Clean up test vector generation script

scripts/generate_field_test_vectors.py

@@ -14,9 +14,10 @@
 
 import sage
 import numpy as np
-from sage.all import GF, PolynomialRing, log, matrix, vector
+from sage.all import GF, PolynomialRing, log, matrix, vector, xgcd
 
 FIELD = None
+RING = None
 SPARSE_SIZE = 20
 PATH = os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "tests")
 
@@ -127,6 +128,26 @@ def random_coeffs(low, high, size_low, size_high):
  return coeffs
 
 
+def list_to_poly(coeffs):
+ """
+ Converts a Python coefficient list (degree-descending order) into a Sage polynomial object.
+ """
+ return RING([F(e) for e in coeffs[::-1]])
+
+
+def poly_to_list(poly):
+ """
+ Converts a Sage polynomial object into a Python list (degree-descending order).
+ """
+ if FIELD.order() <= np.iinfo(np.int64).max:
+ dtype = np.int64
+ else:
+ dtype = np.object_
+ z = np.array([I(e) for e in poly.list()[::-1]], dtype=dtype).tolist()
+ z = z if z != [] else [0]
+ return z
+
+
 def save_pickle(d, folder, name):
  with open(os.path.join(folder, name), "wb") as f:
  pickle.dump(d, f)
@@ -139,7 +160,7 @@ def save_json(d, folder, name, indent=False):
 
 
 def make_luts(field, sub_folder, seed, sparse=False):
- global FIELD
+ global FIELD, RING
  print(f"Making LUTs for {field}")
 
  ###############################################################################
@@ -151,11 +172,11 @@ def make_luts(field, sub_folder, seed, sparse=False):
  os.mkdir(folder)
 
  FIELD = field
+ RING = PolynomialRing(field, names="x")
  characteristic = int(field.characteristic())
  order = int(field.order())
  dtype = np.int64 if order <= np.iinfo(np.int64).max else object
  alpha = field.primitive_element()
- ring = PolynomialRing(field, names="x")
  # assert field.gen() == field.multiplicative_generator()
 
