Bitcoin puzzle transaction ~32 BTC prize to who solves it

[Gianluca95]

I think that there isn't any way to find a solution for this puzzle; the only thing to solve this is the strength of community. It requires many and many power of hash/sec to be solved and with maths you can't do many things.

It would be cool to use something with a speed of an ASIC, in this way you'll be able to discover keys from 66 to 76 in very easy way !

[Denis_Hitov]

Digaran @
You can't offer anything useful. An endless stream of insanity.!

Look who is talking! Why would I offer something which could help breaking ECC? I can only hint at them, but there are already resourceful people around here explaining everything in details.

I wonder, how many halving do I need to reduce a 125 bit key down to 40 bit?

You can always halve a key. However, if your key will be odd, then after halving it, you will end up in a worse situation.

Code:

SHA-256("125-bit")=c383a1ae19ff4401f72fdfbb4ffeb6fc7a38c6692b07b188edcbdc31b0160ee7
           mask125=0000000000000000000000000000000020000000000000000000000000000000
(hash%mask125)=key=000000000000000000000000000000001a38c6692b07b188edcbdc31b0160ee7
             key/2=7fffffffffffffffffffffffffffffff6a73d1a7ed2828e256cf1d5f40262814
             key-1=000000000000000000000000000000001a38c6692b07b188edcbdc31b0160ee6
         (key-1)/2=000000000000000000000000000000000d1c63349583d8c476e5ee18d80b0773

See? You can reach a key with less bits, only if you know if it is even or odd. So, if you want to go from 125-bit key to 40-bit key, then guess what: you have to know the last 85 bits.

I already know that, we don't want +n key to be odd, halving it would halve the entire -n key which is a number near 2^256, and when we reach the middle range the halving reverses. Complex stuff! 😉

digaran
If you are surprised by the doubling of the original key, then you are still at the very beginning of this "jungle". numbers
I will share with you a little bit what the future holds for you if you have the strength and inspiration to explore the Bitcoin curve.
There are amazing things that can make 100 hours of your work useless and make you happy in the most unexpected place and time of working with a curve.
There are special numbers on the curve that can be used to get exactly 1 digit less.
A third of the number you are looking for.
A quarter of the sought number.
You can get the mirror part of the number you are looking for, which can also be compared with the original.
And this is not even a 10th part of what is there.
You can get a lot.



But by carrying out various manipulations with the numbers on the curve, as vjudeu said, you can get into an even more difficult situation and get a .....................labyrinth.

I wish you success.

Mirror, quarter, third, one digit less, I'm not interested in those, I'm interested to find new ways and equations to solve a puzzle.

I live in this jungle, and I rather not pursuit shadows, they take you to dark parts of the woods.

Good luck to you too, may the help of God be with you all brothers! We can do this. 🤣

My algorithm is working, it will be smoother with a few minor adjustments. I tried with Puzzle 115 pubkey and reduced it to 2**28 bits in 2 seconds. It took 1 second for the collider application to find the pubkey. Now writing the code to reverse the Algorithm .

I don't like working, my brain is almost numb from the blood pressure pills
i can't think

I'm sorry my English is bad, I'm writing from translate, but I hope you understand what I mean.

Hello.
Could you share your algorithm?
I wonder how you managed this: "Puzzle 115 pubkey and reduced it to 2**28 bits in 2 seconds".

Sincerely,
be healthy.

[GR Sasa]

fake

[albert0bsd]

Hello.
Could you share your algorithm?
I wonder how you managed this: "Puzzle 115 pubkey and reduced it to 2**28 bits in 2 seconds".

Sincerely,
be healthy.

Don't believe in that, it is fake.

fake

Agree.

Why from 115 to 28 bits? in that case why not up to 1 bit?

Guys please don't believe in that, in any case we only need to know one bit on the right side to break ECDSA

[lordfrs]

Hello.
Could you share your algorithm?
I wonder how you managed this: "Puzzle 115 pubkey and reduced it to 2**28 bits in 2 seconds".

Sincerely,
be healthy.

Don't believe in that, it is fake.

fake

Agree.

Why from 115 to 28 bits? in that case why not up to 1 bit?

