sage: Fix incompatibility with sage 9.4

.cirrus.yml

@@ -322,3 +322,10 @@ task:
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
+
+task:
+  name: "sage prover"
+  << : *LINUX_CONTAINER
+  test_script:
+    - cd sage
+    - sage prove_group_implementations.sage

ci/linux-debian.Dockerfile

@@ -19,7 +19,8 @@ RUN apt-get install --no-install-recommends --no-upgrade -y \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \
         gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross libc6-dbg:ppc64el \
-        wine gcc-mingw-w64-x86-64
+        wine gcc-mingw-w64-x86-64 \
+        sagemath
 
 # Run a dummy command in wine to make it set up configuration
 RUN wine64-stable xcopy || true

sage/group_prover.sage

@@ -164,6 +164,9 @@ class constraints:
   def negate(self):
     return constraints(zero=self.nonzero, nonzero=self.zero)
 
+  def map(self, fun):
+    return constraints(zero={fun(k): v for k, v in self.zero.items()}, nonzero={fun(k): v for k, v in self.nonzero.items()})
+
   def __add__(self, other):
     zero = self.zero.copy()
     zero.update(other.zero)
@@ -177,6 +180,30 @@ class constraints:
   def __repr__(self):
     return "%s" % self
 
+def normalize_factor(p):
+  """Normalizes the sign of primitive polynomials (as returned by factor())
+
+  This function ensures that the polynomial has a positive leading coefficient.
+
+  This is necessary because recent sage versions (starting with v9.3 or v9.4,
+  we don't know) are inconsistent about the placement of the minus sign in
+  polynomial factorizations:
+  ```
+  sage: R.<ax,bx,ay,by,Az,Bz,Ai,Bi> = PolynomialRing(QQ,8,order='invlex')
+  sage: R((-2 * (bx - ax)) ^ 1).factor()
+  (-2) * (bx - ax)
+  sage: R((-2 * (bx - ax)) ^ 2).factor()
+  (4) * (-bx + ax)^2
+  sage: R((-2 * (bx - ax)) ^ 3).factor()
+  (8) * (-bx + ax)^3
+  ```
+  """
+  # Assert p is not 0 and that its non-zero coeffients are coprime.
+  # (We could just work with the primitive part p/p.content() but we want to be
+  # aware if factor() does not return a primitive part in future sage versions.)
+  assert p.content() == 1
+  # Ensure that the first non-zero coefficient is positive.
+  return p if p.lc() > 0 else -p
 
 def conflicts(R, con):
   """Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
@@ -204,10 +231,10 @@ def get_nonzero_set(R, assume):
   nonzero = set()
   for nz in map(numerator, assume.nonzero):
     for (f,n) in nz.factor():
-      nonzero.add(f)
+      nonzero.add(normalize_factor(f))
     rnz = zero.reduce(nz)
     for (f,n) in rnz.factor():
-      nonzero.add(f)
+      nonzero.add(normalize_factor(f))
   return nonzero
 
