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Yes, you can certainly do this, and there has been a lot of theoretical work in the area. At a high level, what this is called is a randomness extractor (Wikipedia): A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weakly random entropy source, together with a short, uniformly random seed, ...

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Theoretically a TRNG provides more security, since its not deterministic and it cannot be predicted. But provided a PRNG is implemented correctly the repetition period is very large $>2^{256}$. Unless you have a cryptographic application that uses the full iteration length the PRNG is not the weakest spot in the cryptosystem. Taken PRNG like ...

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Entropy as defined in information theory and cryptography is a difficult concept. One of the most common fallacies is that a piece of data has or "contains" entropy by itself. People who misunderstand this talk about bit streams having entropy, or measuring entropy of a piece of data. Or measuring entropy of a RNG. To measure entropy you need a data source, ...

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Let us ignore all kinds of encoding or protocol details. We are looking for some string such that $yourprogram(string)=h$, where $h$ is a specific hash value. You will try to crack that password, rather than SHA-256. Let us assume that all the possible messages you have are the 26 lowercase letters of English alphabet. That means that, for every letter in ...

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Bits of entropy The assumption for all cryptographic operations is that a random key of n bits has n bits of entropy. If it doesn't (due to PRNG defect or implementation error) then the key will be weaker than expected but the underlying assumption of all cryptographic primitives is that an n bit key has n bits of entropy. This is the same for all types ...

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In general, collisions in a hash function are a bad thing: if you have different $M_1$ and $M_2$ for which $hash(M_1)=hash(M_2)$, the situation will require special handling. In cryptography, hash functions can be seen as "summary" functions, that reduce a message of arbitrary length to messages of fixed length. Since the message space (all the possible ...

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