Guys please don't believe in that, in any case we only need to know one bit on the right side to break ECDSA

Private Key                                                                    Public key

1090246098153987172547740458951748   # puzzle 110   0309976ba5570966bf889196b7fdf5a0f9a1e9ab340556ec29f8bb60599616167d
545123049076993586273870229475874
272561524538496793136935114737937
136280762269248396568467557368968
68140381134624198284233778684484
34070190567312099142116889342242
17035095283656049571058444671121
8517547641828024785529222335560
4258773820914012392764611167780
2129386910457006196382305583890
1064693455228503098191152791945
532346727614251549095576395972
266173363807125774547788197986
133086681903562887273894098993
66543340951781443636947049496
33271670475890721818473524748
16635835237945360909236762374
8317917618972680454618381187
4158958809486340227309190593
2079479404743170113654595296
1039739702371585056827297648
519869851185792528413648824
259934925592896264206824412
129967462796448132103412206
64983731398224066051706103
32491865699112033025853051
16245932849556016512926525
8122966424778008256463262
4061483212389004128231631
2030741606194502064115815
1015370803097251032057907
507685401548625516028953
253842700774312758014476
126921350387156379007238
63460675193578189503619
31730337596789094751809
15865168798394547375904
7932584399197273687952
3966292199598636843976
1983146099799318421988
991573049899659210994
495786524949829605497
247893262474914802748
123946631237457401374
61973315618728700687
30986657809364350343
15493328904682175171
7746664452341087585
3873332226170543792
1936666113085271896
968333056542635948
484166528271317974
242083264135658987
121041632067829493
60520816033914746
30260408016957373
15130204008478686
7565102004239343
3782551002119671
1891275501059835
945637750529917
472818875264958
236409437632479
118204718816239
59102359408119
29551179704059
14775589852029
7387794926014
3693897463007
1846948731503
923474365751
461737182875
230868591437
115434295718
57717147859
28858573929
14429286964
7214643482
3607321741
1803660870
901830435
450915217
225457608
112728804
56364402
28182201
14091100
7045550
3522775
1761387
880693
440346
220173
110086
55043
27521
13760
6880
3440
1720
860
430
215
107
53
26
13
6
3
1  0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

[albert0bsd]

Private Key                                                                    Public key

1090246098153987172547740458951748   # puzzle 110   0309976ba5570966bf889196b7fdf5a0f9a1e9ab340556ec29f8bb60599616167d
...
1  0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

That is easy if you have the privatekey (X = X % 2 ? X/2 : (X-1)/2), but we can't do that if we don't have the privatekey, because there is no way that know if the publickey belongs to an even or odd privatekey.

But proof your self and show us.. here is a Publickey in the 110 bit range:

0301040c4e33b6ab297ba2a9c2858d15be5f6844febfc003ef7646796608f7f819

[GR Sasa]

1090246098153987172547740458951748   # puzzle 110   0309976ba5570966bf889196b7fdf5a0f9a1e9ab340556ec29f8bb60599616167d
1  0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

What is this mess? This doesn't prove anything XD

[albert0bsd]

What is this mess? This doesn't prove anything XD

Maybe he is trying to reduce the privatekey based only on the current information of the privatekey without do any calculation with the publickey.

[Evillo]

I was trying to figure out a good way to break the key search into ranges.
I decided to use columns, ie. 17 columns. And group them into 4.

group 1  2000 - 2fff
group 2  0000 - ffff
group 3  0000 - ffff
group 4  0000 - ffff
group 5  0123456789abcdef

output:    group 1 has 4096 lines
      group 2 has 65536 lines
      group 3 has 65536 lines
      group 4 has 65536 lines
      group 5 is 16 lines.
         
My idea is to create 2000 0000 0000 0000 0
But I'm still not sure how to bring them together in a string.

On linux or WSL type: paste file1.txt file2.txt > fullrange.txt

Obviously change file names in your command according to your actual file names

[digaran]

Guys I need some help over here! So here is what I have so far.

I have subtracted this from #125.
0000000000000000000000000000000010******************************
The result is :
02c473281c8531d524c1a2b92b9192ffe3e8124448e47ec306f146f2f4f35269ee

Now if I add that result to this one :
0387a3951644f3bf9ee08135bcb9a00a31ed7b09e26ff7850b83713eb6f0582920

I get this key :
000000000000000000000000000000000c******************************

Ok, now I have the distance between the green key above and #125, which is :
000000000000000000000000000000000 4******************************

So why can't I figure the correct key while I have my double triangle, 3 known keys plus 3 unknown keys?

