In order to spend any bitcoin, you need the private key associated with the address.
It is not trivial to get the private key from the public key, in fact, there is no known way to calculate the private key from the public key. Quantum computing may change this, however, we are still a long way away from a Quantum Computer being able to get the private key from the public key.
It can decode 64 bit range with Kangoroo in a maximum of 5 minutes. In other words, the range and public key are certain, and it is clear in how many minutes it will be resolved. I would be glad if you look at it here.
You must be referring to this
puzzle. When I previously responded, it was unclear to me that you were not referring to a transaction whose inputs were not being spent by a private key that was generated with 160 bits of entropy. I am not sure your math is correct, but if it is:
If you were to solve one of these puzzles, you can firstly not enable RBF, so nodes should not accept a double-spend transaction by default. This should make it unlikely that a pool will even know about any competing transaction after someone learns of the private key based on the public key. Although someone could have an existing agreement with a miner to allow them to confirm competing/double-spend transactions.
You can avoid the above by contacting a miner directly and asking them to confirm your transaction without having the transaction previously broadcast publicly. There would still be the risk that the miner would calculate the private key and confirm a competing transaction themselves.
Other than the above, you can also obtain sufficient hash power in order to find a block on your own, and you can confirm the transaction without it being publicly broadcasted.
Yeah probably possible. On the other hand, why would you listen for potentially few years on the nodes with ready to crack hardware to get 1.2 btc to make a potentially successful double spent attack?
1.2 BTC is currently worth close to $75k. Someone could potentially create a program that listens for a transaction that spends one of a set of outputs, rents a VPS and GPUs on GCS, and executes a script that will find the private key, and create a competing transaction.