[SAI_Peregrinus]

> but technically I think it's signature algorithm (ecdsa) can be thought of as a hashing step, followed by a public-key based encryption step.

It really can't. If you're extremely drunk you can think of it as similar to hashing followed by a public-key based decryption step (signing uses the private key, as does decryption) but that's about as good an analogy as calling a tractor-trailer a container ship because both haul cargo. The actual elliptic-curve part of the operation isn't encryption or decryption, and thinking of it as such will lead to error.

RSA does have a simpler correspondence in that the fundamental modular multiplication operation is shared between decryption and signing (or between encryption and verification). But modular multiplication alone isn't secure, it's the "padding" that turns modular multiplication with a particularly-chosen modulus from some basic math into a secure encryption/signature system. And the padding differs, and the correspondence doesn't hold in real systems. RSA without padding is just sparkling multiplication.