We have decrypted several key wraps (.wky) files that were protected by the DKEK shares we have.
When I generate an RSA 2048 key with some devices, export .wky and decrypt them, I get the “type 6” keys which contain so-called Chinese Remainder Theorem attributes, and the CKA_PRIVATE_EXPONENT value (sometimes called d) is notably missing.
The wraps which contain RSA 4096 keys (as mentioned by @sc-hsm in a GitHub comment ) do not have them, only the modulus n public exponent e and a private exponent d. (These seem to be the “type 5” keys).
Now I realize that I don’t have p and q factors stored anywhere. Are they destroyed after the large keys get generated and never included in the key wraps used for backup purposes? Is there some way to recover them from the HSM?
Otherwise this means we lose information and we would need to recalculate p and q, right?