Yes it is possible. Your question, strictly speaking, may not be related to programming. But NFC-related issues tend to blur the boundaries between software and hardware, so I still think this is the right place to pose the question.
NFC tags may contain various chips with different capabilities, depending on the manufacturer. When you look at tags like NFC Forum, there are the following options:
- Type 1 tag: offers the ability to block data, but does not support authentication, AFAICT. The original manufacturer was the Innovative Science and Technology PLC, currently owned by Broadcom.
- Type 2 tag: allows you to lock data. There are various manufacturers. Some chips also offer authentication and write protection, such as MIFARE Ultralight C.
- Type 3 tag: based on Sony FeliCa technology, the main (only?) Manufacturer is Sony. FeliCa chips offer authentication and write protection. FeliCa systems are mainly used in East Asia.
- Type 4 tag: based on the specifications of ISO 14443-4 and ISO 7816-4. Offers the ability to specify write protection. The microcircuits that support this are usually microcontroller cards, which often offer advanced features such as authentication, encryption and write protection, such as the MIFARE DESFire chip family.
Other commonly supported NFC tags:
- MIFARE Classic: offers access control, including write protection. May also support NDEF message storage.
- ISO 15693: some chips offer (limited) authentication and write protection functions, such as ICODE SLIX-S (can also support NDEF message storage).
Then there is the JavaCard family of cards (often compatible with the Global Platform) and other supporting ISO 7816-4 cards. They usually offer very advanced features such as the file system and user programs, including authentication support, encryption, digital signature, etc. Usually they need special equipment and training in order to be able to work with them.
I would recommend looking at MIFARE Classic and, if that does not meet your security requirements, MIFARE DESFire.