 

[NotATether]

Guys I need some help over here! So here is what I have so far.

I have subtracted this from #125.
0000000000000000000000000000000010******************************
The result is :
02c473281c8531d524c1a2b92b9192ffe3e8124448e47ec306f146f2f4f35269ee

Now if I add that result to this one :
0387a3951644f3bf9ee08135bcb9a00a31ed7b09e26ff7850b83713eb6f0582920

I get this key :
000000000000000000000000000000000c******************************

Ok, now I have the distance between the green key above and #125, which is :
000000000000000000000000000000000 4******************************

So why can't I figure the correct key while I have my double triangle, 3 known keys plus 3 unknown keys?

Are the result and green keys public keys or private keys? Because without context, they could be either one.

[kalos15btc]

Guys I need some help over here! So here is what I have so far.

I have subtracted this from #125.
0000000000000000000000000000000010******************************
The result is :
02c473281c8531d524c1a2b92b9192ffe3e8124448e47ec306f146f2f4f35269ee

Now if I add that result to this one :
0387a3951644f3bf9ee08135bcb9a00a31ed7b09e26ff7850b83713eb6f0582920

I get this key :
000000000000000000000000000000000c******************************

Ok, now I have the distance between the green key above and #125, which is :
000000000000000000000000000000000 4******************************

So why can't I figure the correct key while I have my double triangle, 3 known keys plus 3 unknown keys?

 

i told you multiple times, to test that on any other puzzle 100 or 115 you will figure out how it works,, get the private keys of substracted puzzle 110 and you will understand bro, then test it on 125,, when you substract told you to do this  range 0:1fffffffffffffffffffffffffffffff
you will have 125 substracted maybe to 100 or even 80 bit, but you need to know where exactly you can do that -f address

[WanderingPhilospher]

Guys I need some help over here! So here is what I have so far.

I have subtracted this from #125.
0000000000000000000000000000000010******************************
The result is :
02c473281c8531d524c1a2b92b9192ffe3e8124448e47ec306f146f2f4f35269ee

Now if I add that result to this one :
0387a3951644f3bf9ee08135bcb9a00a31ed7b09e26ff7850b83713eb6f0582920

I get this key :
000000000000000000000000000000000c******************************

Ok, now I have the distance between the green key above and #125, which is :
000000000000000000000000000000000 4******************************

So why can't I figure the correct key while I have my double triangle, 3 known keys plus 3 unknown keys?

 

Lol…because you don’t have the distance between any key and #125.

You are taking a priv key and subtracting from a pub key, and then adding the resulting pub key to a pub key in which you know the priv key. But you don’t know the first pub key’s true priv key.

[NotATether]

Guys I need some help over here! So here is what I have so far.

I have subtracted this from #125.
0000000000000000000000000000000010******************************
The result is :
02c473281c8531d524c1a2b92b9192ffe3e8124448e47ec306f146f2f4f35269ee

Now if I add that result to this one :
0387a3951644f3bf9ee08135bcb9a00a31ed7b09e26ff7850b83713eb6f0582920

I get this key :
000000000000000000000000000000000c******************************

Ok, now I have the distance between the green key above and #125, which is :
000000000000000000000000000000000 4******************************

So why can't I figure the correct key while I have my double triangle, 3 known keys plus 3 unknown keys?

 

Lol…because you don’t have the distance between any key and #125.

You are taking a priv key and subtracting from a pub key, and then adding the resulting pub key to a pub key in which you know the priv key. But you don’t know the first pub key’s true priv key.

LOL, ok that makes sense. Didn't realize he was doing arithmetic on public + private keys together. That's not how it works 

[DnrUsso]

Whether there can be similar compressed and uncompressed addresses?. For example uncompressed=13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so and compressed=13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so. But of course with different compressed and uncompressed addresses

[GR Sasa]

Whether there can be similar compressed and uncompressed addresses?. For example uncompressed=13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so and compressed=13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so. But of course with different compressed and uncompressed addresses

Of course! The Address 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so can definitely be found in uncompressed and compressed form. In fact, There are estimated to be 2^96 compressed AND uncompressed addresses which match exactly the same as 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so. The question is that how you will find them. It's like trying to find a small piece of sand in the middle of the biggest oceans. Moreover even harder. It's hard to imagine, but yes there are both compressed and uncompressed that match to the puzzle's address.

In puzzle 66, the address 13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so is known to be in the compressed form.

