Sofar, i figured out that you can divide any pub keys with infinite numbers, and still get infinite valid results which goes back to the original pub key which results in infinite amount of collisions which results in an a big blackhole loop, that will never let you escape from it.
That's why I love Math. I saw some guy describing this as POINT_AT_INFINITY which i really agree with. Very well and nice describing
Topic: Public Key Division - Number Theore (Read 830 times)
Here is what I found, I'm not a mathematician but this should work and it can bend elliptic curve or rather straighten it.
56900346571233247÷5 = 11380069314246649.4 + n/5 + n/4 = 11380069314246649, I just couldn't find any meaningful result before, but I have tried the above method and it works.
It seems we can just divide it after all, but this won't help much if private key is unknown, these things are like fire for a child when they see it for the first time.
I wanted to say a monkey when you perform a magic trick in front of him, have you seen how excited they get? Lol.
n works like zero in real numbers, n/x = n, n+x = x and so on. 56900346571233247÷5 = 11380069314246649.4 + n/5 + n/4 = 11380069314246649, I just couldn't find any meaningful result before, but I have tried the above method and it works.
It seems we can just divide it after all, but this won't help much if private key is unknown, these things are like fire for a child when they see it for the first time.
I wanted to say a monkey when you perform a magic trick in front of him, have you seen how excited they get? Lol.
Quote
56900346571233247÷5 = 11380069314246649.4 + n/5 + n/4 = 11380069314246649, I just couldn't find any meaningful result before, but I have tried the above method and it works.
O, f,it is really work ??
Quote
Here is a problem I'm facing, it seems really easy to figure out, but I can't.
Because there is no solution. You can always divide by 5. In 20% cases, you will reach smaller key, in 80% some bigger one, just because every fifth number is divisible by 5. You can always divide by any number in range from 1 to n-1. Always.You can clearly see that when trying to reach 1/2. In real numbers, it is some value between zero and one. But in ECDSA world, it could be for example 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1. You won't get any error, like "this division is impossible". It will never be rounded down to zero, or rounded up to one.
Division, exactly in the same way as multiplication, is always possible for all numbers from 1 to n-1. If you explore it on some smaller values, for example n=67 from my avatar, then you can clearly see that. You will rotate like in a clock, always getting "some" result, and never getting to the point of "no answer". And this is the beauty of the finite field, this is what makes it strong, and when you understand it, you will see, why you cannot "just divide it".
56900346571233247÷5 = 11380069314246649.4 + n/5 + n/4 = 11380069314246649, I just couldn't find any meaningful result before, but I have tried the above method and it works.
It seems we can just divide it after all, but this won't help much if private key is unknown, these things are like fire for a child when they see it for the first time.
I wanted to say a monkey when you perform a magic trick in front of him, have you seen how excited they get? Lol.
Theoretically, if we could find a big number that by dividing it to the public key resulting in an exact number, we could solve the private key from public key.
But that's way too hard i guess, it's like guessing a whole 254-255 bits..
But that's way too hard i guess, it's like guessing a whole 254-255 bits..
Quote
Here is a problem I'm facing, it seems really easy to figure out, but I can't.
Because there is no solution. You can always divide by 5. In 20% cases, you will reach smaller key, in 80% some bigger one, just because every fifth number is divisible by 5. You can always divide by any number in range from 1 to n-1. Always.You can clearly see that when trying to reach 1/2. In real numbers, it is some value between zero and one. But in ECDSA world, it could be for example 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1. You won't get any error, like "this division is impossible". It will never be rounded down to zero, or rounded up to one.
Division, exactly in the same way as multiplication, is always possible for all numbers from 1 to n-1. If you explore it on some smaller values, for example n=67 from my avatar, then you can clearly see that. You will rotate like in a clock, always getting "some" result, and never getting to the point of "no answer". And this is the beauty of the finite field, this is what makes it strong, and when you understand it, you will see, why you cannot "just divide it".
obviously, if some private key is not divisible by 5, then you won't reach smaller key, you could get some bigger one as well. However, all ECDSA equations will be preserved in a given modulo.
