Guys Quick question, since I can't get my head around how Kangaroo works in terms of Maths, i was wondering if Kangaroo would still consider a private key within the range, a valid key even if it turns out to be just another colliding key of the 2^96 possible keys that resolve to an address on average .. actually thinking of this while writing, I don't see a reason why not .. but would like if someone could confirm
Kangaroo does not know anything about addresses, so the private key you get is the one that can sign coins from any of the 2^96 colliding addresses (the addresses are defined to be any that collide with the input public key).
Wow .. how come I didn't realize this from the beginning! So instead of brute forcing using collision, it will actually try to find one or more of the 2^96 addresses that the public key resolves to .. i can easily assume ALL those addresses would be empty except the one that actually has the puzzle funds 🤣 now i realize why kangaroo is great only for puzzle range search
I am sorry, I do not understand what you are saying, exactly.
IMO, Kangaroo is still doing a brute force, of sorts. Instead of checking every private key sequentially, it makes jumps/strides to private keys, calculates the public key, verifies if public key ends with/starts with user inputted distinguish point, if yes, it stores the public key and the applicable private key, if no, discards the priv/pub keys. But the way you can use a Kangaroo program to look for more than one private key that will unlock one wallet, is to to subtract or add from original public key. So if you created 2^10 new public keys from the original public key, if you find any of those public keys, you can now unlock the original public key's private key.
As for what you say you realized, no programs, whether kangaroo or bitcrack or bsgs, etc are "efficient" for searching the entire key range. Meaning they were designed for the puzzle. However, each one will eventually find what you are looking for, even in the entire keyspace, and that all depends on hardware and time resources.
Ok I'll try to explain how i see it
My conclusion depends on 2 factors:
1- number of private keys, public keys and address in the entire bitcoin space
2- the way hash functions distribute outcome along the entire range
so point 1 above is simple. in bitcoin, every single private key corresponds to only one public key .. however, any single address could be opened with 2^96 private keys .. hence 2^96 public keys would correspond to such address as well
Point 2 has all the magic, as it is deemed certain that good hash functions would have a sort of distribution that ends up almost evenly across a huge space, we can easily assume that every 160 bit in the entire range would encompass all possible bitcoin addresses .. so for example if we look for the address of puzzle number 160 in range from 1 to 160 .. we would have been doing the same as someone searching for that exact address in the next 160 bits .. and same for someone searching in the 3rd 160 bit range and so on until the last 160 bits in the keyspace .. all of those searchers would in theory find the private key that opens that address although all of these private keys are different AND produce different public keys as well ..
So in conclusion, many private keys and public keys will correspond to the same address and the keyword here is 160 bits range .. the advantage of looking for the puzzle wallets is that you narrowed down that 160bits .. in this case, any program will perform better but kangaroo would be the best performer
But this becomes the exact opposite if we choose to look for all funded addresses in any 160 bit range (remember that entire ADDRESS space is gonna get repeated in every 160 bit key range) .. so assuming i wanna search for these addresses (23 million addresses) in the first 2^100 unsearched range (ranges where all the rest of puzzles weren't visited and most likely has all funded addresses lying somewhere within) .. if we decide to use kangaroo, we would have to :
1st find public keys for all these addresses which means we will only be looking for addresses that spent some money.. leaving us with way less addresses than we want to search for
2nd for each public key, we would be searching for the EXACT private key that produced that exact public key which means we are not looking for a colliding key here, we are looking for a 256 bit private key, a well randomized one .. we are not only increasing difficulty by many folds, but also searching in the wrong range .. in order for one to search for a well randomized pvt key, one has to search in not any 160 bit range but in almost the whole keyrange space .. that's why i said kangaroo is only great for puzzles .. while programs like keyhunt or bitcrack can be directed to the first 160 bit range and get us a colliding private key, kangaroo has to shoot blindly in the sky of the entire range in the hopes it lands on a funded address
As for the addition and subtraction point you mentioned, i might need to read up on more about it as I don't yet get why it would get a collision
I understand the whole 2^96 collision theory. That was not the issue. The issue was how you limit the power of Kangaroo versus say keyhunt or bitcrack. Why does Kangaroo have to shoot blindly? Why do you consider it shooting blindly? With your perspective, the same would be for any searching program, even looking for a collision with 2^96 priv keys that would lead to a single funded address.
It all comes down to if you know the public key of a funded address.
I can create 2^96 public keys that if one is found, will lead me back to any public key/private key of an address. You really have to understand how Kangaroo works and the speed up it provides with any given keyspace. You can also create many more addresses for one funded address to increase the chance of a 2^96 collision. If you take one address that is funded, and you know its pub key, from that you can create many more addresses, that if found, would lead you back to the key you want.
For all of the funded addresses where the pub key is known, I can use kangaroo and find 2^31 of those addresses (and I'm certain there aren't that many funded addressed) before bitcrack searches the first 2^160 possibilities (considering GPU speed is the same for both programs).
now i realize why kangaroo is great only for puzzle range search
Perhaps, this is what confused me the most. If you have an address and know its public key, and need to search for it, Kangaroo is trillions x trillions x infinity faster than brute force LOL. That is all. So my rebuttal would be, if you know the public key of ANY key, the most searching you would have to do with Kangaroo is 2^128, whereas with a bruteforce search, it could be anywhere in a 2^160 range. So kangaroo is great, even outside of puzzle ranges.
As for the addition and subtraction point you mentioned, i might need to read up on more about it as I don't yet get why it would get a collision
It's easy to understand. Again, if you know the pub key.
Address a = privkey unknown and pubkey 1
if we add 1 to Address a, we get Address b
So now, if we find Address a then we know its privkey.
But If we find Address b first, then we know Address b privkey - 1 = Address a privkey; thus we have solved and found Address a's privkey.
So if you have a list of 1000 funded addresses, just add or subtract 1 from each and now you have 2000 addresses that will lead to x amount of BTC. Now add or subtract 2 from each, now you have 3000 addresses, etc. etc.
