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The $1/2^{32}$ is an arbitrary figure, based upon one particular value for what counts as an acceptable risk. You need to decide what is an acceptable risk. If you think that a $1/2^{32}$ probability of failure is an acceptable risk, then this calculation is relevant to you. If you think it isn't, then decide what you think is an acceptable risk and re-do ...

4

Yes, this is fine, at the record level. (What you've built would be classified as a "Encrypt-then-Authenticate" scheme in the literature, and there are standard provable security results for such schemes.) Well done on constructing a solid, well-engineered cryptographic scheme. An AEAD mode would spare you from having to invent such a scheme, but what ...

1

I recommend you read a bit more about cryptographic design before getting into design of a HSM. Designing a HSM is basically designing a cryptographic protocol. For instance, using AES-128-CBC is a bad idea, as it does not provide message authentication; instead, you should use authenticated encryption. Similarly, rather than deriving a derived key in ...

3

Designing an HSM or other secure device is relatively easy; making it reliable even in the absence of adversary requires careful engineering; making it safe against adversaries with some level of physical access is hard; demonstrating that it is safe (for some definition of that) is even harder. One thing to worry about is integrity of stored data ...

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