I work in embedded security, but I don't know much about Arduino. So this is the "term I can browse and find" part of your question, w/o any Arduino-specific stuff.
MCUs these days, more and more, are shipping with security features like built in hash processsors, symmetric crypto accelerators (e.g. AES) and sometimes even public key acceleration (RSA, ECC, D-H, etc.) A less common, but very useful feature, is "secure key storage" or "secure enclave" as part of the MCU.
For those MCUs w/o built in key storage, usually a separate IC is used. There are different names and kinds of functionality, but generally the functionality you're looking for would be on a Secure Element, a TPM (Trusted Platform Module) or an HSM (Hardware Security Module). Typically these connect via SPI or I2C. Sparkfun, Microchip, ST Micro, etc. have ICs. For example, ST has the STSAFE-A100, Microchip has the ATTPM20P, ST has the SPC58-HSM-FW , etc. These chips have secure mesh and other physical design features that a normal "consumer grade" MCU wouldn't have.
Also, some hobbyist "HSMs" or "wallets" are really just an embedded MCU without this stuff, for example the Trezor (I think?) is usually a normal STM32F427 MCU.
That should give you enough to chew on for a while.
usage with arduino
\$\endgroup\$