[digaran]

Are the result and green keys public keys or private keys? Because without context, they could be either one.

You mean you don't know the difference between a public key and a private key? Why would I add or subtract a private key starting with 02 or 03 when #125 starts with 32 zeros, lol indeed.
Subtract the public key of 128 dec, from 129 dec, result is G or 1. So what is the difference between adding or subtracting private keys and public keys?
There is no magic here, you are either adding 2 keys or subtracting a smaller one from a greater key, the result is always the same.

[Andzhig]

bald chupacabras method...

for example, we take the square roots of the spaces and the keys themselves

pz65

2^64 √(18446744073709551616)    4294967296
30568377312064202855-18446744073709551616 12121633238354651239
√(12121633238354651239)         3481613596,933
2^63 √(9223372036854775808)     3037000499,976
                                       
4294967296/8                    536870912      
3481613596/8                    435201699,5    
536870912×x=3481613596          x = 6,485
3481613596/536870912                6,485

---

(4294967296/64)×x=(3481613596) x = 51,880085408687591552734375 pz 65

2^64 √(18446744073709551616) 4294967296
     √(12121633238354651239) 3481613596,933                              pz65
      12121633231852051216  3481613596×3481613596
      30568377305561602832  12121633231852051216+18446744073709551616   pz65
      30568377312064202855                                              pz65



and divide into parts, by 2, by 3, by 64, 128, 1024, 2048, 4096, etc.

we catch such a divider into parts so that there are no repetitions

for 64 and 2 table

                           0                                1
            1                                0

_______________1________________|_______________2_______________     2

_______1_______|________2_______|_______3_______|_______4_______     4
 
___1____|___2___|___3___|___4___|___5___|___6___|___7___|___8___      8

|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_          64


00000000000000000000010000000000 00000000000000000000000000000000 22  pz 12   0
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 13   1
00000000000000000000000000000000 10000000000000000000000000000000 33  pz 14   1
00000000000000000000000000000000 01000000000000000000000000000000 34  pz 15   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 16   1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 17   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 18   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 19   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 20   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 21   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 22   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 23   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 24   1
00000000000000000000000000000000 00000000000000000000000000000010 63  pz 25   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 26   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 27   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 28   1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 29   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 30   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 31   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 32   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 33   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 34   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 35   0
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 36   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 37   1
00000000000000010000000000000000 00000000000000000000000000000000 16  pz 38   0
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 39   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 40   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 41   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 42   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 43   1
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 44   1
00000000000000000000001000000000 00000000000000000000000000000000 23  pz 45   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 46   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 47   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 48   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 49   1
00000000000000000100000000000000 00000000000000000000000000000000 18  pz 50   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 51   1
00000000000000000000000000000000 00000000000000000000000000100000 59  pz 52   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 53   1
00000000000000000001000000000000 00000000000000000000000000000000 20  pz 54   0
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 55   1
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 56   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 57   1
00000000000000000000000000000000 00000010000000000000000000000000 39  pz 58   1
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 59   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 60   1
00000000000000000000000000000010 00000000000000000000000000000000 31  pz 61   0
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 62   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 63   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 64   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 65   1
                ...............x.x.x.xx..x...xx.           xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.      pz 66    
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 70   1
00000000000000000000000000000000 00000000000000000000000010000000 57  pz 75   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 80   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 85   1
00000000000000000000000000000000 00000000000000001000000000000000 49  pz 90   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 95   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 100  1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 105  1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 110  1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 115  1
                                                                                                              pz 120
                                                              xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.      pz 125


for example, at 1664 repetitions stop falling out

1664 , 1664/2 832 ,1664/64 26, 26×x=1348 x = 51,846 pz 65

                                                             pz20
[572,924,858,887,1326,1250,1131,1190,1001,1337,1418,1096,1411,1645,1315,1360,1388,1168,1599,1628,1104,1353,1336,687,804,1127,438,701,
1511,950,936,1376,1442,615,1129,1392,996,1120,486,1514,1554,1178,545,1359,793,1594,1035,1508,1637,809,1387,1621,1604,1348,992,1494,
688,1587,1286,1403,1320,1251,941,1158]

