>From the doc of .algebraic_immunity :
Returns the algebraic immunity of the Boolean function. This is the
smallest integer i such that there exists a non trivial annihilator
for self or ~self.
The annihilator you get is for ~f1 (or if you prefer 1+f1)
You can check that: (1+f1)*annihilator_f1 == 0
Best regards
Le mardi 20 août 2013 20:01:03 UTC+2, Martin Albrecht a écrit :
>
> Hi Yann,
>
> I believe you are the original author of this code?
>
> Cheers,
> Martin
>
> ---------- Forwarded Message ----------
>
> Subject: [sage-support] Re: Possible bug in algebraic_immunity( ) function
> in
> crypto toolbox
> Date: Tuesday 20 August 2013, 08:54:18
> From: Oleksandr Kazymyrov <vrona.ak...@gmail.com <javascript:>>
> To: sage-s...@googlegroups.com <javascript:>
>
> 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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> name: Martin Albrecht
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