# Tagged Questions

In cryptography, a pseudo-random generator (PRG) is a deterministic procedure that maps a random seed to a longer pseudo-random string such that no statistical test can distinguish between the output of the generator and the uniform distribution. Pseudo-random generators have numerous applications ...

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### Security of $(k, 2k)$-bit generator for small seeds

Here is the problem I am working on for context. I have $\epsilon \le 1 - 2^{-k}$ and $\epsilon$ approaches 1 as $k \to \infty$ but I'm stuck on part c). The $f$ is secure iff there does not ...
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### generate unpredictable value with a shared key

Is there any function that taek a key to generate (un)predictable value ? I hope you will more understand more what I mean with this example f take in input an array, a key and a round number f(...
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### Combining multiple PRGs together

Got some theoretical questions about PRGs to solve (given by lecturer for self-learning, no score involved). Tried to find on the internet but couldn't figure out how to solve them, so I will mention ...
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### Is there a password hash function with a human component?

Sort of Related: Is there a cryptographic hash function that can be performed with pencil and paper? One problem with hashing passwords is that the attacker has more of everything it seems. More ...
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### Determine whether a given function is a pseudorandom generator/function

I am trying to solve the following three tasks (for exam practice, not as a homework): Define $𝐺 : \{0,1\}^* \rightarrow \{0,1\}^*$ by $G(x_1,...,x_n) = 𝑥_1 \oplus 𝑥_2,𝑥_1,⋅⋅⋅,x_n.$ Prove that ...
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### Understanding the distinguisher for a PRG

Given the following definition of a psuedorandom generator, I'm having trouble understanding what exactly the "distinguisher" D is outputting, and when?
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### Symmetric encryption vulnerable when encrypting and decrypting are the same?

To my understanding, symmetric encryption is where encrypting and decrypting data can occur with the same key. It's possible for symmetric encryption that the encrypting and decrypting algorithms are ...
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### Uniformly distributed sub-sequences of a main PRG sequence

Let $g_s$ be a pseudo-random generator that generates uniform distributions of numbers ($s$ : seed) of a fixed bit-size. One wants to compare the pseudo-randomness of certain subsets of elements ...
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### Given PRNG $G(s)$, why is $G(s) || G(s+1)$ not a PRNG?

I have given a pseudorandom Generator $G(s)$, $|s|=n$ whose expansion $l(n)$ is $>2n$. I also know that $G^\prime(s) := G(s_1,\ldots,s_{\lfloor\frac{n}{2}\rfloor})$ is a pseudorandom generator. Now ...
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### If a PRG is constructed by iterating a PRF, is it backtracking-resistant?

Say we construct a pseudo-random generator from a pseudo-random function $f$ (using some constant key $k$ and some initial value $v_0$). We do this by feeding the output block of the PRF back into the ...
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### Pseudo random generator vs block encryption, which is faster?

If one wishes to encrypt one can either use a pseudo random generator to generate a long sequence and then xor it with plaintext, similarly he can use the seed as key to encrypt the plaintext using ...
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### Deriving a Set of Seeds from a Seed

I need a set of seeds $S=\{s_1,..., s_n\}$, for pseudo-random function where seed $s_i$ is used to generate a set of pseudo-random values. Obviously I need to be able to regenerate the sets of pseudo-...
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### How to clock a linear feedback shift register?

I have some trouble understanding what happens when a LFSR is clocked. I have tried many examples but I do not get the correct result. Can anyone point out my errors? I have the following polynomial: ...
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### Let $G$ be a PRG. Are the following $G'$ constructions based on $G$ necessarily PRGs?

$G$ is a PRG where $|G(s)| > 2 \cdot |s|$. $G'(s) = G(s0^{|s|})$. $G'(s) = G(s_1...s_{n/2})$, where $s = s_1...s_n$. My question here is whether my own proposed solutions are correct and do ...
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### Can it ever be impossible to invert a PRNG?

I've read about the possibility of inverting the Mersenne Twister after 624 numbers of output. 624 matches the state size of my implementation of the Twister. Coincidence? If the generator only ...
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### Cryptographic random numbers for key generation

I am trying to understand how a cryptographic library works (for example, one that provides assymetric encryption such as RSA), but I'm running into a few problems about the key-generation. There are ...
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### Let $F$ be a PRF, is the following $G(x)=F_{0…0}(x)∥F_{0…1}(x)|| … ||F_{1…1}(x)$ a PRG?

$F$ is a PRF with $n$ bit key, input, and output length. I know the answer is "NO it isn't!", but I can't understand why. Is that because on any input $x$, the keys for every $F$ in the concatenation ...
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### Is Pseudo-Random Generator (PRG) in OpenSSL uniformly distributed?

I need to know can we use PRG of OpenSSL as a PRF?