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I found on secp256k1 that if 4 points have same doubling slope their private keys always gives 0
k1+k2+k3+k4=0

On smaller curve
P=967 N=907
β (cube root of 1): 142
λ (eigenvalue at P): 522
1G   (418, 442)


If I have 1st private key I can calculate 1st column.... and I can  calculate all slopes in 1 set of 24 points but I did not find the way to if I have k1 to calculate k2 k3 k4

Also on the big curve I found those sets

f(x) = 9x^4 - 4slope^2x^3 - 28slope^2 = 0

On this way I generated sets of 4 points 48 sets on this curve p=967
I tried other curves with Sagemath
p=1000003 - Number of points: 999006 Number of sets: 41886
p=1001023 - Points: 999066 - Sets:41466
p=1001527 - Points: 1000158 - Sets:41580
p=20000077 - Points: 19992876 - Sets:833040

Finally I tried to search those sets on the big curve. I started with slope 1 and I was searching if current slope will give 4 solutions for that
This is the SageMath code I was using https://justpaste.it/k055b
and I got these Slopes and X values

Slope 5:
e5493c5e5ab1e25795a4f01f362ebc855d3c2611100bb0c24b401d5846f28f93
95b49d5352c6d6893771e5524aced66e9c163010d1cf0dcad80a77d786fc4681
91bfb02411f3bbb0e380f649f876e8692acbb596452df00277c846b1191017f5
817b59b8797719a732f66d2814c4683114c58280bc858a53f32607aac3abb2ec
--------------------
Slope 16:
ff405d7729ed52aa591f7be3f59048c4d506fc28ff83f1b78c84f34c9ec19e50
a1f7ff943ae98653ce8e8b90ea104f1f9a669548bf0208a595810c0d526cb547
2fe5f2ec5aed03af8aae566b6a792fdf5ae94630ba878d2a0206ec505e7cd908
126fe8ebce7506e0868730589974711fc3e20bebbfd606b1bf814d375aff7748
--------------------
Slope 47:
d8a0a502488cf53fe88a7b53b3b86021c151e59ef8df9f0f6fe54b821cef7ac6
6ced29459069a670d859aec16c1e85d426d1eaf84a1a14f8beab86e85934b74b
5b260613d299e1e19673ccf072afac0b94e843b73f24fe1f425f1e2ca885df5b
42da6487e2a865fbe18b97335107a6e2112ccf3fb6c4dc11729e484a8c0095df
--------------------
Slope 54:
f9c2e48f573115eddcbc132f9cf5979ac292e3918ecdec4458589501788f5b90
caeb00411e5011e845e8063c58749613f6e51a083896b935cab902a50815f9c2
217212301587cca0fb1387de3db81428cb7b5e95567786fee35fc43327ea2046
19e008ff74f70b88e2485eb5ccddbe287b0ca3d0e223d386f98ea424577087d6
--------------------
Slope 110:
f494b668f9c24a74dcced225e670cd6d9b343b9d8175354123281ab73564f74a
a3c5694b0a6cce2d90e5cfdc9f3bd9a5bad9fab3a0685ece8a5bd958802b979c
35fbd7fee43dafc765aeb3abe77c60fcaba79fbebd7d5b5ffddd70c9acc27109
15384130a5cc1b246580388a766530d38c830d7e59889ec9382cd4084857b888
--------------------
About 16% of all points on the curve have this property
Of course if you know 1 slope then you know p-slope so in the case of any kind of scanning we can just save the slope and we have info for 8 points
Do you think that those points can be used for solving secp256k1? What do you think about all of this?

https://www.johnsboard.com/

So my nickname is John (my real name is similar), and I created this website where you can submit your banner, and my homepage will link to your website (follow the link - opened in new tab). I saw the story about that guy who sold pixels, and I saw that the website is not working anymore. It is not updated... Most of the links are not working....

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Please if you find any bugs, send me a message here or send me email at admin@johnsboard.com
(I am one man show so the bugs are possible to happen)

Thank you, and I am calling you to submit your website or any kind of "normal link", links to your projects, you can put refferal links just no adult torrent illegal - no links that redirects to something different

Thank you <3

So I am learning about everything and so there is a chance that this post can be lame/noob or something like that

I created a smaller secp256k1, p=43 n=31
I took point G(2, 31) for the generator point and I got the list of all valid points

Code:

G=(2,31)
2G=(7,36)
3G=(35,22)
4G=(21,25)
5G=(12,31)
6G=(29,12)
7G=(25,25)
8G=(32,3)
9G=(20,3)
10G=(42,36)
11G=(40,18)
12G=(37,7)
13G=(13,22)
14G=(34,3)
15G=(38,22)
16G=(38,21)
17G=(34,40)
18G=(13,21)
19G=(37,36)
20G=(40,25)
21G=(42,7)
22G=(20,40)
23G=(32,40)
24G=(25,18)
25G=(29,31)
26G=(12,12)
27G=(21,18)
28G=(35,21)
29G=(7,7)
30G=(2,12)

I printed this and I put it on my wall so when I work (I work from home) sometimes I look into this paper and I tried to find something interesting (interesting for me )

so this is what I found and also those rules can be applied on regular secp256k1 that Bitcoin is using...