 
@@ -222,27 +249,27 @@ def prove_nonzero(R, exprs, assume):
       return (False, [exprs[expr]])
   allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1)
   for (f, n) in allexprs.factor():
-    if f not in nonzero:
+    if normalize_factor(f) not in nonzero:
       ok = False
   if ok:
     return (True, None)
   ok = True
-  for (f, n) in zero.reduce(numerator(allexprs)).factor():
-    if f not in nonzero:
+  for (f, n) in zero.reduce(allexprs).factor():
+    if normalize_factor(f) not in nonzero:
       ok = False
   if ok:
     return (True, None)
   ok = True
   for expr in exprs:
     for (f,n) in numerator(expr).factor():
-      if f not in nonzero:
+      if normalize_factor(f) not in nonzero:
         ok = False
   if ok:
     return (True, None)
   ok = True
   for expr in exprs:
     for (f,n) in zero.reduce(numerator(expr)).factor():
-      if f not in nonzero:
+      if normalize_factor(f) not in nonzero:
         expl.add(exprs[expr])
   if expl:
     return (False, list(expl))
@@ -254,7 +281,7 @@ def prove_zero(R, exprs, assume):
   """Check whether all of the passed expressions are provably zero, given assumptions"""
   r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
   if not r:
-    return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
+    return (False, list(map(lambda x: "Possibly zero denominator: %s" % x, e)))
   zero = R.ideal(list(map(numerator, assume.zero)))
   nonzero = prod(x for x in assume.nonzero)
   expl = []
@@ -279,17 +306,17 @@ def describe_extra(R, assume, assumeExtra):
     if base not in zero:
       add = []
       for (f, n) in numerator(base).factor():
-        if f not in nonzero:
-          add += ["%s" % f]
+        if normalize_factor(f) not in nonzero:
+          add += ["%s" % normalize_factor(f)]
       if add:
         ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base])
   # Iterate over the extra nonzero expressions
   for nz in assumeExtra.nonzero:
     nzr = zeroextra.reduce(numerator(nz))
     if nzr not in zeroextra:
       for (f,n) in nzr.factor():
-        if zeroextra.reduce(f) not in nonzero:
-          ret.add("%s != 0" % zeroextra.reduce(f))
+        if normalize_factor(zeroextra.reduce(f)) not in nonzero:
+          ret.add("%s != 0" % normalize_factor(zeroextra.reduce(f)))
   return ", ".join(x for x in ret)
 
 
@@ -299,22 +326,21 @@ def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require):
 
   if conflicts(R, assume):
     # This formula does not apply
-    return None
+    return (True, None)
 
   describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert)
+  if describe != "":
+    describe = " (assuming " + describe + ")"
 
   ok, msg = prove_zero(R, require.zero, assume)
   if not ok:
-    return "FAIL, %s fails (assuming %s)" % (str(msg), describe)
+    return (False, "FAIL, %s fails%s" % (str(msg), describe))
 
   res, expl = prove_nonzero(R, require.nonzero, assume)
   if not res:
-    return "FAIL, %s fails (assuming %s)" % (str(expl), describe)
+    return (False, "FAIL, %s fails%s" % (str(expl), describe))
 
-  if describe != "":
-    return "OK (assuming %s)" % describe
-  else:
-    return "OK"
+  return (True, "OK%s" % describe)
 
 
 def concrete_verify(c):

sage/prove_group_implementations.sage

@@ -292,15 +292,18 @@ def formula_secp256k1_gej_add_ge_old(branch, a, b):
   return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
 
 if __name__ == "__main__":
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
-  check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
+  success = True
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
+  success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
+  success = success & (not check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old))
 
   if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
-    check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
+    success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
+    success = success & (not check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43))
+
+  sys.exit(int(not success))

sage/weierstrass_prover.sage

@@ -184,6 +184,7 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
       if r:
         points.append(point)
 
+  ret = True
   for za in range(1, p):
     for zb in range(1, p):
       for pa in points:
@@ -211,8 +212,11 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
                         match = True
                       r, e = concrete_verify(require)
                       if not r:
+                        ret = False
                         print("  failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e))
+
   print()
+  return ret
 
 
 def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC):
@@ -244,15 +248,21 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
 
   print("Formula " + name + ":")
   count = 0
+  ret = True
   for branch in range(branches):
     assumeFormula, assumeBranch, pC = formula(branch, pA, pB)
+    assumeBranch = assumeBranch.map(lift)
+    assumeFormula = assumeFormula.map(lift)
     pC.X = lift(pC.X)
     pC.Y = lift(pC.Y)
     pC.Z = lift(pC.Z)
     pC.Infinity = lift(pC.Infinity)
 
     for key in laws_jacobian_weierstrass:
-      res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch))
+      success, msg = check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC)
+      if not success:
+        ret = False
+      res[key].append((msg, branch))
 
   for key in res:
     print("  %s:" % key)
@@ -262,3 +272,4 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
         print("    branch %i: %s" % (x[1], x[0]))
 
   print()
+  return ret