On Fri, Sep 30, 2011 at 5:11 AM, juaninf <[email protected]> wrote:
> Hi everybody,
>
> I want implement a extend Euclidean Algorithm ( to solve a(x)
It's already in Sage. Type
xgcd?
for further details.
> congruence b(x)R(x) mod (g(x))), (egcd
> function), but this give wrong results, below my egcd, please help me
> to fix ...
> I am testing with inverse multiplicative from output of xgcd
> def egcd(p1,p2):
> if p2 == PR(0):
> return (p1,1,0)
> else:
> (q1, r1) = (p1).quo_rem(p2)
> (d,s1,t1) = egcd(p2, r1)
> return (d,t1,(s1 - q1 * t1))
> m = 4
> F.<x> = GF(2)
> Phi.<x> = GF(2^m);
> PR = PolynomialRing(Phi,'z');
> N = 2^m - 1;
> X = PolynomialRing(Phi,repr('z')).gen();
> g = X^4+X^3+X^2+1+x^2; # goppa polynomial
> R = (x^3 + x^2 + 1)*X^3 + (x^3 + x^2 + x)*X^2 + (x^2 + 1)*X + x^3 + x
> (a11,b11,c11) = egcd(g,R)
> print 'testing',((c11.mod(g)*(R))).mod(g)
> (a11,b11,c11) = xgcd(g,R)
> print 'testing',((c11.mod(g)*(R))).mod(g)
>
> On 29 sep, 07:54, juaninf <[email protected]> wrote:
>> in the paper that I reading say use Euclides Algorithm, but I dont
>> know how
>>
>> On 29 sep, 07:29, juaninf <[email protected]> wrote:
>>
>>
>>
>>
>>
>>
>>
>> > g(x) is prime polynomial
>>
>> > On 29 sep, 07:28, juaninf <[email protected]> wrote:
>>
>> > > How do a(x) congruence b(x)R(x) mod (g(x)) in sage?
>>
>> > > thanks by your answers
>
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