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Compared to GCM or XTS modes, how secure is H xor R1, E (R2, R1, Message) for confidentiality and integrity?

Let R1 and R2 be (32 byte) random values, and let a H = Hash (R1, R2, Message) be of the same length as each R value. Provided E (R2, R1, Message) is operating in some chaining mode, are there any ...
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Is it possible to tweak AES-GCM so that it is satisfactory for whole-disk encryption (like XTS mode)?

Is it possible to leverage a preexisting implementation of AES-GCM to provide the key security benefits essential for full-disk encryption (similar to AES-XTS)? GCM is a popular encryption mode ...