Fixup: Elements of finite fields are not instances of FieldElement

src/sage/crypto/mq/rijndael_gf.py

@@ -424,7 +424,7 @@
 
 from sage.matrix.constructor import matrix
 from sage.matrix.constructor import column_matrix
-from sage.structure.element import FieldElement, Matrix
+from sage.structure.element import Element, Matrix
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.structure.sage_object import SageObject
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -757,7 +757,9 @@ def _GF_to_hex(self, GF):
             sage: rgf._GF_to_hex(output)
             'e142cd5fcd9d6d94a3340793034391b5'
         """
-        if not isinstance(GF, (Matrix, list, FieldElement)):
+        if not isinstance(GF, Matrix) and \
+           not isinstance(GF, list) and \
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self._F))
@@ -880,7 +882,9 @@ def _GF_to_bin(self, GF):
             sage: rgf._GF_to_bin(output)
             '11011000000111111111100000011011110110000001111111111000000110111101100000011111111110000001101111011000000111111111100000011011'
         """
-        if not isinstance(GF, (Matrix, list, FieldElement)):
+        if not isinstance(GF, Matrix) and \
+           not isinstance(GF, list) and \
+           not (isinstance(GF, Element) and isinstance(GF.parent(), FiniteField)):
             msg = ("keyword 'GF' must be a matrix over {0}, a list of "
                    "elements from {0}, or a single element from {0}")
             raise TypeError(msg.format(self))

src/sage/crypto/sbox.pyx

@@ -5,7 +5,7 @@ cimport cython
 from cysignals.memory cimport check_allocarray, sig_free
 
 from sage.structure.sage_object cimport SageObject
-from sage.structure.element cimport Element, FieldElement
+from sage.structure.element cimport Element
 
 from sage.combinat.integer_vector import IntegerVectors
 from sage.crypto.boolean_function import BooleanFunction
@@ -17,6 +17,7 @@ from sage.misc.functional import is_even
 from sage.misc.misc_c import prod as mul
 from sage.misc.superseded import deprecated_function_alias
 from sage.modules.free_module_element import vector
+from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.rings.ideal import FieldIdeal, Ideal
 from sage.rings.integer_ring import ZZ
@@ -194,7 +195,7 @@ cdef class SBox(SageObject):
 
         _S_list = []
         for e in S:
-            if isinstance(e, FieldElement) and e.parent().is_finite():
+            if isinstance(e, Element) and isinstance(e.parent(), FiniteField):
                 e = e.polynomial().change_ring(ZZ).subs(e.parent().characteristic())
             _S_list.append(e)
         S = _S_list

src/sage/rings/algebraic_closure_finite_field.py

@@ -59,7 +59,7 @@
 
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.ring import Field
-from sage.structure.element import FieldElement
+from sage.structure.element import Element, FieldElement
 from sage.structure.richcmp import richcmp
 
 
@@ -90,7 +90,7 @@ def __init__(self, parent, value):
             and ``loads(dumps(x))``.
 
         """
-        if isinstance(value, FieldElement) and value.parent().is_finite():
+        if isinstance(value, Element) and isinstance(value.parent(), FiniteField):
             n = value.parent().degree()
         else:
             from sage.rings.integer import Integer

src/sage/rings/padics/padic_template_element.pxi

@@ -37,7 +37,7 @@ from sage.rings.infinity import infinity
 from sage.rings.rational import Rational
 from sage.rings.padics.precision_error import PrecisionError
 from sage.rings.padics.misc import trim_zeros
-from sage.structure.element import canonical_coercion, FieldElement
+from sage.structure.element import canonical_coercion, Element
 import itertools
 
 cdef long maxordp = (1L << (sizeof(long) * 8 - 2)) - 1
@@ -146,7 +146,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement):
         elif sage.rings.finite_rings.integer_mod.is_IntegerMod(x):
             if not Integer(self.prime_pow.prime).divides(x.parent().order()):
                 raise TypeError("p does not divide modulus %s"%x.parent().order())
-        elif isinstance(x, FieldElement) and isinstance(x.parent(), FiniteField):
+        elif isinstance(x, Element) and isinstance(x.parent(), FiniteField):
             k = self.parent().residue_field()
             if not k.has_coerce_map_from(x.parent()):
                 raise NotImplementedError("conversion from finite fields which do not embed into the residue field not implemented")

src/sage/schemes/elliptic_curves/ell_finite_field.py

@@ -30,7 +30,7 @@
 from sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field import HyperellipticCurve_finite_field
 from sage.rings.all import Integer, ZZ, PolynomialRing, GF, polygen
 from sage.rings.finite_rings.finite_field_base import FiniteField
-from sage.structure.element import FieldElement
+from sage.structure.element import Element
 import sage.groups.generic as generic
 from . import ell_point
 from sage.arith.all import gcd, lcm, binomial
@@ -1530,7 +1530,7 @@ def is_j_supersingular(j, proof=True):
         sage: [p for p in prime_range(100) if is_j_supersingular(GF(p)(123456))]
         [2, 3, 59, 89]
     """
-    if not (isinstance(j, FieldElement) and isinstance(j.parent(), FiniteField)):
+    if not (isinstance(j, Element) and isinstance(j.parent(), FiniteField)):
         raise ValueError("%s must be an element of a finite field" % j)
 
     F = j.parent()