> First of all, it is hard to even analyze "total hashing power." There are far too many slippery details for any formal analysis -- you need to know how the ha

> First of all, it is hard to even analyze "total hashing power." There are far too many slippery details for any formal analysis -- you need to know how the hash function is actually implemented, what sort of hardware, etc. I don't understand why you're bringing that up. You don't need any of that. Anyway, the total hashing power is currently 79,854.53 gigahashes per second (where one "hash" is actually a double SHA-256). > That being said, how do you know there are no other double spending attacks? Where is the proof of that? Any double spend in a block will be immediately rejected by all nodes. So the only question is, "Which blocks are actually valid blocks, and which blocks are orphans?" Blocks that form part of the longest extant blockchain are considered valid; all others are orphans. So the only question at that point is, "Which is actually the longest extant blockchain?" If you have massive hashing power, you can create an alternate blockchain and release it, allowing double-spends of transactions in all the blocks back to the point that your alternate blockchain forks from what was previously considered to be the longest blockchain. Mathematically, you need > 50% of the total hashing power to do this. The proof of that is in the paper. (Though it's worth acknowledging that there are a lot of details that are _not_ in the paper, and you have to talk to bitcoin devs or read the wiki or the source or the forums to figure them out.) > Prove it. Preventing double spends (and spending of money that doesn't exist - semantically also a double spend) is the sole purpose of bitcoin's distributed algorithm. All the rest is just verifying that transactions are signed properly. > The fact that ECDSA and SHA256 are used in Bitcoin does not imply that Bitcoin is secure. True, but there are other things that imply that Bitcoin is secure, and my only point here is that the use of ECDSA and SHA256 are nothing to worry about. There certainly can be and have been security flaws in the code, but they're not related to the actual fundamentals. That's why they've always been easy to fix and why Bitcoin has never been "hacked."