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What are the difficulties associated with generating true random numbers? There are no tangible difficulties with generating shed loads of true random numbers. The Haveged daemon claims to generate megabits/s of true entropy without any external hardware. I’m not sure what ‘at scale’ realistically means though. Cycling an AES key per every minute is a ...

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The main difficulty is to find a good source of entropy. It is a measure of "randomness". Well, if we have a value $seed$ such that $H(seed)=n$, we cannot produce a sequence $x, |x|\geq|seed|$ with greater entropy, i.e. $\forall x : x=f(seed)\land|x|\geq|seed|\implies H(x)\leq H(seed)$, where $f$ is some deterministic algorithm (PRNG). Entropy is ...

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I can't speak for your generator as I've not seen it. Is it cryptographically secure (as that's a little tricky to write and just because you can't recover the seed doesn't for one moment mean that others can't). I am not surprised at all that PractRand doesn't detect a loop at >275 GB (See notes). I have no direct experience of PractRand, but ...

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Several observations: Keeping $a$ secret is crucial. If the adversary knows that and sees $y_i, y_{i+1} = (y_i^a) \cdot g^b$, he can compute $g^b = y_{i+1} \cdot y_i^{-a}$, and then go ahead and compute the rest of the sequence. You may say "but we assume the discrete log is hard" - however, you also suggest $p = 8p'+1$ and $a-1 = 4p'$, that is, ...

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My goal is to use it in JavaScript, but I didn't found any implementation You can find the source code, but different JVM/JCE vendors may have different implementation. see: https://github.com/frohoff/jdk8u-jdk/blob/master/src/share/classes/sun/security/provider/SecureRandom.java Additionally, to my problem I want to know how this PRNG works exactly On ...

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The spectral test consists of comparing the length of a shortest vector in a lattice associated with a linear congruential generator with multiplier $a$ and modulus $m$ to the maximum possible length of a shortest vector in any lattice of the same dimension. In particular the spectral test's figure of merit of degree $d$ consists of  \frac{\nu_d}{\gamma_d^{...

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Yes, such PRNGs exist. One example is Blum Blum Shub: There is a proof reducing its security to the computational difficulty of factoring. When the primes are chosen appropriately, and O(log log M) lower-order bits of each xn are output, then in the limit as M grows large, distinguishing the output bits from random should be at least as difficult as ...

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