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Topic: Pollard's kangaroo ECDLP solver - page 75. (Read 60189 times)

jr. member
Activity: 114
Merit: 5
February 18, 2021, 01:57:16 AM
Here is a list of all known public keys in the top 10,000 addresses that I scraped with a python script and blockchain.com's API, each address has at least $10 million worth of bitcoin. Knock yourselves out!

*Edit: here is the API for getting the public key from an address if it is known: https://www.blockchain.com/api/q/pubkeyaddr/{ADDRESS}

PART 1:
Code:
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legendary
Activity: 1568
Merit: 6660
bitcoincleanup.com / bitmixlist.org
February 14, 2021, 02:49:15 PM
...
Pls help me if we can get public key from p2sh or bech addresses. I'll run on 1st richest wallet.

First of all you are better off not using this for random addresses that have a lot of money, because their difficulty is ASTRONOMICALLY GREATER (you probably don't need a lecture about this) than an address with specialized information about it like the puzzle transaction.

As for getting public keys associated with the addresses, this is only possible if there is at least one transaction associated with the address, which'll always be the cease if you're talking about funded addresses. Use blockchain.info to find a transaction involving the address you want to run Kangaroo on, then copy the transaction ID and paste it into blockstream.info, select the "Details" button, and under the address there will be a bunch of of information at "scriptsig (asm)", where you will find the public key there.

We need two block explorers to accomplish this because Blockchain doesn't show public keys, and Blockstream can't search by address.


Don't bother trying to brute force this, it's in a hot wallet that was included in the block mined just now. It'll definitely move somewhere else later.

That red underlined hex number is the public key for the address that Blockstream's block explorer shows.
newbie
Activity: 18
Merit: 1
February 14, 2021, 02:07:24 PM
Broke - Running kangaroo on 120th puzzle transaction with 2^119 search space and get 1.2 BTC

Woke - Running kangaroo on 5th richest BTC address with 2^256 search space and get >84,000 BTC


Pls help me if we can get public key from p2sh or bech addresses. I'll run on 1st richest wallet. If he universe wants me to have those, I'll get those. Only if we are living in a simulation...
legendary
Activity: 1568
Merit: 6660
bitcoincleanup.com / bitmixlist.org
February 12, 2021, 11:28:04 PM
I know its been a month since this was posted, but this couldn't be taking in consideration for kangaroo?

AFAIK, it's already built in by virtue of the algorithm always hopping to valid points.

Since the invalid points derived for each X and Y don't overlap, we have already removed 1/2 * 2/3 = 1/3 of the total possible search space like that.

No, because all the tame and the wild move directly (jump) between the points (with valid coordinates); the points are about 2^256:

(1/2 * 2^256 X coordinates) * (2 valid Y coordinates) = 2^256 points.

However even though we only look at half the private keys with an X coordinate, since we also look at their two Y coordinates this doesn't decrease how many points we're searching at all (still 2^256).
full member
Activity: 706
Merit: 111
February 12, 2021, 02:27:08 PM
For the really smart people out there...I had read somewhere that a pubkey may have 2 X coordinates, maybe 3 X coordinates, can't really remember.

Each pubkey has only 1 X coordinate and 1 Y coordinate. And only 1 private key.

There are 2 pubkeys that share the same X coordinate (for each valid X coordinate) but they have different Y coordinates:

if A = (X,Y) then  B = -A = (X, p-Y)

(p =  2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1)


There are 3 pubkeys that share the same Y coordinate (for each valid Y coordinate) but they have different X coordinates:

if A = (X,Y) then B = k*A = (beta*X, Y) and C = k*k*A = (beta*beta*X, Y)

(k = 0x5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72  
and  beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee)

There are about 2^256 points on secp256k1, (to be precise n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141) and Fp (the field of the coordinates X e Y) has about the same size;

that means that about 1/3 of the all possible values of Y are valid Y coordinates (are coordinates of a point/pub key) and about 1/2 of all the possible values of X are valid X coordinates.