I have this key :
Code:
02228c3cbe2d11af48c3b98bc2955cd2c293375f748e9aea9040ffba42c3f6be1e
Code:
0000000000000000000000000000000000000400000000000000000000000000
Code:
0352a1087d5f64b39c33d54e02f678c50955770b736e2c7c646d0ee04e28fc83e7
Now here is another key :
Code:
038840d5318a6369971b6610cbef8a7cb998d8e106534881da28aabfefeec2f41b
If we subtract the above from this one :
Code:
0000000000000000000000000000000000000080000000000000000000000000
Code:
037f32d1fbba6ec4ed91109538ea93afc9bb4f13e3052d319263c7bb05fcb109a7
Do you think there is a way to find any of the public keys above?
Quote
I tried inversion and it doesn't work
It has to work. Let's test it on some key, where none of us knows the private key:Code:
03 678AFDB0FE5548271967F1A67130B7105CD6A828E03909A67962E0EA1F61DEB6 Satoshi
02 2959350037EACA04CF26538AECA4402432BC2DEC271496446A326B22B7E08742 Satoshi/5=first
02 E8C7430A125F8FDA5B3AEA1C2C6CF7E404EE902B7150FE18CE397F2B4759AEC8 (Satoshi/5)*2
03 E1A4232B81AEA764680A74DC0F6CF58B26CB61048F0F70923DFD2F199B3C986C ((Satoshi/5)*2)*2=second
03 678AFDB0FE5548271967F1A67130B7105CD6A828E03909A67962E0EA1F61DEB6 first+second
Quote
if you divide +n odd key by 5 and then add n/5 to the result, you won't get near the 1/5 of your +n key.
Well, let's see that on some private keys:Code:
SHA-256("garlonicon")=272fc6644fedff1a897d6034bed23f61859e99440ee699033307976590316723
272fc6644fedff1a897d6034bed23f61859e99440ee699033307976590316723 d
a16ff47a7662cc9ee84c4670f2f6d97924556ffe6c267ebe16e623cf335da22e d/5=first
42dfe8f4ecc5993dd0988ce1e5edb2f38dfc031629045d406df9e9119685031b (d/5)*2
85bfd1e9d98b327ba13119c3cbdb65e71bf8062c5208ba80dbf3d2232d0a0636 ((d/5)*2)*2=second
272fc6644fedff1a897d6034bed23f61859e99440ee699033307976590316723 first+secondJust use inversion:
I tried inversion and it doesn't work, if you divide +n odd key by 5 and then add n/5 to the result, you won't get near the 1/5 of your +n key. Code:
n=fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1
-n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
n/4=bfffffffffffffffffffffffffffffff0c0325ad0376782ccfddc6e99c28b0f1
n/5=66666666666666666666666666666665e445f1f5dfb6a67e4cba8c385348e6e7
n/6=d5555555555555555555555555555554463c62c03cbc85871fd9f975582d3661
I always use inversion and I'd never divide by anything other than n/2.
By the way, last time you messed up 1/2 with -1/2
I might have, but I don't recall, as I said I'm like a student learning here.😉
Thanks for nice answers everyone,
Yes, though I thought i was smart and decided to try to keep dividing public key by 2 to the lowest point reaching base point but I Failed Everytime haha.
I think the only way is to guess ODD VS EVEN but that's impossible since private keys are random numbers.
I think it's like guessing 0 or 1 256 times, since there are 5 odd numbers and 5 even numbers in each new value. So the complexity stays the same as before.
Unless of course someone finds a way to know Odd private keys from EVEN, then he can divide by exact reaching his targeting key.
I like your examples guys!
Yes, though I thought i was smart and decided to try to keep dividing public key by 2 to the lowest point reaching base point but I Failed Everytime haha.
I think the only way is to guess ODD VS EVEN but that's impossible since private keys are random numbers.
I think it's like guessing 0 or 1 256 times, since there are 5 odd numbers and 5 even numbers in each new value. So the complexity stays the same as before.
Unless of course someone finds a way to know Odd private keys from EVEN, then he can divide by exact reaching his targeting key.
I like your examples guys!
Quote
The result is not random at all, did you even read my first post and other posts?
Random in, random out. Unknown in, unknown out. Infinity in, infinity out. It is that simple. If you divide some public key, where you don't know the private key, the result is totally random from your perspective. It may be non-random for the key owner, but not for the attacker.Quote
I have tried 4, 5, 6 etc, I couldn't get any meaningful result, I'm still learning.
