DislikedI also don't buy the assumption that the so called " private key" as you name it to be so private.Ignored
It's not always easy to understand the concepts involved in achieving certain forms of encryption, but there are familiar mathematical constructs and formulae that you don't have to understand to see how they can be useful to achieve the "difficulty to decrypt" that makes for stronger and weaker encryption.
These mathematical operations are deterministic, in other words they run one way, in the same way every time, but cannot be reversed without expending tremendous effort. In this case it does not matter how well funded or clever an entity is, the determinism will always require the same effort.
For example, from http://bitcoin.stackexchange.com/que...-a-private-key
DislikedIf we assume it takes the same time to run an ECDSA operation as it takes to check an sha256 hash (it takes much longer), and we use an optimisation that allows us to only need 2^128 ECDSA operations, then the time needed can be calculated:
Inserted Code>>> pow(2,128) / (15 * pow(2,40)) / 3600 / 24 / 365.25 / 1e9 / 1e9 0.6537992112229596
It's 0.65 billion billion years.
That's an very conservative estimate for the time taken to break one single Bitcoin address.
Bitcoin's use of Elliptic Curve cryptography and some quite common and well-understood mathematical trapdoors means that the keys being used are tough.
But once again cracking Bitcoin keys is practically unnecessary since all the details of every transaction are public anyway. The only reason to crack a Bitcoin address would be to steal the coins in that address, and because of the provable effort required to do so, there is no guarantee that the coins would still be in that address by the time the attacker is done! What's more, it is common practice among Bitcoin users to store large amounts of bitcoins in multi-signature transactions - so an attacker would not just need to crack one key but several.