That's all.

that means that about 1/3 of the all possible values of Y are valid Y coordinates (are coordinates of a point/pub key) and about 1/2 of all the possible values of X are valid X coordinates.

Maybe we can use that as an optimization and go through all the X values, and check that (X2 + 7) mod p gives a cubed number which would imply a valid Y. This would eliminate half of the search space. Similarly we can go through all the Y values and calculate Y3 mod p is a square number which implies a valid X and eliminate 2/3s of the search space.

Since the invalid points derived for each X and Y don't overlap, we have already removed 1/2 * 2/3 = 1/3 of the total possible search space like that.

I know its been a month since this was posted, but this couldn't be taking in consideration for kangaroo?
full member
Activity: 1232
Merit: 242
Shooters Shoot...
February 11, 2021, 01:18:01 PM
i am using gtx 970 gpu and win 10. how can i use kangaroo? can anybody instruct me? i downloded kangaroo.exe but i dont know how to use it. thank you in advance

Simplest way:

Setup your input file; line 1 is start range, line 2 is end range, line 3 is public key you are searching for:
Example input file (we will call it input.txt):
Code:
1
FFFFFFFFFFFFFFFFFF
038DB9A3FC1A4A4721A8F79F5A38DA2379D352CA0666554B0E401C33BD4A3DB123

Now, set up batch file (we will call it KangarooStart.bat):
Code:
Kangaroo -t 3 -d 12 -gpu -gpuId 0 -o results.txt input.txt
This is where you tell the program what you want. Kangaroo is the name of the program (.exe file) -t how many cpu threads you want to use -d the number of distinguished points (in bits) you want to search for - gpu lets it know you want to use a gpu, -gpuId is the device number of the gpu you want to use (if you only have one gpu, you can leave out this option) -o is where you want the results to be stored once program finds the key, and the last entry in batch file is the input file we created above (start and end range and public key).

thank you very much for the information. i have one more question, i want to use it in puzzle 64 how can i find publickey?
You cannot find the public key for #64, it has not been exposed in a transaction therefore the Kangaroo program will not help you find #64. You have to look at the ones with known public keys, #120, #125....(incremented by 5) through #160
jr. member
Activity: 102
Merit: 6
February 11, 2021, 12:35:30 PM
i am using gtx 970 gpu and win 10. how can i use kangaroo? can anybody instruct me? i downloded kangaroo.exe but i dont know how to use it. thank you in advance

Simplest way:

Setup your input file; line 1 is start range, line 2 is end range, line 3 is public key you are searching for:
Example input file (we will call it input.txt):
Code:
1
FFFFFFFFFFFFFFFFFF
038DB9A3FC1A4A4721A8F79F5A38DA2379D352CA0666554B0E401C33BD4A3DB123

Now, set up batch file (we will call it KangarooStart.bat):
Code:
Kangaroo -t 3 -d 12 -gpu -gpuId 0 -o results.txt input.txt
This is where you tell the program what you want. Kangaroo is the name of the program (.exe file) -t how many cpu threads you want to use -d the number of distinguished points (in bits) you want to search for - gpu lets it know you want to use a gpu, -gpuId is the device number of the gpu you want to use (if you only have one gpu, you can leave out this option) -o is where you want the results to be stored once program finds the key, and the last entry in batch file is the input file we created above (start and end range and public key).

thank you very much for the information. i have one more question, i want to use it in puzzle 64 how can i find publickey?
full member
Activity: 1232
Merit: 242
Shooters Shoot...
February 11, 2021, 12:24:56 PM
i am using gtx 970 gpu and win 10. how can i use kangaroo? can anybody instruct me? i downloded kangaroo.exe but i dont know how to use it. thank you in advance

Simplest way:

Setup your input file; line 1 is start range, line 2 is end range, line 3 is public key you are searching for:
Example input file (we will call it input.txt):
Code:
1
FFFFFFFFFFFFFFFFFF
038DB9A3FC1A4A4721A8F79F5A38DA2379D352CA0666554B0E401C33BD4A3DB123

