RSA engine with inaccessible private keys - susceptible to any attacks? We are going to integrate some hardware accelerator for RSA into our next system on chip. This chip can accelerate the core RSA operation, i.e. modular exponentiation $y=A^x \mod(N)$. The private key ($x$) to use can either be provided from the outside or will be stored inside the hardware core, unaccessible to any other hardware /software component. Side-channel attacks are not an issue in this question.

We assume that the software can query the accelerator to do the modular exponentiation using the on-chip key ($x$) and just gets the result ($y$) for any arbitrary $A$ he provides. Would this setup be susceptible to any oracle-kind attack which would allow extraction of the on-chip key $x$? If so is there any countermeasure against this (using padding according to PKCS #v1.5 or RSASSA-PSS)?
Would this setup be susceptible to any oracle-kind attack which would allow extraction of the on-chip key $x$?


Not as far as we know.

Any such Oracle attack that could recover the private key would demonstrate that the "RSA problem" and the "factorization problem" are equivalent.  Currently, that is an open question; such an attack would be a noteworthy advance...