A cryptographically secure pseudorandom number generator is a pseudo-random number generator with properties that make it suitable for use in cryptography.

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How to prove the security of the PRNG?

Are there any realties tests or criterias that prove the security of the PRNG? What kind of tests or criteria?
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What stops the Multiply-With-Carry Random Number Generator from being a Cryptographically Secure Pseudo-Random Number Generator?

Despite the fact that Marsaglia's MWC PRNG (multiply-with-carry random number generator) is considered to be "the mother of all RNGs", it does not seem to be considered to be a CSPRNG ...
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How much entropy is lost via hashing when you add known or low entropy data?

(I updated the title, as I think there was some confusion as to the question) Here's the question: For example, if I have a bit stream that is 64K bytes long and there is about 16 *8 bits worth of ...
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Definition of a CSPRNG

I am interested in what conditions are necessary and sufficient to define a cryptographically secure pseudo-random number generator (CSPRNG). Wikipedia lists two defining characteristics: It ...