Just use inversion:Code:
n=fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1
-n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
n/4=bfffffffffffffffffffffffffffffff0c0325ad0376782ccfddc6e99c28b0f1
n/5=66666666666666666666666666666665e445f1f5dfb6a67e4cba8c385348e6e7
n/6=d5555555555555555555555555555554463c62c03cbc85871fd9f975582d3661
By the way, last time you messed up 1/2 with -1/2. This is a common mistake, been there, done that. If you learn more about inversion, you will know why. And if you want a proof, then halve a point using your method, and then double it. If you reach points, where 02 and 03 prefixes are inverted, you will understand, why you need inversion, instead of relying just on standard division, provided by any BigInteger implementation.n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1
-n/2=7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
n/4=bfffffffffffffffffffffffffffffff0c0325ad0376782ccfddc6e99c28b0f1
n/5=66666666666666666666666666666665e445f1f5dfb6a67e4cba8c385348e6e7
n/6=d5555555555555555555555555555554463c62c03cbc85871fd9f975582d3661
Quote
Furthermore, there are ways to accurately divide your key by 2 without any division, but that rock is really big and I'm afraid the glass will shatter
This problem is called "discrete logarithm", that's why you have DL letters in ECDLP. You can always divide a number by two, and finally reach the base point. The problem is: if you try to halve some point in a loop, you will visit a significant portion of the elliptic curve, I guess something above 2^250, maybe n/6 or something like that. So, don't run brute force on that, because you will never reach that answer in any reasonable time. Does dividing a public key by a non division number really result in a random unknown point in the curve? Why is that though? For me, this makes no sense : 
The result is not random at all, did you even read my first post and other posts? Let me give you a solution in order to successfully divide an odd key by 2, I have tried 4, 5, 6 etc, I couldn't get any meaningful result, I'm still learning.
Now the example, you could either add 1 or subtract 1 from your odd private (public key) key and then divide by 2 or you could simply divide the odd key by 2 add n/2 to the result, you will get the same result.
If your key is divisible by 2, 4, 8 etc but the last digit is 1, you could reach key 0x3 by dividing by 2 adding n/2 and dividing the result again by 2 adding n/2 till you reach the lowest point.
Demonstration :
Private key :
Code:
0000000000000000000000000000000000000000000000000000000000008001
Public key :Code:
03a3dd9bdf806a8c86fa43fd7c8af5fe3949b9244d46cfdf42aa716e3168f8e67b
Divided by 2, result:Code:
024d2432b7f67a3b25fe7f6a52164f1bf0235d3f6ce00569f4fc954b823c7c7607
Adding n/2 to above N/2 =
Code:
7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
Result, private key :
Code:
0000000000000000000000000000000000000000000000000000000000004001
Result, public key :Code:
03d7ec238cd058837f44315fb8db2134f01daea15c10320c9173e7d5f68ff2d9d0
And if you keep dividing you will eventually reach 0x3, dividing 3 by 2 will give you 0x2 then 1, and dividing 1 by 2 will give you half, aka n/2 and take a look at 0.5 = n/2, it is a number around 2^255.
Now to simplify it, imagine you have 23 as your odd key, dividing by 2 adding n/2 will give you 12, it's like adding 1 to 23 = 24/2 = 12. You have 2 options.
Furthermore, there are ways to accurately divide your key by 2 without any division, but that rock is really big and I'm afraid the glass will shatter, you should start with small rocks, learn from Musk throwing a big rock at E-truck's window claiming it won't shatter. Lol
Quote
Does dividing a public key by a non division number really result in a random unknown point in the curve?
Yes, of course. For that reason, ECDSA is secure, and simple tricks like "let's divide it" won't work.Quote
Why is that though?
Because we are in finite field. And the beauty of finite fields is that they are, well, finite.Quote
For me, this makes no sense
It makes perfect sense, if you know, how things are calculated.In real numbers, you have things like sqrt(8). In finite fields, you have for example 18.
