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As far as I know, CBC mode, even with a null IV, will encrypt identical plaintext blocks to unique ciphertext blocks within a single file. The purpose of an IV is to obscure the similarities between multiple ciphertexts, not to obscure the similarities within a single ciphertext. So, would it be just as effective to use a null IV as it would be to use a random IV when encrypting a single file? As far as I see it, it's just one less value to store.

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