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You don't actually need 384 bits of key material. The IV for GCM does not need to be secret, and may be chosen deterministically, e.g. as an incremental counter. Thus, you only need 256 bits for the AES key, which you already have. That said, if you did actually need more key material, you could use any standard KDF to expand your 256 bits. Since you ...


The field polynomial used for GHASH limits most definitions to 128-bit block size. That does not mean you could not define it for other sizes – the proposal defined it for 64-bit as well (pdf, see Appendix A) even if NIST did not standardize that. However, defining it for arbitrary block sizes would be more difficult. You would need to define a ...

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