They are doing cryptographic hashes called SHA-256 (look it up). A hash can't be decoded, it can only be brute force matched. What all the miners are doing are computing hashes, which are entered in the blockchain (ledger) when the hash meets a certain criteria. The criteria today is harder than it was two weeks ago, but not as hard as it will be in two weeks. There are something like 300,000 blocks in the blockchain, recording all BTC transactions for the last 4.5 years. Part of the genius of BTC is that the hash of block 300,001 depends on the hash of 300,000, which depends on the hash of 299,999, etc. So an attacker (someone who wants to rewrite block 275,095 to take back a BTC he already spent) has to recompute ALL the hashes from that block forward, and to do that he has to have more hashing power (computer power) than all the other honest miners. He has to have 51% of the BTC network hashing power, which today costs about $15 million in very specialized, hard to come by computer chips, and requires about 5MW of power to run . Therein lies the security of the ledger. (Although Dr. Evil or a government could put 51% hashrate together, they couldn't do it secretly. Everyone can see the blockchain, and an attacker would be visible, although I don't know if they would be stoppable. Somebody smarter has to answer that.)