Code:
18*18=324
324=79*4+8
324 modulo 79=8
See? In finite fields, you can have "18" as a result of "sqrt(8)", and it is perfectly valid, because "18*18" gives you "8" in this field. 324=79*4+8
324 modulo 79=8
Does dividing a public key by a non division number really result in a random unknown point in the curve? Why is that though? For me, this makes no sense :
@digaran i didn't understand anything you wrote here, but could you please help me at least compile the ecctools that Alberto wrote? I will be greatful
I believe there is a makefile for the ecctools at the top level of the repository.
Then again, it's been some time since I last checked it so it's possible that you compile the programs by running GCC directly. Each (?) of the programs are self-contained in a single file.
I have thought about this topic.
We ( I hope) we no need check all subranges.
here my experiment. at the moment without explanation. ok? will do later.
but for setup :
- target pubkey
- control pubkey
We ( I hope) we no need check all subranges.
here my experiment. at the moment without explanation. ok? will do later.
but for setup :
- target pubkey
- control pubkey
Code:
private1 10101010101010
private2 20101050101010
0 81054462466121336796499689506081535496986294995352433067823614199163723147046 81054462466121336796499689506081535496986294995352433067823614199263723547046
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28 diferential -90060513851245929773888543895646150552206994439280481186470682443264125051151 25731575386070265649682441113041757300630569839794423196134480698254036443186
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36 diferential 156250625000 156250625000
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88 diferential 38597363079105398474523661669562635950945854759691634794201721048006057164779 38597363079105398474523661669562635950945854759691634794201721048006057164779
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private2 20101050101010
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0 diferential 100000400000 100000400000
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11 diferential 112360000000 112360000000
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36 diferential 156250625000 156250625000
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45 105265535670287450385064531826079916229852331162795367620550148310654710633052 31579660701086235115519359547823974868955699348838610286165044493506790409383
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47 48064640815489741496576635286625169297404271964899016913534218662707557792008 48064640815489741496576635286625169297404271964899016913534218662896237792008
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I guess I was speaking arabic right? 😅 that is math right there, follow up on it to get some where.
About compiling, I'm the worst person to ask, because I have the same problem as you, when I for example open visual studio it's like an alien world to me. In case you didn't know, I used WP's ready to use for windows tools.
Nono, you werent speaking arabic. You just explain a lot of good things but the way you explain them, nobody but einstein could understand it.
Your examples are good, but as i said the way you explain things are catastrophic.
Thank you for nothing. We probably need help of Wandering around the jungle, i think he is the only and other few who can compile codes. I asked him but unfortunately he ignored me
@digaran i didn't understand anything you wrote here, but could you please help me at least compile the ecctools that Alberto wrote? I will be greatful
I want to do some mathematics, maybe i can get near to #130
I guess I was speaking arabic right? 😅 that is math right there, follow up on it to get some where.I want to do some mathematics, maybe i can get near to #130
About compiling, I'm the worst person to ask, because I have the same problem as you, when I for example open visual studio it's like an alien world to me. In case you didn't know, I used WP's ready to use for windows tools.
@digaran i didn't understand anything you wrote here, but could you please help me at least compile the ecctools that Alberto wrote? I will be greatful
I want to do some mathematics, maybe i can get near to #130
I want to do some mathematics, maybe i can get near to #130
So no, key division does not decrease search time.
Hmm, i dont know if i agree with this statement. When you create 1 million key with the help of subtracting the public key, You have like created a million clones of the targeted public key, and with that, you increase the chance. When you find 1 of the 1 million pubkey, you get back to the original key. So the chances is higher. And so is very similar to dividing.
And if you are dealing with prime numbers, look at N of secp256k1, if you just subtract 1 from it you can divide it by dozens of already known divisor numbers.
@digaran, you are fucking smart with coming up with this idea, but it still wont help us a lot finding the targeted priviate key.
Teach me more tips like that though!
I'm the last person you'd want to teach you something, I just share what I know, they might be incorrect sometimes.
What you need to know about public keys, ignore their size and char length, it's all smoke and mirrors, they are simply representations of private keys, and private keys are simply ordinary numbers but very big ones.