35935527204195940 ~2^54

3+3+3+1+4+1+3+4+4+2+0+2+2+4+4+2+3+2+0+0+0+2+3+4+3+1+3+4+0+1+3+1 72 , 84-72 12,

3     3    3     1    4    1     3     4    4   2      0       2      2       4   4    2     3     2       0    0     0        2       3   4     3      1      3     4      0       1     3   1  < maybe only 4 will drop out here

x     x    x      x    .     x     x     .   .    x       x       x       x       .   .    x     x        x      x      x      x       x      x     .    x      x     x     .       x      x      x   .
33   34  35    36  37   38   39  40  41  42     43     44     45     46  47  48   49     50    51     52    53     54    55   56  57    58    59    60    61    62    63  64

858 887 924  941      992 1035         1104 1120 1158 1178              1251 1286 1320 1337 1359  1403 1411 1442     1494 1508 1554       1587 1621 1645
                  936      996                 1096 1129 1168 1190              1250        1315 1348 1376  1387 1418                    1514              1604 1637
                  950     1001                        1127                                                   1336 1353  1392                           1511              1594 1628
                                                          1131                                                   1326 1360  1388                                                1599

                                                                                                                   1327                                  1482 1509 1534 1560 1586 1612 1638
                                                                                                                   1328                                  1483 1510 1535 1561 1588 1613 1639
                                                                                                                   1329                                  1484 1512 1536 1562 1589 1614 1640
                                                                                                                   1330                                  1485 1513 1537 1563 1590 1615 1641
                                                                                                                   1331                                  1486 1515 1538 1564 1591 1616 1642
                                                                                                                   1332                                  1487 1516 1539 1565 1592 1617 1643
                                                                                                                   1333                                  1488 1517 1540 1566 1593 1618 1644
                                                                                                                   1334                                  1489 1518 1541 1567 1595 1619 1646
                                                                                                                   1335                                  1490 1519 1542 1568 1596 1620 1647
                                                                                                                   1338                                  1491 1520 1543 1569 1597 1622 1648
                                                                                                                   1339                                  1492 1521 1544 1570 1598 1623 1649
                                                                                                                   1340                                  1493 1522 1545 1571 1600 1624 1650
                                                                                                                   1341                                  1495 1523 1546 1572 1601 1625 1651
                                                                                                                   1342                                  1496 1524 1547 1573 1602 1626 1652
                                                                                                                   1343                                  1497 1525 1548 1574 1603 1627 1653
                                                                                                                   1344                                  1498 1526 1549 1575 1605 1629 1654
                                                                                                                   1345                                  1499 1527 1550 1576 1606 1630 1655
                                                                                                                   1346                                  1500 1528 1551 1577 1607 1631 1656
                                                                                                                   1347                                  1501 1529 1552 1578 1608 1632 1657
                                                                                                                   1349                                  1502 1530 1553 1579 1609 1633 1658
                                                                                                                   1350                                  1503 1531 1555 1580 1610 1634 1659
                                                                                                                   1351                                  1504 1532 1556 1581 1611 1635 1660
                                                                                                                                                           1505 1533 1557 1582         1636 1661
                                                                                                                                                           1506 1558 1583                 1662
                                                                                                                                                           1507 1559 1584                 1663
                                                                                                                                                                          1585

in general, everything is slipping somewhere, meaning that taking large divisors, we look in the table for 64 where they will fall out and so we select the spaces for the search.

the main thing is that more drops out on the right side than on the left if the table is divided into 2 equal sides, those that have already fallen out will not fall out, but you need to determine where exactly they can fall out, for example, there are parts that have not yet fallen out of 64, for example 37 40 41 46 47 56 60

we take the ones that haven't dropped yet and fit our search spots to them in the next puzzles

37 40 41 46 47 56 60 for 1664/2 832

833-1664

26×x=1348 x = 51,846 pz 65

962 37  
963 37
964 37
965 37
966 37
967 37
968 37
969 37
970 37
971 37
972 37
973 37
974 37
975 37
976 37
977 37
978 37
979 37
980 37
981 37
982 37
983 37
984 37
985 37
986 37
987 37

1560 60
1561 60
1562 60
1563 60
1564 60
1565 60
1566 60
1567 60
1568 60
1569 60
1570 60
1571 60
1572 60
1573 60
1574 60
1575 60
1576 60
1577 60
1578 60
1579 60
1580 60
1581 60
1582 60
1583 60
1584 60
1585 60

etc

(√(2^19)/2048×1646)^2+2^19        862952,5
                                                 863317    
pz20 (√(2^19)/2048×1647)^2+2^19 863364,125

