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  • CG 12:15 pm on February 23, 2010 Permalink | Reply
    Tags: curve set up, polynomial, ,   

    modifying curve setting up 

    /* CG - February 2010
       the program is supposed to find y for any given x
       [in progress]
       the representation is in polynomial
    */
    
    #include <stdio.h>
    #include <stdlib.h>
    #include "field2n.h"
    #include "poly.h"
    #include "eliptic.h"
    
    unsigned long random_seed;
    extern FIELD2N poly_prime;
    
    void set_field(value, n)
    FIELD2N *value;
    INDEX n;
    {
       value->e[0] = n;
    }
    
    void set_curve(curv)
    CURVE *curv;
    {
       curv->form = 1;
       set_field(&curv->a6, 1L);   
       null(&curv->a2);
    //   set_field(&curv->a2, 0L);
    }	
    
    int main()
    {
       FIELD2N	*data, *data_juga;
       CURVE *curve;
       POINT *point;
       INDEX error;
       FIELD2N f;	
       POINT *pnt;
    
       curve = malloc(sizeof(CURVE));
       if (curve == NULL) {exit(-1);}
    
       point = malloc(sizeof(POINT));
       if (point == NULL) {exit(-1);}
    
       if (!irreducible(&poly_prime)) return(0);
          print_field("poly_prime = ", &poly_prime);
    	
       if (error = init_poly_math())
          {
             printf("Can't initialize S matrix, row = %d\n", error);
    	 return(-1);
          }
    
       printf("setting up curves \n\n");
      
       set_curve(curve); 
       print_curve("the curve after setting up: ", curve);
    	
       return 0;
    }
    
    


    poly_prime =
    8 0 0 0 0 c9
    setting up curves

    the curve after setting up:
    form: 1
    a2: 0 0 0 0 0 0
    a6: 1 0 0 0 0 0

     
    • zakimath 7:28 am on February 24, 2010 Permalink | Reply

      how to find an elliptic curve E with #E (the order of group) is prime…? 🙂

      • CG 9:21 am on February 24, 2010 Permalink | Reply

        hadoh! susah, harus tanya sama dukun math dulu nih 😀

    • zakimath 11:10 am on February 24, 2010 Permalink | Reply

      hehehe, emang susah bgt! masih belum terbayang… 🙂
      Kalo gitu dibalik: Jika diberikan bilangan prima p, apakah terdapat suatu kurva elliptik E sedemikian hingga #E = p ?

      • CG 11:27 am on February 24, 2010 Permalink | Reply

        [berpikir keras] #E itu order kurva ya? berarti jumlah titik dalam kurva? bisa gitu jumlah titiknya ganjil (prima) kan titik2xnya sepasang? y^2?

    • zakimath 12:59 pm on February 24, 2010 Permalink | Reply

      Iya bu, #E itu banyaknya titik dalam suatu kurva E… bener gk sih simbolnya? koq jd lupa, he2… Contohnya kurva elliptik E: y^2 = x^3 + 12x + 20 atas field F_23 itu mempunyai jumlah titik 17, yaitu #E = 17 yg merupakan bilangan prima, akibatnya setiap titiknya merupakan generator dari E. CMIIW…

    • zakimath 1:03 pm on February 24, 2010 Permalink | Reply

      Hmmm, tp rasanya ada yg salah dg komentarku… #E = 17 itu sudah termasuk titik infinity blom ya? aduh, koq jadi lupa… 😦

      • CG 9:23 pm on February 24, 2010 Permalink | Reply

        eh baru aja saya mau bales, iya bner ganjil kan ditambah point of infinity 🙂

    • HongKong 10:09 pm on February 27, 2010 Permalink | Reply

      jawabannya sih.. bisa bilangan ganjil dan bisa juga bilangan genap ((x,0) kan gak punya pasangan)
      ada teoremanya sih:
      untuk setiap bilangan prima p selalu dapat dicari kurva eliptik atas Fp dengan orde (banyaknya titik) p

      • CG 6:26 am on February 28, 2010 Permalink | Reply

        thank you, HongKong 🙂

      • CG 5:33 pm on February 28, 2010 Permalink | Reply

        baru inget kalau si HongKong = the geometer 😀

  • CG 10:14 am on January 30, 2009 Permalink | Reply
    Tags: normal bases, polynomial   

    Questions on polynomial and normal bases 

    1. How to convert from polynomial to normal bases?
    2. For what conditions ONB representation is available?
     
  • CG 6:51 pm on October 14, 2008 Permalink | Reply
    Tags: , polynomial   

    More on fields and polynomial 

    Have just learned that:

    F_{2}=Z_{2}=\left\{ \bar{0},\bar{1}\right\}

    F_{4}=\left\{\left(a,b: a,b \epsilon F_{2}\right) \right\} means that the elements are

    \left(\bar{0},\bar{0} \right) , \left(\bar{0},\bar{1} \right) , \left(\bar{1},\bar{0} \right) and \left(\bar{1},\bar{1} \right)

    F_{8}=F_{2^{3}}\left\{\left(a, b, c: a, b, c \epsilon F_{2} \right) \right\}

    F_{2^{n}} means that we’ll have n tuple, thus we’ll have a polynomial with n degree

    (degree is the highest exponent of the polynomial).

    Example:

    \left(\bar{1}, \bar{0}, \bar{1}, \bar{1} \right) means x^{3}+x+1

    Important notes:

    F_{p}=Z_{p} is only if p is prime. F_{8}\neq Z_{8}

     
  • CG 5:31 am on October 14, 2008 Permalink | Reply
    Tags: polynomial   

    Polynomial 

    The phd student had just found out more about F_{2^{n}} representation. For 2^{n} , there are n tuples. The tuples turn out to be the degree of a polynomial!

    She is so happy to know the basic terms and concepts in math. Interesting!

    [will write more about this, the phd student needs to get ready for a morning jog 😉 ]

     
  • CG 1:44 am on September 29, 2008 Permalink | Reply
    Tags: , polynomial   

    Math Polynomial 

    Move forward to Galois Field representation in C. Zooming in all the modules of math for polynomial representation with the prime number 2 as the modulus (means that the coefficient and only take values of 0 or 1).

    The text converting code is halfway to go.

     
    • yuti 9:53 pm on January 1, 2009 Permalink | Reply

      Aaaaaa…. selalu pengen belajar Galois, waktu itu pernah mau belajar tentang Galois waktu sedang seneng baca tentang ehmm…mmm… kayanya tentang social network dan transformasi-transformasi gitu… aaaaaa… cerita-cerita

    • CG 4:44 am on January 2, 2009 Permalink | Reply

      yuti: hah, gue sampe skarang juga belum ngerti2x yut 😀

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