Every Y has 3 different X values... When you calculate G of those points you always get n=31
so G=(2,31) + 5G=(12,31) + 25G=(29,31) = 31G, also for all other points 2G=(7,36) + 10G=(42,36) + 19G=(37,36) = 31G
If you change generator points those positions will remain the same so for n=31 you will always get the same Y on the same sets of points 1 5 25, 2 10 19... there are 10 sets of this points

There are negative points set with 1 5 25 and 6 26 30 (6 26 30 starting from the "end" to start" basically) When you do positive set + negative set of points those point will always return 93G or 3n

I found that if you do for one set of point X1 + X2 +X3 you sometimes get 2P and sometimes get only P I do not know why...

so on original curve where y is 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
you have 3 X
first   x: c994b69768832bcbff5e9ab39ae8d1d3763bbf1e531bed98fe51de5ee84f50fb
second   x: 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
third   x: bcace2e99da01887ab0102b696902325872844067f15e98da7bba04400b88fcb

If you do X1 + X2 + X3 in this case you will get 2P in some other cases I found that I only get 1P
Y 4218f20ae6c646b363db68605822fb14264ca8d2587fdd6fbc750d587e76a7ee

first   x: 1
second   x: 7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
third   x: 851695d49a83f8ef919bb86153cbcb16630fb68aed0a766a3ec693d68e6afa40
In this case you get only P when you do X1 + X2 + X3

I found that for symmetrical points if you do Y1+Y2 you always get P
b7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777 + 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 = p
.
.
.

Is there and useful way that we can use those points if we can calculate their G positions? I am testing bigger and bigger curves and always looking for n that number of points mod 6 = 0 (+ infinity point)
p = 937 n = 973
1G 235G 737G

So I am trying to make a connection between 1st and 2nd point for any p and any n....
If I know 1st and 2nd point I can easily calculate 3rd = n - 1st - 2nd
then I can calculate the position of other 3 points that has different Y but same 3 X

If we know the relations between those points maybe we can scan keys faster or see some periodical groups I do not know

So I am exploring this everything and I am learning a lot about bitcoin technical side and structure and also I am learning to programing at Python...

And I made like simple program where you can add dots on elliptic curve like Q+Q or Q+G and also I made G-Q, X*G and

 I made like Q:1/2 so this code will give me for 8G I will get 4G dot...

But when I did that for 3G I expected some error mistake or something because we do not have 1.5G...

So What am I doing wrong here? How I get the result for 3G... or 5G or any odd number * G

Thank you

[but I found that this is not a public key of private key 2]

So yes I did choose a topic for my college final exam. I will make a presentation about bitcoin and everything...

I know how technically the bitcoin address is generated but I just do not know how to generate a public key but just calculating with a "calculator"

So I tried to do it by myself...

I know that Sha256 1st private key 0000000...001 will give this public  key 0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C 4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
because this is the start point of G point (04 is the prefix then 64 letters are X and next 64 letters are Y)... So I understand this...

But in the case where I choose the second private key 0000000...002 I tried to do this...

I know for this multiplication so in my case number 2 is "10" binary so my multiplication will look like this

0 1*G

1 2*G

0 4*G

0 8*G

0 16*G

0 32*G

0 64*G

0 128*G

...

So I tried to do this manually (I know PHP GMP functions)

Hex to decimal "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C46 55DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8" = 6376237641841063197511976314280597438149211753541909917794154839912978489307502 705320406087313832827571435203289817719151821525032884964596839752540411064

Then I did 2G and I got
1275247528368212639502395262856119487629842350708381983558830967982595697861500 5410640812174627665655142870406579635438303643050065769929193679505080822128

Now dec to hex
F37CCCFDF3B97758AB40C52B9D0E160E0537F9B65B9C51B2B3E502B62DF02F309075B4EE4D4788C ABB49F7F81C221151FA2F68914D0AA833388FA11FF621A970
And I should add 04 on the beginning ... but I found that this is not a public key of private key 2
Correct public key is
04C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE51AE168FEA63DC 339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A

so what I did wrong?

How much money I can get if I offer the 326TH contract on sale. The contract will last until mid of December.

This is the proof that I own this account

http://prntscr.com/jkvbqq

I know PHP so I made something like Brainwallet brute force... I made it record every address that has been used then it will monitoring all founded address because maybe they will be used again in the future.

So I founded a lot of address where 0.00005460 BTCs are received and 0.00005460 BTCs are sent. That's it. Why this amount and why so many addresses

I need something like - I paste list of private keys and click "OK"

or

Browse - and I found txt file where are my private keys and then I click OK...

Hello. I want to ask does anyone have PHP function or class or something about this problem.
I want to generate valid bitcoin address from "12 words"

I want to register 1 address for each user that register on my website. Each address must be unique and Valid.

Is this even possible??? Thank you for help