Use exhaustive generation of some params in CM generation.

1 files changed, 45 insertions, 0 deletions

diff --git a/src/cm/supersingular.c b/src/cm/supersingular.c
new file mode 100644
index 0000000..a3cebfc
--- /dev/null
+++ b/src/cm/supersingular.c
@@ -0,0 +1,45 @@
+/*
+ * ecgen, tool for generating Elliptic curve domain parameters
+ * Copyright (C) 2017-2018 J08nY
+ */
+#include "supersingular.h"
+
+GENERATOR(supersingular_gen_equation) {
+	if (equalis(curve->field, 2)) {
+		return -2;
+	}
+	if (mod4(curve->field) == 3) {
+		curve->a = mkintmod(subis(curve->field, 1), curve->field);
+		curve->b = mkintmod(stoi(0), curve->field);
+		return 1;
+	}
+	GEN q = stoi(3);
+	while (!(mod4(q) == 3 && kronecker(curve->field, q) == -1)) {
+		q = nextprime(addis(q, 1));
+	}
+
+	if (equalis(q, 3)) {
+		curve->a = mkintmod(stoi(0), curve->field);
+		curve->b = mkintmod(stoi(1), curve->field);
+		return 1;
+	} else {
+		GEN H = polclass(negi(q), 0, 0);
+		GEN r = FpX_roots(H, curve->field);
+		GEN root = gel(r, 1);
+		curve->a = mkintmod(
+		    Fp_div(Fp_mul(stoi(27), root, curve->field),
+		           Fp_mul(stoi(4), Fp_sub(stoi(1728), root, curve->field),
+		                  curve->field),
+		           curve->field),
+		    curve->field);
+		curve->b = gneg(curve->a);
+		return 1;
+	}
+}
+
+GENERATOR(supersingular_gen_order) {
+	// copy field to order
+	curve->order = addis(curve->field, 1);
+	obj_insert(curve->curve, 1, curve->order);
+	return 1;
+}