Modulus illusion

[satashi_nokamato]

I have difficulties to understand the following results, can someone explain?

I have these keys
#1=

Code:

03f4bef7834ec36e40f1c007a4c27c2f7d2ded709fda3333fdd5801625736ed152

#2=

Code:

03389523df912b20e7f5b2223f50a3e074551d3859487701d9e6297b950c9a78ea

Adding two keys gives me this one
#3=

Code:

0390823e1bb57e0b3492019544a0b3d4fcdfe51e843b417becd3d3285c9c154d0d
Private_key= 
0x000000000000000000000000000000000000000000000200ddfe92f46681b20a

If I subtract #2 from #1, we'd have this
#4=

Code:

032b0d9abd02f210631ca0fdf138a19c6725f6b67f2dba6c22bf181c73e81abd08

Then if we subtract #4 from #3, it would give us double of #2.
But I'm going to make it much easier for you to understand by showing scalar instead of points.
We have these
#1=
0x1c16e0f93f27c98dfa5
#2=
0x3f6feeff01e9e8d265
#3=
0x200ddfe92f46681b20a
#4=
0x181fe2094f092b00d40

Everything I do with 4 keys above is related to key #3, but I can't solve any of the other 3 keys even though whatever I do always gives me correct points, where is my mistake?

Note that scalar 1, 2 and 4 result in different points than above points but they do behave similar when working with 3. Why is that?

[1714467389]

1714467389

[1714467389]

1714467389

[1714467389]

1714467389

[1714467389]

1714467389

[1714467389]

1714467389

[1714467389]

1714467389

[BlackHatCoiner]

Note that scalar 1, 2 and 4 result in different points than above points but they do behave similar when working with 3. Why is that?

Because they are all mathematically related.

• #1 + #2 = #3
• #1 - #2 = #4

Given these, #3 - #4 = #1 + #2 - (#1 - #2) = #1 + #2 - #1 + #2 = 2 * #2. So, yes, if you subtract #4 from #3, you get double #2.

[satashi_nokamato]

Of course, I already know what you explained,  my question is where should I look for any of the 3 unknown points or any of their offsets?  Whether I can find any of them  below the range of scalar #3 or above that range?  As I have tried kangaroo with no success.

[ymgve2]

As far as I can tell you can't use the fact that key 1 and 2 are a known distance away from each other to discern anything about them. It's a single equation with two unknowns. Example: X + Y = 123, but X and Y could be 0 and 123, or they could be -113258881385746098181140976018376643534 and 113258881385746098181140976018376643657, or any other number.

Another way to think about it: Pick any arbitrary random public key from the blockchain, like say, the genesis block coinbase key, and call it #A1. Calculate #3 - #A1, and call the result #B1. You now have two keys #A1 and #B1 that when added gives #3, the exact same situation in your original question.

If this process would give you any insight into the private key of #A1, elliptic curve cryptography would be fundamentally broken.

[ElDalmatino]

You get the "between" keys ( i call them brothers and sisters ), relevant to your base keys. That´s why you don´t find and see them, and that is the reason kangaroo won´t work.

Look at my post, remember when you ask to search for a public key.

https://bitcointalk.org/index.php?topic=5483513.0

[NotATether]

As far as I can tell you can't use the fact that key 1 and 2 are a known distance away from each other to discern anything about them. It's a single equation with two unknowns. Example: X + Y = 123, but X and Y could be 0 and 123, or they could be -113258881385746098181140976018376643534 and 113258881385746098181140976018376643657, or any other number.

Another way to think about it: Pick any arbitrary random public key from the blockchain, like say, the genesis block coinbase key, and call it #A1. Calculate #3 - #A1, and call the result #B1. You now have two keys #A1 and #B1 that when added gives #3, the exact same situation in your original question.

If this process would give you any insight into the private key of #A1, elliptic curve cryptography would be fundamentally broken.

This is basically the only possible answer.

While you could get the *public keys* of this sort of operation if you were doing the arithmetic between private keys (and indeed this is what I initially thought the OP was trying to do until I saw the 02 and 03 at the beginning of all the strings), it does not work the other way around.

Public key arithmetic without the private keys is really only interesting to cryptographers.