A currency that anyone could generate any amount of money from on demand would have no purchasing power. The amount of money available in this currency, as opposed to goods and services, would approach infinity. Cryptocurrencies take advantage of the relative rarity of byte sequences that produce a specific final value, a hash, through predefined cryptographic algorithms.
That this system can work is illustrated by the example of email encryption using a pair of keys, one private and one public generated from it. There is nothing secret about the public key. The public key, the key to be used for encryption, is published. The private key must be carefully guarded by the recipient of the e-mail. With the private key, with long keys only with the private key, an encrypted message can be decrypted. Even the sender of the message could not algorithmically decrypt it again, the fact that he usually keeps an unencrypted copy of the message does not change the basic principle.
For this procedure, key lengths of 4096 bits are now standard for asymmetric procedures such as RSA (after the inventors Ron Rivest, Adi Shamir and Leonard Adleman). At this key length, it is practically impossible for someone to decrypt an encrypted e-mail without knowing the private key. With shorter key lengths, on the other hand, decryption would be possible with high but feasible effort. It would be rare and expensive in the algorithmic sense (runtime of the algorithm) and in the economic sense (hardware, power costs). This is precisely the relative scarcity that can be used to create digital resource usable as currency.
