ec: hasse interval

script/research/elliptic_curves/pairing/2.2.4-deuring.sage

@@ -0,0 +1,22 @@
+import math
+def hasse_interval(q):
+    interval = (q + 1 - 2 * sqrt(q)).n(), (q + 1 + 2 * sqrt(q)).n()
+    return math.ceil(interval[0]), math.floor(interval[1])
+
+q = 23
+K = GF(q)
+
+low, high = hasse_interval(23)
+
+for i in range(100):
+    a = K.random_element()
+    b = K.random_element()
+
+    try:
+        E = EllipticCurve(K, [a, b])
+    except:
+        continue
+
+    assert E.cardinality() >= low
+    assert E.cardinality() <= high
+