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Yes, and that's how it's normally done. This even applies to AEAD schemes like GCM, CCM, and EAX (which all encrypt with CTR and MAC as a separate matter with some other algorithm); with non-AEAD schemes, you have systems like CBC+HMAC in TLS, and (with stream ciphers for encryption) ChaCha20+Poly1305 (which are two completely independent algorithms). ...

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