Hexadecimal keys can make our work easier, for instance, if you have a large number like 3637343230303931363537383831353435
By the time you can figure out how to extract a certain number out of that, you'd be spending a few minutes, but if you convert to hex you will get this
b355b9d94ef43E58a7f80fe3b85b
And in seconds I can select my target and then by guess work I'd take b as my first char assuming we know the first char is b, so I'd go with b000000000000E00000000000000 then I subtract from target to get
355b9d94ef43058a7f80fe3b85b
Then I go with this
bffffffffffffeffffffffffffff subtracting target from it to reach
caa4626b10bc0a75807f01c47a4 and then I add the last result to this + 355b9d94ef43058a7f80fe3b85b to reach =
ffffffffffff0ffffffffffffff
And just like that I now know the E I guessed is really there otherwise I'd see something else instead of 0 in the middle of fs = ffffffffffff0ffffffffffffff . 😉
Fun fact, 99% of times when I share something I know with others, I learn something new then and later on, this is why we need to share our knowledge, we gain more than we already have by sharing.
So no, key division does not decrease search time.
And if you are dealing with prime numbers, look at N of secp256k1, if you just subtract 1 from it you can divide it by dozens of already known divisor numbers.
Hmm, i dont know if i agree with this statement. When you create 1 million key with the help of subtracting the public key, You have like created a million clones of the targeted public key, and with that, you increase the chance. When you find 1 of the 1 million pubkey, you get back to the original key. So the chances is higher. And so is very similar to dividing.
@digaran, you are fucking smart with coming up with this idea, but it still wont help us a lot finding the targeted priviate key.
Teach me more tips like that though!
So no, key division does not decrease search time.
Thanks for your answer,
Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also. And what if a PubKey is a prime? Lol then, there is no way to divide it, correct?
Since you don't know anything about the private key, the easiest way is to guess the last digit and if it's even, at least you can divide by 2 for sure.Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also. And what if a PubKey is a prime? Lol then, there is no way to divide it, correct?
And if you are dealing with prime numbers, look at N of secp256k1, if you just subtract 1 from it you can divide it by dozens of already known divisor numbers.
Anyways for now the puzzle #125 has been solved, it's time to focus on the next one #130, we'd either find it or die trying, right? 🤣
Thanks for answer everyone,
After doing researches, I found a decent ecctools that does public key math made and developed by Alberto
https://github.com/albertobsd/ecctools
However, it's made for ubuntu, and i have Windows operating system. Can anyone help me compile the tools for windows?
I'll be grateful
Thanks
After doing researches, I found a decent ecctools that does public key math made and developed by Alberto
https://github.com/albertobsd/ecctools
However, it's made for ubuntu, and i have Windows operating system. Can anyone help me compile the tools for windows?
I'll be grateful
Thanks
Use MinGW software to create a Unix build environment in Windows, and run it from there. It doesn't have any external dependencies.
Thanks for your answer,
Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also.
Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also.
It's like having a spectrum of a numerical range that extremes from 0 to your maximum value 2^N.
0 |----------------| 2^N
Division cuts that spectrum into two lengths, so that there are 2^(N-M) keys remaining on the left, and then on the right there are 2^M possible remainders there may be that should be tried for each of the keys on the left.
2^(M-N)
0 |-----------|----| 2^N
Since reminders have to be tried for all remaining keys, the total search space is these two values multiplied together: 2^M * 2^(N-M) = 2^(M+N-M) = 2^N. Exactly the same range as before.
So no, key division does not decrease search time.
Thanks for answer everyone,
After doing researches, I found a decent ecctools that does public key math made and developed by Alberto
https://github.com/albertobsd/ecctools
However, it's made for ubuntu, and i have Windows operating system. Can anyone help me compile the tools for windows?
I'll be grateful
Thanks
After doing researches, I found a decent ecctools that does public key math made and developed by Alberto
https://github.com/albertobsd/ecctools
However, it's made for ubuntu, and i have Windows operating system. Can anyone help me compile the tools for windows?
I'll be grateful
Thanks
Quote
Wouldn't it possible to reduce 120 bits to 100 bits?
You can generate 2^20 keys, based on some 120-bit key, and then one of them will have only 100 bits. But you won't know which one, and you will have to check all of them, so it won't solve anything.
Wouldn't it possible to reduce 120 bits to 100 bits?
For the targeted public key below: 0233709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
For the targeted public key below: 0233709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
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Why do you divide by 2 though?
