Pollard's kangaroo ECDLP solver

[WanderingPhilospher]

@WanderingPhilospher Please explain if I divide a public key with a range of 2 ^ 255 by 0, 1, 2, 3, 4, 5, ... up to 2 ^ 155 the probability is much more likely to get 2 ^ 100 than, for example, to split public key with a range of 2 ^ 255 by 2 ^ 235 to end up with the smallest 5 times range of 2 ^ 20 ?
I don't really understand number theory. Does all this have to do with modular multiplication? That is, getting 2 ^ 100 is more efficient and expected in theory the probability due to the fact that the module is 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141?

I'm not sure I understand your question 100% but,

dividing doesn't necessarily equal probability.  It just shrinks the search range BUT adds more pubkeys you have to search for in that smaller range.

With Pollard's Kangaroo, starting from scratch (meaning no previous tames and tamed wilds) I think it will take you longer to solve; unless you get lucky and pubkey is towards the beginning.

With BSGS, you save a little time searching say 100 pubkeys versus 1 pubkey, from not having to generate baby steps 100 times (most time consuming in BSGS)

With brute force like bitcrack, it would save time but since the more pubkeys you have in your input file, impacts the overall speed, then there is very little speed up, if any. But also, bitcrack is exponentially slower than Kangaroo or BSGS, just searching for 1 pubkey/address, so this would not be an option for me, at all.

But the biggest thing to remember is, can you write to file, the amount of pubkeys you wish to shrink the range by. If you want to shrink the range by more than 2^26, then it starts to take awhile/unfeasible to write all of those pubkeys to an input file. Just my 2 cents.

[1714505150]

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[WanderingPhilospher]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

[WanderingPhilospher]

Also, I have accomplished what brainless has done now/in the past, but with a twist. 

I created 57 million pubkeys that all link to #120's pubkey but they all lie within the 2^120 range (the original search range 80000...FFFFF) They are all proportionately spaced out. I basically created a certain length "jump" if you will.

I first started the process to see how long it would take to create that many pubkeys, and after 20 million I just let it keep going and finally stopped it around 57 million.

I have the pubkeys and the applicable compressed addresses to each pubkey.  I secondly was going to run a test and search for all 57 million addresses with my modified VanBitcracken (one could do it with bitcrack as well, I think. When I once tried loading an input file of over 25 million addresses, bitcrack wouldn't start/run) and see how much of an impact it had on GPU speed.  I have yet to run that test.  Funny thing is, I can run python on 1 CPU thread and check 2,000 keys per second no matter how many addresses I search, 1 or 57 million.  Your only limitation is the amount of RAM you have.

[brainless]

Also, I have accomplished what brainless has done now/in the past, but with a twist. 

I created 57 million pubkeys that all link to #120's pubkey but they all lie within the 2^120 range (the original search range 80000...FFFFF) They are all proportionately spaced out. I basically created a certain length "jump" if you will.

I first started the process to see how long it would take to create that many pubkeys, and after 20 million I just let it keep going and finally stopped it around 57 million.

I have the pubkeys and the applicable compressed addresses to each pubkey.  I secondly was going to run a test and search for all 57 million addresses with my modified VanBitcracken (one could do it with bitcrack as well, I think. When I once tried loading an input file of over 25 million addresses, bitcrack wouldn't start/run) and see how much of an impact it had on GPU speed.  I have yet to run that test.  Funny thing is, I can run python on 1 CPU thread and check 2,000 keys per second no matter how many addresses I search, 1 or 57 million.  Your only limitation is the amount of RAM you have.

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist. 
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

[WanderingPhilospher]

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist.
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

Haha! Got it!

Ok, so what are you working on NOW? I know you are always doing some kind of pubkey manipulation/tinkering. Any newly found secrets or tips you have found?

