Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it

can anyone know, or explain to me please,

how it will be easy to find private keys which has spend transaction for the wallet in compare to wallet which hasn't spend transaction ?
please explain if anybody know , i am confused so, thanks.

When there is no spend transaction the search method is:

   Next Private Key -> Public Key -> Hash -> Bitcoin Address -> Compare Bitcoin Address, repeat until found

   Note that due to the hashing functions used the Bitcoin Address match is expected within a private key range of only 2¹⁶⁰

A spend transaction exposes the public key so when there is a spend transaction the search method is:

   Next Private Key -> Public Key -> Compare Public Key, repeat until found

   Note that the private key range in this case is the full 2²⁵⁶ but there are ways to speed up the process so the effective security is reduced to only 128 bits.

See the following:

Quote

Baby-step giant-step - https://en.wikipedia.org/wiki/Baby-step_giant-step
Pollard Kangaros - https://en.wikipedia.org/wiki/Pollard%27s_kangaroo_algorithm

So the two situations are:

Full entropy 256 bit private keys with multiple spend transactions have 128 bits of security

160 bit Bitcoin address from a full entropy 256 bit private key with no spend transactions have 160 bits of security

So Bitcoins kept on a Bitcoin address with no spend transactions are safer (160 bits of security) than Bitcoins kept on a Bitcoin address that has spend transactions (only 128 bits of security).

thanks, let's say we got a spend transaction on bitcoin puzzle wallet #120, we got hash of it, so how do we calculate with bitcrack for 2^128 possibles?

Please go back and read what I wrote way more carefully. A spend transaction exposes the public key so you no longer have to do any hashing. Bitcrack is for brute forcing when you do not have the public key. You would need/want to use one of the more advanced methods (see the links in my post) to calculate the private key directly from the public key because it will be so much faster than the primitive bitcrack program. There is no hashing involved any more since you no longer have to deal with the Bitcoin address - you have the public key. BTW there is a spend transaction on #120 so the public key for that address is in the block chain and is available. The person that solves #120 will not be using the primitive brute force bitcrack method. #120 will most certainly be solved using the Pollard Kangaros method. Depending on how much HW you can afford it will take between 116 days and about 8 years to find it.

See:

Quote from: j2002ba2 on July 21, 2019, 01:18:49 PM

Quote from: BurtW on July 21, 2019, 12:15:00 PM

What is your expected time for #105?

I was using 4x Tesla V100 for it. Here is a table with expected times:

|------+-------------------+-------------------| | bits | 4x V100 | 100x V100 | |------+-------------------+-------------------| | 100 | 2d 19:52:51 | 02:42:54 | | 105 | 16 days | 15:21:34 | | 110 | 90 days | 3d 14:53:14 | | 115 | 1 year 147 days | 20 days | | 120 | 7 years 341 days | 116 days | | 125 | 44 years 323 days | 1 year 290 days | | 130 | 253 years | 10 years 57 days | | 135 | 1,436 years | 57 years 166 days | | 140 | 8,125 years | 325 years | | 145 | 45,964 years | 1,838 years | | 150 | 260,011 years | 10,400 years | | 155 | 1,470,848 years | 58,833 years | | 160 | 8,320,376 years | 332,815 years | |------+-------------------+-------------------|
Looks like a "world record" would be 120 bits.