You can multiply or divide by any number, it doesn't matter.Quote
Why not like 1000 or any larger number? (for more reducing).
You won't reduce anything by using division. You are in a finite field, so you can always divide your key by any number, and you will always reach a valid result. If you have 1234 as your key, and divide it by 1000, you will get "1.234" key, so you will end up in fractions, just they will be expressed as large, 256-bit numbers.Quote
And what if a PubKey is a prime?
It doesn't matter. You can divide a key equal to 31337 by 127, and then you will just get a fraction 31337/127, expressed as some 256-bit number.Quote
Lol then, there is no way to divide it, correct?
For each and every key, you can multiply or divide it by any other key, in the whole range from 1 to N-1, and you will always get some valid key as a result.
Thanks for your answer,
Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also. And what if a PubKey is a prime? Lol then, there is no way to divide it, correct?
Why do you divide by 2 though? Why not like 1000 or any larger number? (for more reducing). Seems dividing is just as complicated as bruteforcing a whole key. It can reduce range, but it can mess it up also. And what if a PubKey is a prime? Lol then, there is no way to divide it, correct?
Multiply your public key by this key
7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
Key above is N/2, or 0.5 and if you for example multiply 4 by 0.5 you'd get 2, this is a simple operation.
There is also a java calculator on github, https://github.com/MrMaxweII/Secp256k1-Calculator
You can put public key and select division then put 2 and divide or any other number you like.
About dividing you should know, every single even public key has an odd pair we call it inverse key, aka 02 and 03.
If the pub key starts with 02 and it's private key ends with 1, 3, 5, 7, 9 the inverse key must end with 2, 4, 6, 8, 0.
Now let us practice :
Our target pub key :
03f42cde25a364c9764a4c60f762337c0a1a9d27805c89b59bc845e18a93db4ac9
It's private key :
00000000000000000000000000000000000000002880422a1ab3e513482869b2
Decimal ( 12534455350639729112533985714 ) ends with 4 so it is even.
Inverse pub key :
02f42cde25a364c9764a4c60f762337c0a1a9d27805c89b59bc845e18a93db4ac9
It's private key :
fffffffffffffffffffffffffffffffebaaedce686c85e11a51e7979880dd78f
Decimal ( 115792089237316195423570985008687907852837564279062369927254523412405627508623 ) ends with 3 so it is odd.
Now it doesn't matter which one of the pub keys you are dividing, it will divide the even one because there is no fraction in ECC.
If we divide our target pub by 2 we will see :
0312d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Private key :
0000000000000000000000000000000000000000144021150d59f289a41434d9
Decimal ( 6267227675319864556266992857 )
Inverse pub :
0212d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Private key :
fffffffffffffffffffffffffffffffebaaedce69b087f26b2786c032c220c68
Decimal ( 115792089237316195423570985008687907852837564279068637154929843276961894501480 )
Then if you try to divide this
0312d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Or the -n aka 02 version of it, doesn't matter which one since both will give you the same result which is :
0222db101c46b9d0f52e30f1be2565c67a9e75d3104fda0b75fcbec3fae320b88d
Private key :
7fffffffffffffffffffffffffffffff5d576e734d843f93593c360196110634
Decimal ( 57896044618658097711785492504343953926418782139534318577464921638480947250740 )
Inverse key :
0322db101c46b9d0f52e30f1be2565c67a9e75d3104fda0b75fcbec3fae320b88d
Private key :
7fffffffffffffffffffffffffffffff5d576e7361c460a86696288b3a253b0d
Decimal ( 57896044618658097711785492504343953926418782139540585805140241503037214243597 )
So, tell me, are we close to our target or did we just distanced ourselves from target by 2^255 difference? If you had more questions, happy to answer if I know the answer.😉
7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0
Key above is N/2, or 0.5 and if you for example multiply 4 by 0.5 you'd get 2, this is a simple operation.
There is also a java calculator on github, https://github.com/MrMaxweII/Secp256k1-Calculator
You can put public key and select division then put 2 and divide or any other number you like.
About dividing you should know, every single even public key has an odd pair we call it inverse key, aka 02 and 03.
