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Although your scheme is secure - especially with a random key of 32 bytes or higher - it won't offer any benefit over HMAC. It's therefore not recommended to use such a scheme. Also note that `bcrypt has been designed for key stretching which is deliberately not efficient. You have ample entropy in your key so there is no need for key stretching.


The question is how much is this schema secure? Not significantly more secure than sha256(m + k) is and may be less secure. An attacker who could arrange a collision for that would trivially also get a collision for the bcrypt hash of that, regardless of the salt value. While SHA-256 is collision resistant, there are MACs that have better bounds, like ...


Tape is a basic concept from Turing machines. The random tape is the tape with random bits on it.


As SEJPM said in his comment: one proceeds by contrapositive, first suppose that such an adversary with an unfair advantage exists and use that adversary to break a well known assumption, e.g.: the adversary can be used to factorise a large composite integer (as defined in RSA). As of today, we have no efficient algorithm to factorise large composite ...

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