6 files changed, 158 insertions, 187 deletions

diff --git a/gp.c b/gp.c
index 722d864..fa70fe7 100644
--- a/gp.c
+++ b/gp.c
@@ -8,7 +8,43 @@ init_gp(void)	  /* void */
   return;
 }
 
-/* Finds random point of order n on curve e of order o.
+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;
+}
+
+GEN
+pack_params(GEN p, GEN a, GEN b, GEN G)	  /* vec */
+{
+  pari_sp ltop = avma;
+  GEN p1 = gen_0;	  /* vec */
+  p1 = cgetg(8, t_VEC);
+  gel(p1, 1) = gcopy(p);
+  gel(p1, 2) = gcopy(a);
+  gel(p1, 3) = gcopy(b);
+  gel(p1, 4) = lift(gel(gel(G, 1), 1));
+  gel(p1, 5) = lift(gel(gel(G, 1), 2));
+  gel(p1, 6) = gcopy(gel(G, 2));
+  gel(p1, 7) = gcopy(gel(G, 3));
+  p1 = gerepilecopy(ltop, p1);
+  return p1;
+}
+
+/**
+* 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
@@ -38,7 +74,8 @@ find_point(GEN e, GEN o, GEN n)	  /* vec */
   return p1;
 }
 
-/* Finds random points of orders given by vector p.
+/**
+* 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
@@ -103,32 +140,6 @@ minprime_order(GEN e, GEN o)
   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
@@ -163,30 +174,44 @@ prime_orders(GEN e, GEN o)
   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
+/**
+* E(Fp): y^2 = x^3 + ax + b mod p
+* @returns [p, a, b, G.x, G.y, n, h], G has the largest prime order possible
+* @param p
+* @param a
+* @param b
 */
 GEN
-get_points(GEN e, GEN o, GEN f)	  /* vec */
+largest_prime(GEN p, GEN a, GEN b, long prec)
 {
   pari_sp ltop = avma;
-  GEN p1 = gen_0;	  /* vec */
-  p1 = find_points(e, o, closure_callgen1(f, o));
-  p1 = gerepilecopy(ltop, p1);
-  return p1;
+  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 = pack_params(p, a, b, G);
+  p2 = gerepilecopy(ltop, p2);
+  return p2;
 }
 
-/* E(Fp): y^2 = x^3 + ax + b mod p
-* @returns [p, a, b, [G.x, G.y], n, h]
+/**
+* E(Fp): y^2 = x^3 + ax + b mod p
+* @returns [p, a, b, G.x, G.y, n, h], G has the smallest prime order possible
 * @param p
 * @param a
 * @param b
 */
 GEN
-largest_prime(GEN p, GEN a, GEN b, long prec)
+smallest_prime(GEN p, GEN a, GEN b, long prec)
 {
   pari_sp ltop = avma;
   GEN e = gen_0, o = gen_0, G = gen_0;
@@ -201,27 +226,21 @@ largest_prime(GEN p, GEN a, GEN b, long prec)
     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));
+  G = find_point(e, o, minprime_order(o, gen_0));
+  p2 = pack_params(p, a, b, G);
   p2 = gerepilecopy(ltop, p2);
   return p2;
 }
 
-/* E(Fp): y^2 = x^3 + ax + b mod p
-* @returns [p, a, b, G, n, h]
+/**
+* E(Fp): y^2 = x^3 + ax + b mod p
+* @returns [p, a, b, G.x, G.y, n, h=1], G is generator of E(Fp)
 * @param p
 * @param a
 * @param b
 */
 GEN
-smallest_prime(GEN p, GEN a, GEN b, long prec)
+generator(GEN p, GEN a, GEN b, long prec)
 {
   pari_sp ltop = avma;
   GEN e = gen_0, o = gen_0, G = gen_0;
@@ -236,20 +255,14 @@ smallest_prime(GEN p, GEN a, GEN b, long prec)
     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));
+  G = find_point(e, o, o);
+  p2 = pack_params(p, a, b, G);
   p2 = gerepilecopy(ltop, p2);
   return p2;
 }
 
-/* E(Fp): y^2 = x^3 + ax + b mod p
+/**
+* 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
@@ -279,18 +292,7 @@ all_prime(GEN p, GEN a, GEN b, long prec)
     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;
-    }
+      gel(p3, X) = pack_params(p, a, b, gel(G, X));
   }
   p3 = gerepilecopy(ltop, p3);
   return p3;
@@ -298,14 +300,15 @@ all_prime(GEN p, GEN a, GEN b, long prec)
 