2048 , 2048/2 1024 ,2048/64 32 , 32×x=1660 x = 51,875 pz 65

                                                                  pz20
[704,1137,1056,1092,1632,1538,1392,1465,1232,1646,1746,1349,1737,2025,1619,1674,1708,1437,1969,2004,1359,1666,1645,846,989,1387,539,863,
1860,1169,1152,1694,1775,757,1390,1714,1226,1379,599,1864,1912,1450,671,1673,976,1962,1275,1856,2015,996,1707,1996,1974,1660,1221,1839,
847,1953,1583,1727,1625,1540,1158,1426]

and so we are looking for where nothing has fallen out at all

pz67
(√(2^66)/2^30×536870912)^2+2^66 92233720368547758080
(√(2^66)/2^30×536870913)^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^30×536870912)^2+2^67 184467440737095516160
(√(2^67)/2^30×536870913)^2+2^67 184467440874534469760
184467440874534469760-184467440737095516160 137438953600 ~2^37

pz69
(√(2^68)/2^30×536870912)^2+2^68 368934881474191032320
(√(2^68)/2^30×536870913)^2+2^68 368934881749068939520
368934881749068939520-368934881474191032320 274877907200 ~2^38


pz67
(√(2^66)/2^30×(2^30/2+0))^2+2^66 92233720368547758080
(√(2^66)/2^30×(2^30/2+1))^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^31×(2^31/2+0))^2+2^67 184467440737095516160
(√(2^67)/2^31×(2^31/2+1))^2+2^67 184467440805814992928
184467440805814992928-184467440737095516160 68719476768 ~2^36

pz69
(√(2^68)/2^32×(2^32/2+0))^2+2^68 368934881474191032320
(√(2^68)/2^32×(2^32/2+1))^2+2^68 368934881542910509072
368934881542910509072-368934881474191032320 68719476752 ~2^36


***

pz65
(√(2^64)/1664×1348)^2+2^64 30552526466155465467,455
                           30568377312064202855
(√(2^64)/1664×1349)^2+2^64 30570494229757563437,443
30570494229757563437−30552526466155465467 17967763602097970  ~2^53

pz65
(√(2^64)/2048×1660)^2+2^64 30566001039707734016
                           30568377312064202855
(√(2^64)/2048×1661)^2+2^64 30580606952171110400
30580606952171110400−30566001039707734016 14605912463376384  ~2^53


pz66
(√(2^65)/2048×1660)^2+2^65 61132002079415468032
(√(2^65)/2048×1661)^2+2^65 61161213904342220800
61161213904342220800-61132002079415468032 29211824926752768 ~2^54

pz66
(√(2^65)/1664×1348)^2+2^65 61105052932310930934,911
(√(2^65)/1664×1349)^2+2^65 61140988459515126874,887
61140988459515126874-61105052932310930934    35935527204195940 ~2^54
                                                                     18014398509481984 2^54
                                                                     36028797018963968 2^55
                                
pz66
(√(2^65)/4096×3320)^2+2^65 61132002079415468032
(√(2^65)/4096×3321)^2+2^65 61146605792855588864
61146605792855588864-61132002079415468032    14603713440120832
                                                                     18014398509481984 2^54                        

pz67                      
(√(2^66)/2048×1660)^2+2^66 122264004158830936064
(√(2^66)/2048×1661)^2+2^66 122322427808684441600
122322427808684441600-122264004158830936064    58423649853505536 ~2^56   
                                                                        36028797018963968 2^55

(√(2^66)/4096×3320)^2+2^66 122264004158830936064
(√(2^66)/4096×3321)^2+2^66 122293211585711177728
122293211585711177728-122264004158830936064    29207426880241664 ~2^54   
                                                                        36028797018963968 2^55

pz68                      
(√(2^67)/2048×1660)^2+2^67 244528008317661872128
(√(2^67)/2048×1661)^2+2^67 244644855617368883200
244644855617368883200-244528008317661872128    116847299707011072 ~2^56   
                                                                        144115188075855872 2^57
pz68                      
(√(2^67)/4096×3320)^2+2^67 244528008317661872128
(√(2^67)/4096×3321)^2+2^67 244586423171422355456
244586423171422355456-244528008317661872128   58414853760483328 ~2^56   
                                                                       144115188075855872 2^57

pz69                      
(√(2^68)/2048×1660)^2+2^68 489056016635323744256
(√(2^68)/2048×1661)^2+2^68 489289711234737766400
489289711234737766400-489056016635323744256    233694599414022144 ~2^56   
                                                                         288230376151711744  2^58
                                                                         36028797018963968     2^55