Now, set up batch file (we will call it KangarooStart.bat):
Code:
Kangaroo -t 3 -d 12 -gpu -gpuId 0 -o results.txt input.txt
This is where you tell the program what you want. Kangaroo is the name of the program (.exe file) -t how many cpu threads you want to use -d the number of distinguished points (in bits) you want to search for - gpu lets it know you want to use a gpu, -gpuId is the device number of the gpu you want to use (if you only have one gpu, you can leave out this option) -o is where you want the results to be stored once program finds the key, and the last entry in batch file is the input file we created above (start and end range and public key).
jr. member
Activity: 102
Merit: 6
February 11, 2021, 12:01:54 PM
i am using gtx 970 gpu and win 10. how can i use kangaroo? can anybody instruct me? i downloded kangaroo.exe but i dont know how to use it. thank you in advance
legendary
Activity: 1568
Merit: 6660
bitcoincleanup.com / bitmixlist.org
January 31, 2021, 01:58:24 PM
..

32 + 29 = 61 When you merged both work files they both should be 2^29 each, then they should equal to 61 or close to it.

Ah ok, so this is measuring just the number of DPs Kangaroo needs for a 50% collision, not all the possible DPs in a range.

Oh well that depends on what size of the DP you're using then. So does it looks for x and y bit DPs or just x bit DPs?

The algorithm for deriving the y point from the x point uses two modular exponentations so chances are it's probably not going to have the same leading zeros for x if at all, i.e only x DPs are considered.
full member
Activity: 706
Merit: 111
January 31, 2021, 10:53:25 AM
Quote
As you see in the images above the person that solved #110 and #115.

Example with #120 using 32 bit Dp: Operations = 2^(120/2+1) = 2^61.

61 - 32 = 29

32 + 29 = 61 When you merged both work files they both should be 2^29 each, then they should equal to 61 or close to it.

So 32 bit Dps for #120 is 536,870,912

That is the expected # you have to find before finding the solution, not how many x bit DPs exist in the range.



Oh well that depends on what size of the DP you're using then. So does it looks for x and y bit DPs or just x bit DPs?
full member
Activity: 1232
Merit: 242
Shooters Shoot...
January 31, 2021, 10:46:24 AM
Quote
because Jean_Luc's Kangaroo just makes DPs by putting zeros at the left of the number until there are 32, or whatever the size of the DP, bits left.
The program doesn't add or just make DPs or just add zeros, those are actual DPs within the actual pubkey.

If you take this private key:
43de528a515bcced5665c496838b

The actual public key is:
0200000000b1dc84f28a1d971aec280000104f08c1ff34fa980ffe0ab97846c7d4

So as you can see, it has (take away the leading 02) 00000000 leading DPs which equals a 32 bit DP, 8 zeros times 4.
full member
Activity: 1232
Merit: 242
Shooters Shoot...
January 31, 2021, 10:41:02 AM
Quote
As you see in the images above the person that solved #110 and #115.

Example with #120 using 32 bit Dp: Operations = 2^(120/2+1) = 2^61.

61 - 32 = 29

32 + 29 = 61 When you merged both work files they both should be 2^29 each, then they should equal to 61 or close to it.

So 32 bit Dps for #120 is 536,870,912

That is the expected # you have to find before finding the solution, not how many x bit DPs exist in the range.

full member
Activity: 706
Merit: 111
January 31, 2021, 10:37:21 AM




As you see in the images above the person that solved #110 and #115.

Example with #120 using 32 bit Dp: Operations = 2^(120/2+1) = 2^61.

61 - 32 = 29

32 + 29 = 61 When you merged both work files they both should be 2^29 each, then they should equal to 61 or close to it.

So 32 bit Dps for #120 is 536,870,912
legendary
Activity: 1568
Merit: 6660
bitcoincleanup.com / bitmixlist.org
January 31, 2021, 07:52:07 AM
So you don't half the search space first then subtract the DP?

To be honest I don't understand why the search space would have to be halved in the first place. Can you enlighten me how you reached that conclusion?

