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6

PRGs get an input (seed) and generates a larger output value than the input. Indeed. The standard definition of a PRG makes it a deterministic polynomial-time algorithm with input a seed in $\{0,1\}^n$ and output in $\{0,1\}^{\ell(n)}$ with $\forall n, \ell(n)>n$; and an other characteristic (pseudorandomness). is it possible that some outputs will ...


0

Linear Congruential Generators Let's start at the beginning: linear congruential generators1. A linear congruential generator has the form: $X_{N+1} = aX_N + c \pmod m$ Let's also define $b = a - 1$. A linear congruential generator that produces all outputs in its range is called (no big surprise) a full range generator. A full range generator will produce ...


3

The usual definition for the Blum-Blum-Shub (BBS) generator goes as follows: Let $N$ be a Blum-Integer of unknown factorization. Let $j$ be the "extraction rate". Let $x_0$ be a uniformly random non-negative integer smaller than $N$. Define $x_{i+1}=x_{i}^2\bmod N$. For a request of $M=jk$ random bits, compute all $x_i$ up until at least $x_k$ and ...


2

I only found this: n sollte hinreichend groß sein; für kryptografische Anwendung mindestens etwa 200 Dezimalstellen. (German Wikipedia) which translated means as much as n should be sufficiently large; for cryptographic application at least about 200 decimal digits. This was added in 15th September 2008 before that it has been 100 digits. So I would ...


0

It's mathematics and psychology. People tend to create patterns that aren't random even when they try not to. Randomness isn't just any gibberish that doesn't mean anything, it's data NOT HAVING ANY PATTERN. Humans create patterns.


0

I suppose the problem is not that a human would generate a biased random number. Computers also use biased random sources, but as long as there is entropy in them, they could be hashed into a shorter random enough number. However bad humans are, what humans think of obviously has entropy in it. The problem is, humans are bad at memorizing true random numbers,...


15

Randomness is a measurable, statistical property of a set of values. It doesn't mean the same as "hard for a human to guess." Your sample string is hard for a human to guess, but it isn't very random. There is a tool called "ent" for most Unix systems that can quantify the randomness, by some measures, of a file. Available here: https://...


9

Evidence suggests that people asked to generate random data will produce repetition in the data substantially less often than random chance would. For example, let's assume you were asked to generate random digits (i.e., just 0 through 9). In purely random data, a sequence like NN (i.e., the same digit twice in a row) happens about 10% of the time. That is, ...


18

Why would a dice rolled be "more random" than simply coming up with a sequence in your head, and then changing some of them? Humans have too many biases regarding what a random sequence is. If you ask humans to generate a random sequence, they will probably pay attention not to use the same character in a row, i.e., aa or bb, as they think that ab ...


107

In short, it is more than a belief: there is strong evidence that humans are not good entropy sources. There is a test for this Man vs. Machine. Or, why Man is not a Particularly Good Source of Entropy. Try to win! So we don't rely on whether generating a random number from the mind or random keyboard typings and mouse movements that seem like a monkey ...


14

People are not that bad, but we're slow. See How were one-time pads and keys historically generated? In summary, MB's of 100% secure key material were generated for one time pads by people simply key smashing on type writers. Sufficient to win three world wars. It's just that a human's entropy rate is a little lower than a laser phase based TRNG. ...


30

For me, the fraud-related applications of Benford's Law come to mind. When people make up data they tend to create overly uniform data, even when it's not appropriate. There's a definite psychology going on that may cause people to be less random than they are intending to be (Wikipedia links to a paper claiming humans are in fact bad at this). Or perhaps ...


1

Do any (non-hardware) RNGs exist which could be used (or securely abused) to create an OTP for crypto purposes? This can be quite an epistemological question, and undermines the legitimacy of von Neumann's famous quotation. In a sense he was correct for his time, but perhaps not entirely correct these days. Algorithms have to be executed on hardware (...


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