While NIST defines many methods for light-weight cryptography, they only define one method for asymmetric encryption - ELLI (Elliptic Light). This uses a prestored private key and a signed version of it, and is defined in ISO/IEC 29192-4:2013/Amd 1:

https://asecuritysite.com/encryption/elli

Does anyone recommend a strong asymmetric method for RFID devices and which uniquely authenticates the tag?

https://asecuritysite.com/encryption/elli

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