Solve a set of non linear Equations on Galois Field M 1 = y 1 − y 0 x 1 − x 0 M 2 = y 2 − y 0 x 2 − x 0 M 1 , M 2 , x 1 , y 1 , x 2 , y 2 ,, are known and they are chosen from a G F ( 2 m ) .. I want to find x 0 , y 0 I ll restate my question. Someone chose three distinct x 0 , x 1 , x 2 , as well as y 0 , y 1 , y 2 , then computed M 1 , M 2 , and finally revealed M 1 , M 2 , x 1 , y 1 , x 2 , y 2 , but not x 0 , y 0 . to us.All the variables are chosen from a Galois Field.I want to recover the unknown x 0 , y 0 .. Is it possible to accomplish that?If a set of nonlinear equations have been constructed with the aforementioned procedure e.g. M 1 = k 1 − ( y 0 + ( y 1 − y 0 x 1 − x 0 ) ( l 1 − x 0 ) ) ( l 1 − x 0 ) ( l 1 − x 1 ) M 2 = k 2 − ( y 0 + ( y 1 − y 0 x 1 − x 0 ) ( l 2 − x 0 ) ) ( l 2 − x 0 ) ( l 2 − x 1 ) M 3 = k 3 − ( y 0 + ( y 1 − y 0 x 1 − x 0 ) ( l 3 − x 0 ) ) ( l 3 − x 0 ) ( l 3 − x 1 ) M 4 = k 4 − ( y 0 + ( y 1 − y 0 x 1 − x 0 ) ( l 4 − x 0 ) ) ( l 4 − x 0 ) ( l 4 − x 1 ) where x 0 , y 0 x 1 , y 1 are the unknown GF elements. Can I recover the unknown elements?My question was if the fact that the set of equations is defined on a Galois Field imposes any difficulties to find its solution.If not I suppose that the set can be solved. Is this true?

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Solve a set of non linear Equations on Galois Field      M      1    =                    y        1            −              y        0                            x        1            −              x        0                  M      2    =                    y        2            −              y        0                            x        2            −              x        0                  M    1    ,      M    2    ,      x    1    ,      y    1    ,      x    2    ,      y    2    ,, are known and they are chosen from a   G  F  (      2    m    )  .. I want to find       x    0    ,      y    0  I ll restate my question. Someone chose three distinct       x    0    ,      x    1    ,      x    2  , as well as       y    0    ,      y    1    ,      y    2  , then computed       M    1    ,      M    2  , and finally revealed       M    1    ,      M    2    ,      x    1    ,      y    1    ,      x    2    ,      y    2  , but not       x    0    ,      y    0    . to us.All the variables are chosen from a Galois Field.I want to recover the unknown       x    0    ,      y    0    .. Is it possible to accomplish that?If a set of nonlinear equations have been constructed with the aforementioned procedure e.g.      M    1    =                    k        1            −      (              y        0            +      (                                    y            1                    −                      y            0                                                x            1                    −                      x            0                              )      (              l        1            −              x        0            )      )              (              l        1            −              x        0            )      (              l        1            −              x        1            )            M    2    =                    k        2            −      (              y        0            +      (                                    y            1                    −                      y            0                                                x            1                    −                      x            0                              )      (              l        2            −              x        0            )      )              (              l        2            −              x        0            )      (              l        2            −              x        1            )            M    3    =                    k        3            −      (              y        0            +      (                                    y            1                    −                      y            0                                                x            1                    −                      x            0                              )      (              l        3            −              x        0            )      )              (              l        3            −              x        0            )      (              l        3            −              x        1            )            M    4    =                    k        4            −      (              y        0            +      (                                    y            1                    −                      y            0                                                x            1                    −                      x            0                              )      (              l        4            −              x        0            )      )              (              l        4            −              x        0            )      (              l        4            −              x        1            )      where       x    0    ,      y    0        x    1    ,      y    1   are the unknown GF elements. Can I recover the unknown elements?My question was if the fact that the set of equations is defined on a Galois Field imposes any difficulties to find its solution.If not I suppose that the set can be solved. Is this true?

Ordettyreomqu · Accepted Answer

The first system can be solved in the usual way, provided the &quot;slopes&quot;       M    i  i are distinct. Solve each for the knowns       y    k  ,   k  =  1  ,  2 and subtract. You can then get to      x    0    =                    M        2                    x        2            −              M        1                    x        1            −              y        2            +              y        1                            M        2            −              M        1              ,and then use one of the equations you already formed with this       x    0   plugged in to get       y    0    .. Since this method only uses addition/subtraction multiplication/(nonzero)division it works in any field, in particular in your Galois field.

Solve a set of non linear Equations on Galois Field M 1 </msub> =

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