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Do not invent your own authenticated encryption mode. Use a standardized one, and use a well-supported library to implement it in your code. AES-GCM, AES-CCM, AES-OCB, and AES-CBC with HMAC-SHA256 over the ciphertext are all common options. Some great direction from Matt Green here: How to choose an Authenticated Encryption mode
Both the AES key size and the RSA key size matter, because it's no use adding security beyond the weakest link. Here the weakest link is 2048-bit RSA, which is considered roughly equivalent in security to 100-128-bit symmetric keys (depending on who you ask). So having a password with much more than 100 bits of entropy would be fairly useless. In practice, ...
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