How calacul K publickey

[Kostelooscoin]

if i understand

Ax = a34b99f22c790c4e36b2b3c2c35a36db06226e41c692fc82b8b56ac1c540c5bd
Ay = 5b8dec5235a0fa8722476c7709c02559e3aa73aa03918ba2d492eea75abea235

BxBy = G

CxCy = G2

[1714779689]

1714779689

[1714779689]

1714779689

[1714779689]

1714779689

[j2002ba2]

Your private key is not a valid point. A point is supposed to start with "02" or "03" but yours starts with "e3".

Wait. Why should a private key start with "02" or "03"? A public key start with these prefixes to define if y is odd or even.
A private key is any number between 1 and 2²⁵⁶ - 2³² - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁴ - 1. No?

No. A private key is between 1 and 2²⁵⁶ - 432420386565659656852420866394968145599.

[BlackHatCoiner]

432420386565659656852420866394968145599.

What does that number mean? And why that?

[o_e_l_e_o]

432420386565659656852420866394968145599.

What does that number mean? And why that?

2²⁵⁶ - 432420386565659656852420866394968145599 in hex is:

Code:

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

This number is the order n of the curve, and is the upper limit for a valid private key.

The number you gave on the previous page, 2²⁵⁶ - 2³² - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁴ - 1 in hex is:

Code:

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F

This number is the field p of the curve, which is the field of integers over which the curve is defined.

[bigvito19]

432420386565659656852420866394968145599.

What does that number mean? And why that?

2²⁵⁶ - 432420386565659656852420866394968145599 in hex is:

Code:

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

This number is the order n of the curve, and is the upper limit for a valid private key.

The number you gave on the previous page, 2²⁵⁶ - 2³² - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁴ - 1 in hex is:

Code:

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F

This number is the field p of the curve, which is the field of integers over which the curve is defined.

What's 2^128 in decimal and in hex?

[o_e_l_e_o]

What's 2^128 in decimal and in hex?

In decimal:
340,282,366,920,938,463,463,374,607,431,768,211,456
3.4...*10³⁸

In hex:
100000000000000000000000000000000

[NotATether]

if i understand

Ax = a34b99f22c790c4e36b2b3c2c35a36db06226e41c692fc82b8b56ac1c540c5bd
Ay = 5b8dec5235a0fa8722476c7709c02559e3aa73aa03918ba2d492eea75abea235

BxBy = G

CxCy = G2

Your (Ax, Ay) point is the same as point kG in my example, and your (Bx, By) coordinates are for G.

To get G*2 (I am assuming this is the value you are trying to compute, correct me if I'm wrong), you have to add G + G.

There is an algorithm for doing this point doubling C = B*2 by hand. First, take lambda = (3Bx² + a)/(2By) , where (Bx, By) are the coordinates of the point B you are trying to double, and a is a parameter whose value is given along with the type of curve you are using. Since you are using the secp256k1 curve, a = 0.

So for the secp256k1 this expression becomes lambda = (3Bx²)/(2By) (I'm using red to color x coordinates and blue to color y coordinates).

Next you compute Cx = lambda² -2Bx, then you compute Cy = lambda*(Bx - Cx) - By . And this is how you get coordinates (Cx, Cy) of the point C = B*2.

The algorithm for doing point addition is so similar I might as well include it here too. To get C = A + B, where A != B  (in other words A and B must not be the same point. If that's the case, use point doubling instead):

- lambda = (By - Ay)/(Bx - Ax)   (Note: no a term, even if the curve is not secp256k1!)
- Cx = lambda² - Ax - Bx
- Cy = lambda*(Ax - Cx) - Ay