[NotATether]

This was previously posted in this thread but deleted for some reason, it's a snippet from iceland2k14's Github that divides a pubkey by an arbitrary number and returning all the parts in between. I polished it a bit to print the compressed and uncompressed keys: https://gist.github.com/ZenulAbidin/286a652b160086b3b0f184a886ba68ca

Here's the script output when called with a random (uninteresting - with no balance) pubkey, divided by 48. The keys divided by 0, 1, 2, 3 and so on are printed in order:

Code:

>>> shiftdown("0267830f83723fa565ccb8677c14d13f7d47bf1008fea826833359f27f866632ab", 48)
023f81e98df59d891264d3fca9bca16552feaf1c7dba1bebd9a774c5fd6041f248 043f81e98df59d891264d3fca9bca16552feaf1c7dba1bebd9a774c5fd6041f24873afd6e4fe6e2e93db77f96f04428dc8f66831960a6122c81e8a6095428f8b94
03b7d16572d1c71e629645c311078ca3cfbdd15b752de69ac606d9b0076f8373ca 04b7d16572d1c71e629645c311078ca3cfbdd15b752de69ac606d9b0076f8373ca90d73ee0e478d1f9440ce9ae6a08d65d35a7f0c3b1b34d14e7d1bce7f51b3fc1
0227216fdb90bd046064c3b93d10270a047233d17073ec6dae0ece6fe5d5f3942c 0427216fdb90bd046064c3b93d10270a047233d17073ec6dae0ece6fe5d5f3942c4813f1e70df2d6222bc3c5fd822cd750ed63bc899651f89fe39d6630999360e4
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*edit: some text was cut off*

[brainless]

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist.
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

Haha! Got it!

Ok, so what are you working on NOW? I know you are always doing some kind of pubkey manipulation/tinkering. Any newly found secrets or tips you have found?

If i post 260 pubkeys in 110 bit rang. Maybe zieler with his gpu bank could find in a year.
If i print 720 pubkeys in 90 bitrange. How much days need to find ?

[WanderingPhilospher]

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist.
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

Haha! Got it!

Ok, so what are you working on NOW? I know you are always doing some kind of pubkey manipulation/tinkering. Any newly found secrets or tips you have found?

If i post 260 pubkeys in 110 bit rang. Maybe zieler with his gpu bank could find in a year.
If i print 720 pubkeys in 90 bitrange. How much days need to find ?

Probably 1.5 to 2 hours per pubkey; but all Tames would be players, which may speed it up, especially the latter pubkeys.  Would probably go with a little higher DP to try and cut down on tame and wild file size.

How many pubs would be in the 2^90 range?

[brainless]

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist.
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

Haha! Got it!

Ok, so what are you working on NOW? I know you are always doing some kind of pubkey manipulation/tinkering. Any newly found secrets or tips you have found?

If i post 260 pubkeys in 110 bit rang. Maybe zieler with his gpu bank could find in a year.
If i print 720 pubkeys in 90 bitrange. How much days need to find ?

Probably 1.5 to 2 hours per pubkey; but all Tames would be players, which may speed it up, especially the latter pubkeys.  Would probably go with a little higher DP to try and cut down on tame and wild file size.

How many pubs would be in the 2^90 range?

1/720. 90bit
16/260 110bit

[WanderingPhilospher]

Good job
just correct one line
Also, I have accomplished what brainless has done now/in the past, but with a twist.
now/in the past >>  in the past
remove "now", as no one know whats NOW
and in the past aprox a year ago

Haha! Got it!

Ok, so what are you working on NOW? I know you are always doing some kind of pubkey manipulation/tinkering. Any newly found secrets or tips you have found?

If i post 260 pubkeys in 110 bit rang. Maybe zieler with his gpu bank could find in a year.
If i print 720 pubkeys in 90 bitrange. How much days need to find ?

Probably 1.5 to 2 hours per pubkey; but all Tames would be players, which may speed it up, especially the latter pubkeys.  Would probably go with a little higher DP to try and cut down on tame and wild file size.

