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SHA-256 is not a Key Derivation Function (KDF), and should not be used as one. SHA-256 can be part of a KDF, such as HKDF-SHA256 which uses HMAC-SHA256 which in turn uses SHA256. HKDF is subject to misuse which can break its security, be sure you're using it correctly (if you use it). HKDF is ONLY SUITABLE FOR HIGH-ENTROPY INPUTS, like other keys or the ...

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If you need the security given by 256 bit entropy password, hashing alone will not help you if starting key < 256 bit of entropy because hashes are fast functions, so testing original key from its reduced-size space or the hashed key is almost the same. A Key Derivation Function (aka a CPU and/or memory/storage hard functions) could mitigate the problem, ...

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The bitlength of an algorithm does not reflect security in a 1:1 relation. The reason for this is, that for security we consider the most efficient algorithm known. security "bits" is not so much a measure of how long any specific number is, but it is a measure of the complexity for the attack. For your specific case: The most efficient attack on ...

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If you're wondering why a 256-bit key offers any greater security, you need to realize that a 128-bit block cipher is essentially a way of mapping $2^{128}$ input values to $2^{128}$ output values. That means the set of all possible 128-bit block ciphers has a size of $2^{128}!$, which is about $10^{10^{40}}$. A 128-bit key allows you to choose one of \$2^{...

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Even for AES128 we don't use the key directly. Each round gets its own key in the process called key expansion. Those round keys are used to transmute a matrix. The original key is never applied directly. AES256 adds more rounds. Each round stays the same, only the key derivation for them changes slightly. This allows for less dependant round keys, which ...

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