A naïve hash of the data you’re encrypting stuffed into the nonce leaks whether two plaintexts are the same (or…collided). A hash of the key and plaintext leaks whether the two plaintexts are the same under the same key. Using a proper keyed MAC prevents any rainbow table style attack in either case.
Generally speaking leaking that two plaintexts are the same is better than leaking two plaintexts XORed together. If you’re in a use case where that’s liable to happen (i.e., you don’t rekey “frequently”) I’d happily take the former leaked bit over the latter leaked messages.
There are also a handful of existing constructions you can just take off the shelf rather than rolling your own thing and getting it wrong.
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A naïve hash of the data you’re encrypting stuffed into the nonce leaks whether two plaintexts are the same (or…collided). A hash of the key and plaintext leaks whether the two plaintexts are the same under the same key. Using a proper keyed MAC prevents any rainbow table style attack in either case.
Generally speaking leaking that two plaintexts are the same is better than leaking two plaintexts XORed together. If you’re in a use case where that’s liable to happen (i.e., you don’t rekey “frequently”) I’d happily take the former leaked bit over the latter leaked messages.
There are also a handful of existing constructions you can just take off the shelf rather than rolling your own thing and getting it wrong.