                                                                         103864266406232064       3072 48*64 ((√(2^68)/3072×1661)^2+2^68)−((√(2^68)/3072×1660)^2+2^68)
                                                                         82065593209862371,555  3456 54*64 ((√(2^68)/3456×1661)^2+2^68)−((√(2^68)/3456×1660)^2+2^68)
                                                                         58423649853505536       4096 64*64 ((√(2^68)/4096×1661)^2+2^68)−((√(2^68)/4096×1660)^2+2^68)
pz69                      
(√(2^68)/4096×3320)^2+2^68 489056016635323744256
(√(2^68)/4096×3321)^2+2^68 489172846342844710912
489172846342844710912-489056016635323744256    116829707520966656 ~2^56   
                                                                         288230376151711744 2^58

i.e. 4096/2 2048 for right side of table 64 (33-64(-1); 2049-4096) and 2048/32 64 segments of the search space of the puzzle, for 37 40 41 46 47 56 where not, fell out, coincidence.

the larger the divisor, the larger the segments for the table will be in 64, etc.

I do not know why this forum distorts the text so much, but it's tin.

[BTC_Backdoor]

Hello.
Could you share your algorithm?
I wonder how you managed this: "Puzzle 115 pubkey and reduced it to 2**28 bits in 2 seconds".

Sincerely,
be healthy.

Don't believe in that, it is fake.

fake

Agree.

Why from 115 to 28 bits? in that case why not up to 1 bit?

Guys please don't believe in that, in any case we only need to know one bit on the right side to break ECDSA

Private Key                                                                    Public key

1090246098153987172547740458951748   # puzzle 110   0309976ba5570966bf889196b7fdf5a0f9a1e9ab340556ec29f8bb60599616167d
545123049076993586273870229475874
272561524538496793136935114737937
136280762269248396568467557368968
68140381134624198284233778684484
34070190567312099142116889342242
17035095283656049571058444671121
8517547641828024785529222335560
4258773820914012392764611167780
2129386910457006196382305583890
1064693455228503098191152791945
532346727614251549095576395972
266173363807125774547788197986
133086681903562887273894098993
66543340951781443636947049496
33271670475890721818473524748
16635835237945360909236762374
8317917618972680454618381187
4158958809486340227309190593
2079479404743170113654595296
1039739702371585056827297648
519869851185792528413648824
259934925592896264206824412
129967462796448132103412206
64983731398224066051706103
32491865699112033025853051
16245932849556016512926525
8122966424778008256463262
4061483212389004128231631
2030741606194502064115815
1015370803097251032057907
507685401548625516028953
253842700774312758014476
126921350387156379007238
63460675193578189503619
31730337596789094751809
15865168798394547375904
7932584399197273687952
3966292199598636843976
1983146099799318421988
991573049899659210994
495786524949829605497
247893262474914802748
123946631237457401374
61973315618728700687
30986657809364350343
15493328904682175171
7746664452341087585
3873332226170543792
1936666113085271896
968333056542635948
484166528271317974
242083264135658987
121041632067829493
60520816033914746
30260408016957373
15130204008478686
7565102004239343
3782551002119671
1891275501059835
945637750529917
472818875264958
236409437632479
118204718816239
59102359408119
29551179704059
14775589852029
7387794926014
3693897463007
1846948731503
923474365751
461737182875
230868591437
115434295718
57717147859
28858573929
14429286964
7214643482
3607321741
1803660870
901830435
450915217
225457608
112728804
56364402
28182201
14091100
7045550
3522775
1761387
880693
440346
220173
110086
55043
27521
13760
6880
3440
1720
860
430
215
107
53
26
13
6
3
1  0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

He is just a breastfeeding baby and even haven't reached the feeder yet. He thinks he can perform division (with obvious no clue how badd_ASS division it is)

[digaran]

If the target key is not a prime number, you could find a divisor for it, it could either be an even number or an odd number, I guess nobody has ever tried it yet.😉

I'd imagine finding the correct divisor is as difficult as solving the DLP, maybe solving DLP  is exactly finding the correct divisor, I wouldn't know, because I never finished high school.🤣