@@ -175,24 +175,24 @@ laws_jacobian_weierstrass = {
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def check_exhaustive_jacobian_weierstrass (name , A , B , branches , formula , p ):
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"""Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field"""
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F = Integers (p )
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- print "Formula %s on Z%i:" % (name , p )
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+ print ( "Formula %s on Z%i:" % (name , p ) )
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points = []
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- for x in xrange (0 , p ):
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- for y in xrange (0 , p ):
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+ for x in range (0 , p ):
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+ for y in range (0 , p ):
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point = affinepoint (F (x ), F (y ))
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r , e = concrete_verify (on_weierstrass_curve (A , B , point ))
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if r :
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points .append (point )
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- for za in xrange (1 , p ):
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- for zb in xrange (1 , p ):
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+ for za in range (1 , p ):
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+ for zb in range (1 , p ):
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for pa in points :
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for pb in points :
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- for ia in xrange (2 ):
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- for ib in xrange (2 ):
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+ for ia in range (2 ):
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+ for ib in range (2 ):
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pA = jacobianpoint (pa .x * F (za )^ 2 , pa .y * F (za )^ 3 , F (za ), ia )
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pB = jacobianpoint (pb .x * F (zb )^ 2 , pb .y * F (zb )^ 3 , F (zb ), ib )
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- for branch in xrange (0 , branches ):
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+ for branch in range (0 , branches ):
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assumeAssert , assumeBranch , pC = formula (branch , pA , pB )
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pC .X = F (pC .X )
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pC .Y = F (pC .Y )
@@ -206,13 +206,13 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
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r , e = concrete_verify (assumeLaw )
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if r :
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if match :
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- print " multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA .X , pA .Y , pA .Z , pA .Infinity , pB .X , pB .Y , pB .Z , pB .Infinity )
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+ print ( " multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA .X , pA .Y , pA .Z , pA .Infinity , pB .X , pB .Y , pB .Z , pB .Infinity ) )
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else :
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match = True
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r , e = concrete_verify (require )
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if not r :
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- 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 )
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- print
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+ 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 ) )
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+ print ()
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def check_symbolic_function (R , assumeAssert , assumeBranch , f , A , B , pa , pb , pA , pB , pC ):
@@ -242,9 +242,9 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
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for key in laws_jacobian_weierstrass :
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res [key ] = []
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- print ("Formula " + name + ":" )
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+ print ("Formula " + name + ":" )
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count = 0
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- for branch in xrange (branches ):
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+ for branch in range (branches ):
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assumeFormula , assumeBranch , pC = formula (branch , pA , pB )
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pC .X = lift (pC .X )
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pC .Y = lift (pC .Y )
@@ -255,10 +255,10 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula):
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res [key ].append ((check_symbolic_function (R , assumeFormula , assumeBranch , laws_jacobian_weierstrass [key ], A , B , pa , pb , pA , pB , pC ), branch ))
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for key in res :
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- print " %s:" % key
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+ print ( " %s:" % key )
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val = res [key ]
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for x in val :
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if x [0 ] is not None :
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- print " branch %i: %s" % (x [1 ], x [0 ])
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+ print ( " branch %i: %s" % (x [1 ], x [0 ]) )
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- print
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+ print ()
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