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#52 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:47:31

It is 135=2mod19 which is right. (Always I think..)

#53 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:43:10

I verified it with the calculator. It seems right!

#55 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:24:10

You first multiply then tou do modulo p. The division, you first find the reverse of the number mod p and then multiply
I do not know how square root is computed.

#56 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:14:18

The operations are not like those o f standard arithmetic. If mathematica does the solving may has their definitions. GF elements are not integers they seem like integers. Different properties

#57 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:07:00

ok. but this is not the problem.the problem is to have the definition of addition multiplication division square root etc on GF.You cannot use integer arithmetic

#58 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 05:00:33

That right! All the problem is define over GF.

#60 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 04:48:17

I do not know if what I have is helpful. All I have is the abiltiy to select the coef. of the polynomial and to evaluate it to some x_i s.

#61 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 00:05:18

Hmm...I can create a polynomial and pre select its leading coefficient. Also I can pselect random points from it.

By I m not able to constrct polynomials which have intersection points...

#62 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-22 00:02:08

This was very helpful to me
http://www.dragonwins.com/domains/getteched/crypto/polynomial_arithmetic_in_gf%28p%5En%29.htm

#63 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 23:55:02

Is this helpful? I ll try to find more...
http://mathworld.wolfram.com/FiniteField.html

#64 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 23:46:24

If all the parameteres of the problem are defined correctly I think that there will be no rpoblem. But I remind you that GF elements are not numbers the look like number. I used polynomial basis representation when I worked over GF @^128.

#65 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 23:40:53

Yes, its the same problem tha we were discussing in the previous post only that the elements now are selected by a GF(2^128).

#66 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 23:00:05

In GF(p) all the operations are executed modulo p.

In a order to construct an extension field GF(2^128) an irreducible polynomial is employed in order the elements of the field to be generated. Then all the operations are executed modulo this ir. pol.

#67 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 22:32:41

I think that I can provide you with points of polynomials over GF(2^128). I can also choose the leading coefficient. But I think that in order the resuls to be right both of us have to employ the same irreducible polynomial.

I mean that if it is easy to "feed in" Mathematica with the irreducible polynomial, the required points the leading coefficient I can give you this info.

#68 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 18:52:05

I thought that you can transform the set of equations to linear. Now I think that is not true so the square roots etc... will stay on but i do not think that this i s aproblem to mathematica.

#69 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 18:32:54

I think that my post #194 is wrong. If you substitute the differences (x_i-x_0) with variables, the list of unknown variables become larger and larger...

#71 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 01:10:15

May mathematica has library for GF but i am nto familiar with it.

#72 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 01:05:00

the initial points will be lements of the gf e.g. (x3,y3)=(2,7) etc. The problem is how can you implement add, multiplication and division to have the right results?

#74 Re: Help Me ! » Define the intersection points of polynomials » 2013-07-21 00:55:40

Multiplications addtion and division over the gf is not as standard opeerations. More generally all the operations executed over GF are performed modulop. e.g 5+15=20modp=3mod17.

The algorithms for the operations are different thats why all the results  end up to b.e Gf elements

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