I'm also having trouble comprehending why the DP size should be subtracted from the power of two, because you can't possibly have more than 2^(DP size) DPs and have them all fit in the DP's bit length. For example for the 32-bit DPs in the 120-bit range example your calculation lead to 2^28 32-bit DPs. This doesn't really make sense to me because Jean_Luc's Kangaroo just makes DPs by putting zeros at the left of the number until there are 32, or whatever the size of the DP, bits left.
full member
Activity: 706
Merit: 111
January 31, 2021, 06:50:15 AM
So you don't half the search space first then subtract the DP?
legendary
Activity: 1568
Merit: 6660
bitcoincleanup.com / bitmixlist.org
January 31, 2021, 05:39:42 AM
2^-87? negative 87? Well that's definitely not right. Maybe you meant 2^32 / 2^119 ? Even 2^32 / sqrt(2^119) wouldn't be right. But maybe if you take (2^32 / sqrt(2^119)) and multiply that back by the range = 350,142,318,592,413,374,492,074,613. That would come out to be about .0000054 percent of the 2^119 range.

It's a ratio of 2^-87 to 1. Where the 1 is proportional to the range 2^120 and the 2^-87 is proportional to the number of DPs in that range. That means there are 2^120-87=33 or 8,589,934,592 DPs in the 120-bit range.
Been looking at different numbers; so how many 36bit Distinguished Points in a 72 bit range?

Applying what you said earlier, (2^36-72) = 2^-36. Then use 2^72-36 = 36 or 68,719,476,736 36bit DPs in a 72 bit range?

That sounds about right according to the paper's formula. Except you forgot to subtract 1 from 72 so it would actually be 2^(36-71) or 2^-35 of the space being DPs, or equivalently 137,438,953,472 DPs.

It's getting interesting how as the search space is getting smaller, this is still returning a fairly large number of DPs for large bit counts (relative to the search space). I wonder if this is how it's supposed to work? 137 billion DPs sounds like a lot for a 72-bit search space.
full member
Activity: 1232
Merit: 242
Shooters Shoot...
January 31, 2021, 12:30:28 AM
2^-87? negative 87? Well that's definitely not right. Maybe you meant 2^32 / 2^119 ? Even 2^32 / sqrt(2^119) wouldn't be right. But maybe if you take (2^32 / sqrt(2^119)) and multiply that back by the range = 350,142,318,592,413,374,492,074,613. That would come out to be about .0000054 percent of the 2^119 range.

It's a ratio of 2^-87 to 1. Where the 1 is proportional to the range 2^120 and the 2^-87 is proportional to the number of DPs in that range. That means there are 2^120-87=33 or 8,589,934,592 DPs in the 120-bit range.
Been looking at different numbers; so how many 36bit Distinguished Points in a 72 bit range?

Applying what you said earlier, (2^36-72) = 2^-36. Then use 2^72-36 = 36 or 68,719,476,736 36bit DPs in a 72 bit range?
sr. member
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January 30, 2021, 06:14:16 PM
is there any kangaroo version for ethereum?

This tool finds the private key for the know public key. ETH uses the same elliptic curve, so this tool will work for ETH as well.
full member
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Shooters Shoot...
January 30, 2021, 10:42:02 AM
2^-87? negative 87? Well that's definitely not right. Maybe you meant 2^32 / 2^119 ? Even 2^32 / sqrt(2^119) wouldn't be right. But maybe if you take (2^32 / sqrt(2^119)) and multiply that back by the range = 350,142,318,592,413,374,492,074,613. That would come out to be about .0000054 percent of the 2^119 range.

It's a ratio of 2^-87 to 1. Where the 1 is proportional to the range 2^120 and the 2^-87 is proportional to the number of DPs in that range. That means there are 2^120-87=33 or 8,589,934,592 DPs in the 120-bit range.
Ok, I misread your first post.

Now, from the 8,589,934,592 32 bit DPs, I wonder how many are trailing, leading, and in between? If it's an equal spread or one occurs more than the other.
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