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How to find "k" in system of equations ?

asked 2021-02-09 16:32:49 +0200

Duglas gravatar image

updated 2021-02-09 16:34:03 +0200

This is a y^2=x^3+7 elliptic curve points - Q,G_1,G_2,G_3. k_1,k_2,k? - secret exponents:

k_1*G1( x_1,y_1) = Q(X,Y)

k_2*G2( x_2,y_2) = Q(X,Y)

k?*G3( x_3,y_3) = Q(X,Y)

How to find a "k?" ???

Q,G_1,G_2,G_3. k_1,k_2 - are known

k? - need to find.

Big Thank You

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answered 2021-02-09 19:41:55 +0200

Max Alekseyev gravatar image

G_1,G_2, k_1,k_2 do not look helpful as they are unrelated to the equation defining k.

What you need is .discrete_log() function -- see this page for documentation and examples.

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Q is related from G1,G2,G3. And Q is a constant. No possibility find a k ?

Duglas gravatar imageDuglas ( 2021-02-10 08:30:13 +0200 )edit

You need to use function G3.discrete_log(Q) to find k from given G3 and Q. But G1, G2, k1, k2 are useless here.

Max Alekseyev gravatar imageMax Alekseyev ( 2021-02-10 15:52:37 +0200 )edit

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Asked: 2021-02-09 16:32:49 +0200

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Last updated: Feb 09