  d = {
@@ -259,8 +280,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
  for i in range(len(X)):
  x = F(X[i])
  p = x.charpoly()
- z = np.array([I(e) for e in p.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(p)
  Z.append(z)
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "characteristic_poly_element.pkl")
@@ -274,8 +294,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
  X.append(x)
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  p = x.charpoly()
- z = np.array([I(e) for e in p.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(p)
  Z.append(z)
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "characteristic_poly_matrix.pkl")
@@ -286,8 +305,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
  for i in range(len(X)):
  x = F(X[i])
  p = x.minpoly()
- z = np.array([I(e) for e in p.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(p)
  Z.append(z)
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "minimal_poly_element.pkl")
@@ -338,7 +356,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  y = randint_matrix(0, order, Y_shapes[i])
  X.append(x)
  Y.append(y)
- dtype = x.dtype
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  y = matrix(FIELD, [[F(e) for e in row] for row in y])
  z = x * y
@@ -354,7 +371,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  for i in range(len(shapes)):
  x = randint_matrix(0, order, shapes[i])
  X.append(x)
- dtype = x.dtype
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  z = x.rref()
  z = np.array([[I(e) for e in row] for row in z], dtype)
@@ -372,7 +388,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  # Ensure X has a PLU decomposition with P = I, which means it has an LU decomposition
  x = randint_matrix(0, order, shapes[i])
  x_orig = x.copy()
- dtype = x.dtype
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  p, l, u = x.LU()
  if p == matrix.identity(FIELD, shapes[i][0]):
@@ -393,7 +408,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  P = []
  for i in range(len(shapes)):
  x = randint_matrix(0, order, shapes[i])
- dtype = x.dtype
  X.append(x)
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  p, l, u = x.LU()
@@ -413,7 +427,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  for i in range(len(shapes)):
  while True:
  x = randint_matrix(0, order, shapes[i])
- dtype = x.dtype
  x_orig = x.copy()
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  if x.rank() == shapes[i][0]:
@@ -432,7 +445,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  for i in range(len(shapes)):
  x = randint_matrix(0, order, shapes[i])
  X.append(x)
- dtype = x.dtype
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  z = I(x.determinant())
  Z.append(z)
@@ -448,7 +460,6 @@ def make_luts(field, sub_folder, seed, sparse=False):
  while True:
  x = randint_matrix(0, order, shapes[i])
  x_orig = x.copy()
- dtype = x.dtype
  x = matrix(FIELD, [[F(e) for e in row] for row in x])
  if x.rank() == shapes[i][0]:
  break
@@ -478,11 +489,10 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [random_coeffs(0, order, MIN_COEFFS, MAX_COEFFS) for i in range(20)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
- y = ring([F(e) for e in Y[i][::-1]])
+ x = list_to_poly(X[i])
+ y = list_to_poly(Y[i])
  z = x + y
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Y": Y, "Z": Z}
  save_pickle(d, folder, "add.pkl")
@@ -492,11 +502,10 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [random_coeffs(0, order, MIN_COEFFS, MAX_COEFFS) for i in range(20)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
- y = ring([F(e) for e in Y[i][::-1]])
+ x = list_to_poly(X[i])
+ y = list_to_poly(Y[i])
  z = x - y
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Y": Y, "Z": Z}
  save_pickle(d, folder, "subtract.pkl")
@@ -506,11 +515,10 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [random_coeffs(0, order, MIN_COEFFS, MAX_COEFFS) for i in range(20)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
- y = ring([F(e) for e in Y[i][::-1]])
+ x = list_to_poly(X[i])
+ y = list_to_poly(Y[i])
  z = x * y
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Y": Y, "Z": Z}
  save_pickle(d, folder, "multiply.pkl")
@@ -520,11 +528,10 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [random.randint(1, 2*characteristic) for i in range(20)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  y = Y[i]
  z = x * y
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Y": Y, "Z": Z}
  save_pickle(d, folder, "scalar_multiply.pkl")
@@ -539,15 +546,13 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Q = []
  R = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
- y = ring([F(e) for e in Y[i][::-1]])
+ x = list_to_poly(X[i])
+ y = list_to_poly(Y[i])
  q = x // y
  r = x % y
- q = np.array([I(e) for e in q.list()[::-1]], dtype=dtype).tolist()
- q = q if q != [] else [0]
+ q = poly_to_list(q)
  Q.append(q)
- r = np.array([I(e) for e in r.list()[::-1]], dtype=dtype).tolist()
- r = r if r != [] else [0]
+ r = poly_to_list(r)
  R.append(r)
  d = {"X": X, "Y": Y, "Q": Q, "R": R}
  save_pickle(d, folder, "divmod.pkl")
@@ -558,13 +563,12 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [0, 1, 2, 3]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  ZZ = []
  for j in range(len(Y)):
  y = Y[j]
  z = x ** y
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  ZZ.append(z)
  Z.append(ZZ)
  d = {"X": X, "Y": Y, "Z": Z}
@@ -576,7 +580,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Z = np.array(np.zeros((len(X),len(Y))), dtype=dtype)
  for i in range(len(X)):
  for j in range(len(Y)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  y = F(Y[j])
  z = x(y)
  Z[i,j] = I(z)
@@ -588,8 +592,7 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [randint_matrix(0, order, (2,2)) for i in range(20)]
  Z = []
  for i in range(len(X)):
- dtype = Y[i].dtype
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  y = matrix(FIELD, [[F(e) for e in row] for row in Y[i]])
  z = x(y)
  z = np.array([[I(e) for e in row] for row in z], dtype)
@@ -605,10 +608,9 @@ def make_luts(field, sub_folder, seed, sparse=False):
  X = [random_coeffs(0, order, MIN_COEFFS, MAX_COEFFS) for i in range(20)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  z = x.reverse()
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "reverse.pkl")
@@ -617,9 +619,8 @@ def make_luts(field, sub_folder, seed, sparse=False):
  X = [random_coeffs(0, order, MIN_COEFFS, MAX_COEFFS) for i in range(20)]
  R = []
  M = []
- dtype = randint_matrix(0, order, 1).dtype
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  roots = x.roots()
  RR, MM = [], []
  for root in roots:
@@ -640,10 +641,9 @@ def make_luts(field, sub_folder, seed, sparse=False):
  Y = [1,]*10 + [random.randint(2, FIELD.degree() + 1) for i in range(10)]
  Z = []
  for i in range(len(X)):
- x = ring([F(e) for e in X[i][::-1]])
+ x = list_to_poly(X[i])
  z = x.derivative(Y[i])
- z = np.array([I(e) for e in z.list()[::-1]], dtype=dtype).tolist()
- z = z if z != [] else [0]
+ z = poly_to_list(z)
  Z.append(z)
  d = {"X": X, "Y": Y, "Z": Z}
  save_pickle(d, folder, "derivative.pkl")