If the pub key starts with 02 and it's private key ends with 1, 3, 5, 7, 9 the inverse key must end with 2, 4, 6, 8, 0.
Now let us practice :
Our target pub key :
03f42cde25a364c9764a4c60f762337c0a1a9d27805c89b59bc845e18a93db4ac9
It's private key :
00000000000000000000000000000000000000002880422a1ab3e513482869b2
Decimal ( 12534455350639729112533985714 ) ends with 4 so it is even.
Inverse pub key :
02f42cde25a364c9764a4c60f762337c0a1a9d27805c89b59bc845e18a93db4ac9
It's private key :
fffffffffffffffffffffffffffffffebaaedce686c85e11a51e7979880dd78f
Decimal ( 115792089237316195423570985008687907852837564279062369927254523412405627508623 ) ends with 3 so it is odd.
Now it doesn't matter which one of the pub keys you are dividing, it will divide the even one because there is no fraction in ECC.
If we divide our target pub by 2 we will see :
0312d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Private key :
0000000000000000000000000000000000000000144021150d59f289a41434d9
Decimal ( 6267227675319864556266992857 )
Inverse pub :
0212d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Private key :
fffffffffffffffffffffffffffffffebaaedce69b087f26b2786c032c220c68
Decimal ( 115792089237316195423570985008687907852837564279068637154929843276961894501480 )
Then if you try to divide this
0312d8734901f0f88e3b396c4fa66454543cd8837bbb31ea177cc19b99a8a79ed1
Or the -n aka 02 version of it, doesn't matter which one since both will give you the same result which is :
0222db101c46b9d0f52e30f1be2565c67a9e75d3104fda0b75fcbec3fae320b88d
Private key :
7fffffffffffffffffffffffffffffff5d576e734d843f93593c360196110634
Decimal ( 57896044618658097711785492504343953926418782139534318577464921638480947250740 )
Inverse key :
0322db101c46b9d0f52e30f1be2565c67a9e75d3104fda0b75fcbec3fae320b88d
Private key :
7fffffffffffffffffffffffffffffff5d576e7361c460a86696288b3a253b0d
Decimal ( 57896044618658097711785492504343953926418782139540585805140241503037214243597 )
So, tell me, are we close to our target or did we just distanced ourselves from target by 2^255 difference? If you had more questions, happy to answer if I know the answer.😉
Hi,
We all (hopefully) have heard about the current ongoing-puzzle that was recently increased its prize by 10x and which is still not all solved for long time.
Since I'm very interesting in math and dealing with big numbers, I would love to get to learn about dividing public keys. I will mainly focus for the next possible puzzle (#125) which has its public key revealed.
Puzzle #125:
Since public key for puzzle #125 is revealed, we can do many things with it so we can try to slightly reduce the targeted range by XXX amount.
I already know Addition, Subtraction, and striding public keys, but weirdly i haven't managed to know how to divide public keys in the correct way.
Can you help me give me an detailed example of dividing public key into lower ranges, and if possible which tools is needed for the process?
What could be the advantages and disadvantages of dividing public keys? Is it a problem if the divided public key has a decimal in it? I think if i understood correctly, the newly divided keys could be invalid and could lead to infinity if its wrongly divided (Correct me, if I'm wrong).
Thanks to all, and Goodluck hunting!
We all (hopefully) have heard about the current ongoing-puzzle that was recently increased its prize by 10x and which is still not all solved for long time.
Since I'm very interesting in math and dealing with big numbers, I would love to get to learn about dividing public keys. I will mainly focus for the next possible puzzle (#125) which has its public key revealed.
Puzzle #125:
Code:
0233709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
Since public key for puzzle #125 is revealed, we can do many things with it so we can try to slightly reduce the targeted range by XXX amount.
I already know Addition, Subtraction, and striding public keys, but weirdly i haven't managed to know how to divide public keys in the correct way.
Can you help me give me an detailed example of dividing public key into lower ranges, and if possible which tools is needed for the process?
What could be the advantages and disadvantages of dividing public keys? Is it a problem if the divided public key has a decimal in it? I think if i understood correctly, the newly divided keys could be invalid and could lead to infinity if its wrongly divided (Correct me, if I'm wrong).
Thanks to all, and Goodluck hunting!
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