I'm new to Salesforce and working on a problem being raised by my team. They have a requirement to encrypt all PII passing between our systems and Salesforce . Our company only allows for this data to be encrypted using RSA asymmetric key encryption. I am being told that this is not supported by Salesforce. Is this the case?
Salesforce doesn't support asymmetric data encryption at the user level, you can look at the Crypto class to see what is supported in Apex. It isn't supported because there isn't really a use case for it (it does support asymmetric encryption algorithms for signing data, since that is an appropriate use case for asymmetric encryption and not symmetric). Once you've given someone the public key for the data you encrypted, it's effectively irrelevant whether or not you used asymmetric or symmetric encryption for the purpose of keeping the data secret, and symmetric encryption is both secure at smaller key sizes and faster overall due to the smaller size.
Candidly, if your security team doesn't understand the use cases of asymmetric vs symmetric encryption, I'd be very concerned that they are being trusted to secure PII. Your company may want to consider hiring an outside firm to help educate your security team and test your existing implementations.
With Salesforce Shield Platform Encryption you can generate your own keys with your HSM and use Bring Your Own Keys (BYOK), but RSA/asymmetric encryption is not the technology we use to do encryption of data at rest. Since the encrypt/decrypt operations happen solely on the Salesforce platform it doesn't make sense to use asymmetric encryption - symmetric encryption (AES in this case) is more appropriate, and is what we use (AES-256).