How many pubs would be in the 2^90 range?

1/720. 90bit
16/260 110bit

The above was an estimate using my hardware. I ran tests in the 92 bit range, with high DP (32) and it took around 1.5 hours.
If you are asking about Zielar's hardware, I would imagine he could run each pubkey, combine and check for solve, in around 33 days total. Maybe faster with 90 bit.

[unclevito]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

So I understand you subtract C00000000000000000000000000000 from 02CEB6CBBCDBDF5EF7150682150F4CE2C6F4807B349827DCDBDD1F2EFA885A2630 the public key for 120 and for example if you wanted to search F then you would subtract F00000000000000000000000000000 from 120 public key? and then search the same range 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

[WanderingPhilospher]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

So I understand you subtract C00000000000000000000000000000 from 02CEB6CBBCDBDF5EF7150682150F4CE2C6F4807B349827DCDBDD1F2EFA885A2630 the public key for 120 and for example if you wanted to search F then you would subtract F00000000000000000000000000000 from 120 public key? and then search the same range 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Correct.

[unclevito]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

So I understand you subtract C00000000000000000000000000000 from 02CEB6CBBCDBDF5EF7150682150F4CE2C6F4807B349827DCDBDD1F2EFA885A2630 the public key for 120 and for example if you wanted to search F then you would subtract F00000000000000000000000000000 from 120 public key? and then search the same range 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Correct.

i was thinking last night that we treat each keyspace as if they were  separated by a wall but they are not so i measured the distance between 115 and the center of 60 then reduced the public key of 115 by that amount. i hit the 115 public key ( i scanned a thru f on 60 and about one hour later I got a hit. Key found privkey fc07a1825367bbc
Publickey 0242257a130fe109c25c2ca6c60af60e5849305f77370401299b63da2094ec0297 and the addition  + 31464123230573851029232324144930570 . Trying it on 120 but so far no luck. i wish I had this kind of luck on 120 or the powerball lol. I have a image of the hit but don't think I can post it. The addition goes to the private key found

[WanderingPhilospher]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

So I understand you subtract C00000000000000000000000000000 from 02CEB6CBBCDBDF5EF7150682150F4CE2C6F4807B349827DCDBDD1F2EFA885A2630 the public key for 120 and for example if you wanted to search F then you would subtract F00000000000000000000000000000 from 120 public key? and then search the same range 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Correct.

i was thinking last night that we treat each keyspace as if they were  separated by a wall but they are not so i measured the distance between 115 and the center of 60 then reduced the public key of 115 by that amount. i hit the 115 public key ( i scanned a thru f on 60 and about one hour later I got a hit. Key found privkey fc07a1825367bbc
Publickey 0242257a130fe109c25c2ca6c60af60e5849305f77370401299b63da2094ec0297 and the addition  + 31464123230573851029232324144930570 . Trying it on 120 but so far no luck. i wish I had this kind of luck on 120 or the powerball lol. I have a image of the hit but don't think I can post it. The addition goes to the private key found

Awesome!

So the center of 60, which was what, in your calculation? so you took 115 - minus middle of 60 = x and subtracted x from original 115 pubkey, right?
And then you did a search in the 2^60 range?

[unclevito]

Just FYI, for my 2 cents, if you know the range a key lies in, or want to gamble and take a chance where you think the key may lie, then I think subtraction is better.

Like I said a few posts back; we will take #120 puzzle for example. The private key can only start with 1 of 8 possibilities: 8, 9, A, B, C, D, E, F

Let's say you think it starts with C. You can then take the pubkey and subtract by C00000000000000000000000000000. Let us now say for example purposes the private key is:
C23BD97E765A75F0D6D4A6C6B67221.

So for your search range, after subtracting the C000....would be 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

By subtracting, you went from a search range of 2^120 to 2^116; 16 times smaller the original search range. BUT if you guessed wrong and the key does not start with C, then you will not find the key.

