Factor before providing to qfbsolve

shared/ecc.py

@@ -5,6 +5,7 @@
 from sage.all import EllipticCurve
 from sage.all import GF
 from sage.all import cyclotomic_polynomial
+from sage.all import factor
 from sage.all import is_prime
 from sage.all import kronecker
 from sage.all import next_prime
@@ -168,10 +169,11 @@ def generate_with_order(m, D=None, c=None):
  :param c: the parameter c to use in the CM method (default: random value)
  :return: a generator generating random elliptic curves
  """
+ factor_4m = factor(4 * m)
 
- def get_q(m, D):
+ def get_q(D):
  # We can't use qfbcornacchia here, because it does not return all (or any) solutions...
- for t in set(map(lambda sol: int(sol[0]), pari.qfbsolve(pari.Qfb(1, 0, -D), 4 * m, 1))):
+ for t in set(map(lambda sol: int(sol[0]), pari.qfbsolve(pari.Qfb(1, 0, -D), factor_4m, 1))):
  if is_prime(m + 1 - t):
  return m + 1 - t
  if is_prime(m + 1 + t):
@@ -183,15 +185,15 @@ def get_q(m, D):
  if not (D % 4 == 0 or D % 4 == 3):
  continue
 
- q = get_q(m, -D)
+ q = get_q(-D)
  if q is not None:
  break
 
  assert q is not None, "Unable to find appropriate D value for m."
  D = int(-D)
  logging.info(f"Found appropriate D value = {D}")
  else:
- q = get_q(m, D)
+ q = get_q(D)
  assert q is not None, "Invalid values for m and D."
 
  yield from generate_with_trace_q(q + 1 - m, q, D, c)
@@ -267,6 +269,7 @@ def generate_mnt(k, h_min=1, h_max=4, D_min=7, D_max=10000, c=None):
  a = l * h + d
  b = 4 * h - d
  f = a ** 2 - b ** 2
+ factor_f = 0 if f == 0 else factor(f)
  for D in range(D_min, D_max + 1):
  if not (D % 4 == 0 or D % 4 == 3):
  continue
@@ -275,7 +278,7 @@ def generate_mnt(k, h_min=1, h_max=4, D_min=7, D_max=10000, c=None):
  if is_square(g):
  continue
 
- ys = set(map(lambda sol: int(sol[0]), pari.qfbsolve(pari.Qfb(1, 0, -g), f, 1)))
+ ys = set(map(lambda sol: int(sol[0]), pari.qfbsolve(pari.Qfb(1, 0, -g), factor_f, 1)))
  for y in ys:
  if (y - a) % b != 0:
  continue