If you minimize the size of the signature, then RSA is a bad choice to start with. DSA and ECDSA both provide shorter signatures with much greater strength than RSA. However, neither the DSA nor ECDSA will come close to the signature verification speed for the RSA 384.
If, however, you must continue to use the keys that you have, you will have to change your code to avoid using the Microsoft Cryptography API. You can use, for example, the Bouncycastle C # library if you use C #. Finally, you can complain to Microsoft about it. I doubt that everything will be fine, but you can always try.
James k polk
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