curve, 4), gel(curve, 5), gel(curve, 6), gel(curve, 7)));
avma = ltop;
return;
}
void
print_params_pub(GEN curve) /* void */
{
pari_sp ltop = avma;
printf0("%x,%x,%x,%x,%x,%x,%x,%x,%x,%x\n", mkvecn(10, gel(curve, 1), gel(curve, 2), gel(curve, 3), gel(curve, 4), gel(curve, 5), gel(curve, 6), gel(curve, 7), gel(curve, 8), gel(curve, 9), gel(curve, 10)));
avma = ltop;
return;
}
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