I have the same problem. My output (Mac OS 10.8.4 with sage 5.11) for #!/usr/bin/env sage
from sage.crypto.boolean_function import BooleanFunction
P = BooleanPolynomialRing(4,'x')
P.inject_variables()
f = BooleanFunction(x0*x2 + x2*x3 + 1)
print "f.algebraic_immunity() = {0}".format(f.algebraic_immunity())
print "f.annihilator(f.algebraic_immunity()) =
{0}".format(f.annihilator(f.algebraic_immunity()))
print "f.algebraic_immunity(annihilator=True) =
{0}".format(f.algebraic_immunity(annihilator=True))
g = BooleanFunction(f.algebraic_immunity(annihilator=True)[1])
print "f = {0}".format(f.algebraic_normal_form())
print "g = {0}".format(g.algebraic_normal_form())
print "g*f =
{0}".format(g.algebraic_normal_form()*f.algebraic_normal_form())
is
Defining x0, x1, x2, x3
f.algebraic_immunity() = 1
f.annihilator(f.algebraic_immunity()) = None
f.algebraic_immunity(annihilator=True) = (1, x2 + 1)
f = x0*x2 + x2*x3 + 1
g = x2 + 1
g*f = x2 + 1
Therefore algebraic_immunity returns wrong degree. g*f = 0 for degree 2,
which is the correct answer.
On Tuesday, February 12, 2013 6:35:05 PM UTC+1, akhil wrote:
>
> Hello,
>
> SAGE returns an incorrect annihilator when algebraic_immunity(annihilator
> = True) is used in the following code:
>
> from sage.crypto.boolean_function import BooleanFunction
> R = BooleanPolynomialRing(4,'x')
> f1 = R.gen(0)*R.gen(1)*R.gen(2) + R.gen(0)*R.gen(1)*R.gen(3) +
> R.gen(0)*R.gen(2)*R.gen(3) + R.gen(1)*R.gen(2)*R.gen(3) + 1
> annihilator_f1 = BooleanFunction(f1).algebraic_immunity(annihilator =
> True)[1]
> print (annihilator_f1 * f1)
>
> annihilator_f1 is incorrect, because the response comes as:
>
> x0 + x1 + x2 + x3 + 1
>
>
> and not 0 as expected.
>
> The annihilator( ) function however, returns the correct answer, as
> checked with the following code:
>
> for i in range(1,f1.total_degree() + 1):
> if BooleanFunction(f1).annihilator(i) == None:
> continue
> else:
> p = BooleanFunction(f1).annihilator(i)
> print p
> print (p*f1 == 0)
> break
>
> Output:
>
> x0*x1*x2 + x1*x2*x3
> True
>
>
> The above code was written in online notebook version of SAGE.
>
> Thanks,
> AKHIL.
>
>
>
>
>
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