RSA can be used to prevent unwanted software modifications on an embedded system. How can this encryption algorithm be implemented physically? I mean, which peripheral/main units can be used to check the digital signature and how do they do this?
RSA is a software algorithm. You can probably implement it in most microcontrollers, in FPGA and simmilar and using dedicated crypto-ICs.
Googling for RSA will quickly find you the detals of RSA and for implementations for various platforms.
What you use depends on how fast you need it to be, which depends on volumes.
RSA isn't a magic security dust you can add to a product. Creating a secure product is a significant undertaking. You need to consider all the attack vectors.