It's all signed and counter-signed and counter-counter-signed etc with cryptographic functions and it's part of one huge "chain", acting as some kind of a general ledger, where each block and each transaction in each block is signed such and so.

You can generate any transaction you want, but as long the (heavily signed) blockchain doesn't agree with you that the coins in that transaction exist and you own them, noone else will accept them as such.

the cryptographic functions behind it are so far unbroken. I'm told the math behind is is beautiful
trying to break those with the only known method (brute force) with current computing power would take more time than the universe has existed so far.
building a (conventional) computer to crack it fast enough would require more matter than the earth contains.