 /*####################################################################*/
 
-/* 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]
+/**
+* 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], G is generator of E(Fp), P has the smallest prime order
 */
 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 e = gen_0, o = gen_0, G = gen_0, f = gen_0, n = 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);
@@ -321,28 +324,21 @@ small_pubkey(GEN p, GEN a, GEN b, long prec)
   {
     G = genrand(e);
     n = o;
-    h = gen_1;
+    r = o;
     P = genrand(e);
   }
   else
   {
+    G = find_point(e, o, o);
     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));
+    n = gcopy(gcoeff(f, 1, 1));
+    /*
+    until(r % n == 0,
+    G = random(e);
+    r = ellorder(e, G);
+    );
+    */
+    P = ellmul(e, G, gdivent(o, n));
   }
   p2 = cgetg(11, t_VEC);
   gel(p2, 1) = gcopy(p);
@@ -359,21 +355,3 @@ small_pubkey(GEN p, GEN a, GEN b, long prec)
   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;
-}
-
diff --git a/gp.gp b/gp.gp
index a7a996a..f5c36b2 100644
--- a/gp.gp
+++ b/gp.gp
@@ -1,2 +1,3 @@
+\rutils
 \rpoints
 \rsea
diff --git a/gp.h b/gp.h
index 740b4c2..254173c 100644
--- a/gp.h
+++ b/gp.h
@@ -2,34 +2,32 @@
 #include <pari/pari.h>
 /*
 GP;install("init_gp","v","init_gp","./gp.gp.so");
+GP;install("print_params","vD0,G,","print_params","./gp.gp.so");
+GP;install("print_params_pub","vD0,G,","print_params_pub","./gp.gp.so");
+GP;install("pack_params","D0,G,D0,G,D0,G,D0,G,","pack_params","./gp.gp.so");
 GP;install("find_point","D0,G,D0,G,D0,G,","find_point","./gp.gp.so");
 GP;install("find_points","D0,G,D0,G,D0,G,","find_points","./gp.gp.so");
 GP;install("maxprime_order","D0,G,D0,G,","maxprime_order","./gp.gp.so");
 GP;install("minprime_order","D0,G,D0,G,","minprime_order","./gp.gp.so");
-GP;install("max_order","D0,G,D0,G,","max_order","./gp.gp.so");
-GP;install("get_point","D0,G,D0,G,D0,G,","get_point","./gp.gp.so");
 GP;install("prime_orders","D0,G,D0,G,","prime_orders","./gp.gp.so");
-GP;install("get_points","D0,G,D0,G,D0,G,","get_points","./gp.gp.so");
 GP;install("largest_prime","D0,G,D0,G,D0,G,p","largest_prime","./gp.gp.so");
 GP;install("smallest_prime","D0,G,D0,G,D0,G,p","smallest_prime","./gp.gp.so");
+GP;install("generator","D0,G,D0,G,D0,G,p","generator","./gp.gp.so");
 GP;install("all_prime","D0,G,D0,G,D0,G,p","all_prime","./gp.gp.so");
 GP;install("small_pubkey","D0,G,D0,G,D0,G,p","small_pubkey","./gp.gp.so");
-GP;install("print_params","vD0,G,","print_params","./gp.gp.so");
-GP;install("print_params_pub","vD0,G,","print_params_pub","./gp.gp.so");
 */
 void init_gp(void);
+void print_params(GEN curve);
+void print_params_pub(GEN curve);
+GEN pack_params(GEN p, GEN a, GEN b, GEN G);
 GEN find_point(GEN e, GEN o, GEN n);
 GEN find_points(GEN e, GEN o, GEN p);
 GEN maxprime_order(GEN e, GEN o);
 GEN minprime_order(GEN e, GEN o);
-GEN max_order(GEN e, GEN o);
-GEN get_point(GEN e, GEN o, GEN f);
 GEN prime_orders(GEN e, GEN o);
-GEN get_points(GEN e, GEN o, GEN f);
 GEN largest_prime(GEN p, GEN a, GEN b, long prec);
 GEN smallest_prime(GEN p, GEN a, GEN b, long prec);
+GEN generator(GEN p, GEN a, GEN b, long prec);
 GEN all_prime(GEN p, GEN a, GEN b, long prec);
 GEN small_pubkey(GEN p, GEN a, GEN b, long prec);
-void print_params(GEN curve);
-void print_params_pub(GEN curve);
 /*End of prototype*/
diff --git a/points.gp b/points.gp
index 647e565..428704e 100644
--- a/points.gp
+++ b/points.gp
@@ -1,4 +1,5 @@
-/* Finds random point of order n on curve e of order o.
+/**
+ * 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
@@ -13,7 +14,8 @@ find_point(e, o, n) = {
 	return([P, n, h]);
 }
 
-/* Finds random points of orders given by vector p.
+/**
+ * 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
@@ -41,40 +43,14 @@ minprime_order(e, o) = {
 	);
 }
 
-max_order(e, 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
- */
-get_point(e, o, f) = {
-	return(find_point(e, o, f(o)));
-}
-
 /*####################################################################*/
 
 prime_orders(e, o) = {
 	local(f);
 	if(isprime(o),
-		return([o]);;
+		return([o]);
 	,
 		f = factor(o);
 		return(vector(length(f),X,f[X,1]));
 	);
 }
-
-/* 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
- */
-get_points(e, o, f) = {
-	return(find_points(e, o, f(o)));
-}
diff --git a/sea.gp b/sea.gp
index 5f5cf2c..a24ee2b 100644
--- a/sea.gp
+++ b/sea.gp
@@ -1,6 +1,6 @@
-\rpoints
-/* E(Fp): y^2 = x^3 + ax + b mod p
- * @returns [p, a, b, [G.x, G.y], n, h]
+/**
+ * E(Fp): y^2 = x^3 + ax + b mod p
+ * @returns [p, a, b, G.x, G.y, n, h], G has the largest prime order possible
  * @param p
  * @param a
  * @param b
@@ -12,11 +12,12 @@ largest_prime(p, a, b) = {
 	if(!o, return);
 
