Merge commit 'd029ddea8396d7a39910028dd5ae436a3bd3e9bb' as 'jubjub'

jubjub/doc/derive/.gitignore

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+*.sage.py

jubjub/doc/derive/derive.sage

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+q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+Fq = GF(q)
+
+# We wish to find a Montgomery curve with B = 1 and A the smallest such
+# that (A - 2) / 4 is a small integer.
+def get_A(n):
+   return (n * 4) + 2
+
+# A = 2 is invalid (singular curve), so we start at i = 1 (A = 6)
+i = 1
+
+while True:
+    A = Fq(get_A(i))
+    i = i + 1
+
+    # We also want that A^2 - 4 is nonsquare.
+    if ((A^2) - 4).is_square():
+        continue
+
+    ec = EllipticCurve(Fq, [0, A, 0, 1, 0])
+    o = ec.order()
+
+    if (o % 8 == 0):
+        o = o // 8
+        if is_prime(o):
+            twist = ec.quadratic_twist()
+            otwist = twist.order()
+            if (otwist % 4 == 0):
+                otwist = otwist // 4
+                if is_prime(otwist):
+                    print "A = %s" % A
+                    exit(0)