On 11 May 2017 at 08:16, Vincent Delecroix <20100.delecr...@gmail.com> wrote: > Hi, > > "primitive element" is meant as "generator for the multiplicative group > GF(p)^*" and not the additive group GF(p). The OP question is about the > former and Johan answer is about the latter.
Not really: generators of the additive group are coprime to p, not to p-1. Perhaps Johan was thinking of the fact that if g is one multiplicative generator (aka primitive root) then g^k is another if and only if gcd(k,p-1)=1. John Cremona > > For very large p such as what you asked for is likely to be delicate (but I > am not a specialist). > > Vincent > > > On 11/05/2017 08:45, Johan S. H. Rosenkilde wrote: >> >> Hi Panos >> >> In GF(p) then an element g is primitive if its embedding into ZZ is >> coprime with p-1. Since Euclidean algorithm is so fast, you can test >> this: >> >> sage: p = Primes().next(2^2048) #long >> sage: g1 = 3 >> sage: gcd(g1, p-1) >> 3 >> sage: g2 = 5 >> sage: gcd(g2, p-1) >> 1 >> >> So 3 is not a primitive element in GF(p) but 5 is. (Since 5 is also a >> prime, you could also have done g2.divides(p-1) instead) >> >> Best, >> Johan >> >> >> Panos Phronimos writes: >> >>> Hello everyone, >>> >>> I am trying to calculate a primitive element (g) of a big Finite Field: >>> GF(p) where p is prime number > 2^2048 >>> >>> So then, i could share a secret integer (r) as: m=g^r, but it seems >>> impossible to calculate it with function primitive_element() >>> Is there another way i can use to calculate it? >>> >>> Thanks in advance, >>> Panos >> >> > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
