[adhoc32]

A bitcoin address is the double hash with two different algorithms of the public key. Hardware wallets do not expose the public key to check the balance, they use the address. The public key is broadcasted when a transaction is signed so the network can verify the signature. This is the reason why bitcoin addresses should never be reused. It gives the attacker the information and the time to break the encryption (theoretically).

[xiphias2]

The address is the double hash of the hierarchically derived public key using BIP32 key derivation. To be able to compute multiple addresses the master public key is used in the computer's memory that may contain malicious code.