Staying with the same example, if you thought it started with C, D, E, or F and you subtracted by C000....then you could search the range of:
0:3FFFFFFFFFFFFFFFFFFFFFFFFFFFFF, and now you've went from 2^120 down to 2^117, 8 times smaller. BUT again, if the key does not start with C, D, E, or F, you won't find the key.

Dividing is fascinating because in your mind you see a much smaller search range, BUT the amount of pubkeys you have to search GROWS the smaller you cut the search range.

So I understand you subtract C00000000000000000000000000000 from 02CEB6CBBCDBDF5EF7150682150F4CE2C6F4807B349827DCDBDD1F2EFA885A2630 the public key for 120 and for example if you wanted to search F then you would subtract F00000000000000000000000000000 from 120 public key? and then search the same range 0:FFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Correct.

i was thinking last night that we treat each keyspace as if they were  separated by a wall but they are not so i measured the distance between 115 and the center of 60 then reduced the public key of 115 by that amount. i hit the 115 public key ( i scanned a thru f on 60 and about one hour later I got a hit. Key found privkey fc07a1825367bbc
Publickey 0242257a130fe109c25c2ca6c60af60e5849305f77370401299b63da2094ec0297 and the addition  + 31464123230573851029232324144930570 . Trying it on 120 but so far no luck. i wish I had this kind of luck on 120 or the powerball lol. I have a image of the hit but don't think I can post it. The addition goes to the private key found

Awesome!

So the center of 60, which was what, in your calculation? so you took 115 - minus middle of 60 = x and subtracted x from original 115 pubkey, right?
And then you did a search in the 2^60 range?

Yes but i got so excited i overwrote the calculations wanting to try 120 lol. I used a python script to reduce it though
 

[WanderingPhilospher]

Yes but i got so excited i overwrote the calculations wanting to try 120 lol. I used a python script to reduce it though

Understandable for sure.

[NotATether]

Yes but i got so excited i overwrote the calculations wanting to try 120 lol. I used a python script to reduce it though

As we speak, I'm reducing #120 to 100 bit keyspace with the custom python script in my post and it should be done in an hour or so and I'll post a link to them here.

I already reduced it to 110-bit keyspace and the compressed keys can be downloaded from https://files.notatether.com/public/misc/puzzle/120div10.txt .

[unclevito]

The difference between 110 and 60 is a few months to a few hours to know if it will work. But 110 is certainly better than 120 a huge reduction. One problem i see is going from a such an immense keyspace like 120  or 115 is not knowing where the actual key lies in 120 so I believe one would need to scan the 50's and 60's in the event not found in 60. i am working on logic totally  with limited knowledge regarding these issues so i could be wrong.

[unclevito]

Yes but i got so excited i overwrote the calculations wanting to try 120 lol. I used a python script to reduce it though

As we speak, I'm reducing #120 to 100 bit keyspace with the custom python script in my post and it should be done in an hour or so and I'll post a link to them here.

I already reduced it to 110-bit keyspace and the compressed keys can be downloaded from https://files.notatether.com/public/misc/puzzle/120div10.txt .

I am going to try your keys now. Thanks

[WanderingPhilospher]

Yes but i got so excited i overwrote the calculations wanting to try 120 lol. I used a python script to reduce it though

As we speak, I'm reducing #120 to 100 bit keyspace with the custom python script in my post and it should be done in an hour or so and I'll post a link to them here.

I already reduced it to 110-bit keyspace and the compressed keys can be downloaded from https://files.notatether.com/public/misc/puzzle/120div10.txt .

That's over 1 million public keys to search individually!

Group ops of 100 bit range is 2^50 group ops, now times that by 2^20, so group ops is now 2^70 when 120 bit range is only 2^60 group ops.
Do you see? Now you are doing more work than just running original pub and range.  Not to mention you will have to set the -m option which will increase your group ops or you may never know if the pubkey was in the range or not; but with original, you know it's in the range.