 	G = find_point(e, o, maxprime_order(o));
-	return([p, a, b, lift(G[1][1]), lift(G[1][2]), G[2], G[3]]);
+	return(pack_params(p, a, b, G));
 }
 
-/* E(Fp): y^2 = x^3 + ax + b mod p
- * @returns [p, a, b, G, n, h]
+/**
+ * E(Fp): y^2 = x^3 + ax + b mod p
+ * @returns [p, a, b, G.x, G.y, n, h], G has the smallest prime order possible
  * @param p
  * @param a
  * @param b
@@ -28,10 +29,28 @@ smallest_prime(p, a, b) = {
 	if(!o, return);
 
 	G = find_point(e, o, minprime_order(o));
-	return([p, a, b, lift(G[1][1]), lift(G[1][2]), G[2], G[3]]);
+	return(pack_params(p, a, b, G));
 }
 
-/* E(Fp): y^2 = x^3 + ax + b mod p
+/**
+ * E(Fp): y^2 = x^3 + ax + b mod p
+ * @returns [p, a, b, G.x, G.y, n, h=1], G is generator of E(Fp)
+ * @param p
+ * @param a
+ * @param b
+ */
+generator(p, a, b) = {
+	local(e, o, G);
+	e = ellinit([a, b], p);
+	o = ellsea(e);
+	if(!o, return);
+
+	G = find_point(e, o, o);
+	return(pack_params(p, a, b, G));
+}
+
+/**
+ * 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
@@ -44,50 +63,38 @@ all_prime(p, a, b) = {
 	if(!o, return);
 
 	G = find_points(e, o, prime_orders(o));
-	return(vector(length(G),X,[p, a, b, lift(G[X][1][1]), lift(G[X][1][2]), G[X][2], G[X][3]]));
+	return(vector(length(G),X,pack_params(p, a, b, G[X])));
 }
 
 /*####################################################################*/
 
-/* 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]
+/**
+ * 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], G is generator of E(Fp), P has the smallest prime order
  */
-small_pubkey(p,a,b) =
-{
-	local(e, o, f, G, n, h, r, P);
-	e = ellinit([a,b],p);
+small_pubkey(p, a, b) = {
+	local(e, o, G, f, n, r, P);
+	e = ellinit([a, b], p);
 	o = ellsea(e);
 	if(!o, return);
 
 	if(isprime(o),
 		G = random(e);
 		n = o;
-		h = 1;
+		r = o;
 		P = random(e);
-		,
+	,
+		G = find_point(e, o, o);
 		f = factor(o);
-		f = vecsort(f);
-		n = f[1,2];
-		h = o\n;
-
-		\\printf("%s %u %u\n", f, n, h);
+		n = f[1,1];
+		/*
 		until(r % n == 0,
 			G = random(e);
 			r = ellorder(e, G);
-			\\printf("%s %s\n", G, r);
 		);
-		P = ellmul(e,G,r\n);
+		*/
+		P = ellmul(e, G, o\n);
 	);
 
-	return([p,a,b,lift(G[1]),lift(G[2]),r,o\r,lift(P[1]),lift(P[2]),n]);
-}
-
-print_params(curve) =
-{
-	printf("%x,%x,%x,%x,%x,%x,%x\n", curve[1], curve[2], curve[3], curve[4], curve[5], curve[6], curve[7]);
-}
-
-print_params_pub(curve) =
-{
-	printf("%x,%x,%x,%x,%x,%x,%x,%x,%x,%x\n", curve[1], curve[2], curve[3], curve[4], curve[5], curve[6], curve[7], curve[8], curve[9], curve[10]);
+	return([p, a, b, lift(G[1]), lift(G[2]), r, o\r, lift(P[1]), lift(P[2]), n]);
 }
diff --git a/utils.gp b/utils.gp
new file mode 100644
index 0000000..bfd0326
--- /dev/null
+++ b/utils.gp
@@ -0,0 +1,11 @@
+print_params(curve) = {
+	printf("%x,%x,%x,%x,%x,%x,%x\n", curve[1], curve[2], curve[3], curve[4], curve[5], curve[6], curve[7]);
+}
+
+print_params_pub(curve) = {
+	printf("%x,%x,%x,%x,%x,%x,%x,%x,%x,%x\n", curve[1], curve[2], curve[3], curve[4], curve[5], curve[6], curve[7], curve[8], curve[9], curve[10]);
+}
+
+pack_params(p, a, b, G) = {
+	return([p, a, b, lift(G[1][1]), lift(G[1][2]), G[2], G[3]]);
+}