Hi @crypto.piotr, let me explain this. As I found on Reddit, currently the NEO network makes use of Elliptic Curve Cryptography just like many other cryptocurrencies. In the future this method of creating a safe environment for the storage and transactions on a cryptocurrency network could be endangered. A Quantum Computer will be able to quickly calculate any private key based on a public address through trial and error. Further down the road NEO wants to implement NEOQS (NEO Quantum Safe). This is a algorithm based on Lattice-based Cryptography which is quantum computer resistant.

So right now, NEO is not quantum-computing resistant at this moment (so I was wrong with that statement) but will be in the future. But some other cryptos are even now.

As I know, even the public address, where you send your Bitcoin for example, cannot give the attacker the opportunity to guess the private key. The public address is hashed public key. So once you use some address to send some crypto, you reveal your public key and the elliptic curve can be calculated by brute force of some quantum computer or some very very very high capable computer.