Quote from: satashi_nokamato on February 28, 2024, 10:16:45 PM

Quote from: kTimesG on February 28, 2024, 11:35:09 AM

Pure math is reasoning

What do you know about math? if you know how to solve a key by using pure math, then this is for you if you know things.
We have 4 points and 4 scalar, 3 points are unknown but they do relate to all 4 scalar keys. Can you point out a hint as to how we can solve any of the 3 points?

Here are our 3 points

Code:

P1=
03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152
P2=
03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea
P3=
032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Here are 4 scalar

Code:

A1=
0x1c16e0f93f27c98dfa5
A2=
0x3f6feeff01e9e8d265
A3=
0x181fe2094f092b00d40
A4=
0x200ddfe92f46681b20a

P1+P2= A4, P2-P1= P3, P3-A4= P2*2, P1-A4/2= P3/2.
Here is the trick, A1, A2 and A3 point to different public keys, however if we subtract A1-1 from P1, subtract A2-1 from P2 and add the results, we would get 2, which means P1 and P2 are close they are also close to P3 because half of A4 subtracted from P1 equals half of P3. This is pure math, but how can we solve any of the 3 points while we only have A4 and why A1, A2 and A3 behave similar to our 3 points? They are in close range with each other but where are they exactly?

Quote from: satashi_nokamato on February 28, 2024, 10:16:45 PM

Quote from: kTimesG on February 28, 2024, 11:35:09 AM

Pure math is reasoning

What do you know about math? if you know how to solve a key by using pure math, then this is for you if you know things.
We have 4 points and 4 scalar, 3 points are unknown but they do relate to all 4 scalar keys. Can you point out a hint as to how we can solve any of the 3 points?

Here are our 3 points

Code:

P1=
03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152
P2=
03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea
P3=
032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Here are 4 scalar

Code:

A1=
0x1c16e0f93f27c98dfa5
A2=
0x3f6feeff01e9e8d265
A3=
0x181fe2094f092b00d40
A4=
0x200ddfe92f46681b20a

P1+P2= A4, P2-P1= P3, P3-A4= P2*2, P1-A4/2= P3/2.
Here is the trick, A1, A2 and A3 point to different public keys, however if we subtract A1-1 from P1, subtract A2-1 from P2 and add the results, we would get 2, which means P1 and P2 are close they are also close to P3 because half of A4 subtracted from P1 equals half of P3. This is pure math, but how can we solve any of the 3 points while we only have A4 and why A1, A2 and A3 behave similar to our 3 points? They are in close range with each other but where are they exactly?

It seems you're dealing with elliptic curve cryptography (ECC) where you have points on a curve and scalar multiplication operations. From your provided information, you have points P1, P2, and P3, as well as scalars A1, A2, A3, and A4.

Your hint suggests that A1, A2, and A3 are related to P1, P2, and P3 respectively, in a way that when you subtract 1 from each scalar and subtract that from its corresponding point, adding the results gives you 2. This indicates that P1, P2, and P3 are likely related to A1-1, A2-1, and A3-1 respectively in some manner.

The relationship between P1, P2, and P3 is also given in terms of scalar operations involving A4. From the relationships provided:

P1 + P2 = A4:

If you add point P1 and point P2 together on the elliptic curve, you get the point A4.
P2 - P1 = P3:

If you subtract point P1 from point P2 on the elliptic curve, you get the point P3.
P3 - A4 = 2P2:

If you subtract point A4 from point P3 on the elliptic curve, you get twice the value of point P2.
P1 - (A4 / 2) = (P3 / 2):

If you subtract half of the value of A4 from point P1 on the elliptic curve, you get half of point P3.

Given only A4 and these relationships, it's possible to find the coordinates of at least one of the points P1, P2, or P3 by performing scalar operations with A4.

To find the exact coordinates of the points P1, P2, and P3, you can use scalar multiplication operations on a known base point on the elliptic curve, which is usually provided in ECC. By performing scalar multiplication operations with A4 and using the provided relationships, you can compute the coordinates of at least one of the points. Once you have the coordinates of one point, you can use the relationships between the points to deduce the coordinates of the others.

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