# Tagged Questions

Usage of randomness (i.e. non-predictable data, usually in the form of bits or numbers) for cryptographic purposes.

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### Does it necessarily mean that an RSA moduli generated with poor randomness is not random?

In 2012 a group of researchers collected a large amount of RSA moduli and calculated their greatest common divisor in order to find common factors between them. By finding a common factor they could ...
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### Data Switching and Information Leakage

Hypothesis: Let $z,a$ be uniformly random elements of a field $\mathbb{F}_p$ where $p$ is a large prime number. Also, let $(-z)$ be additive inverse of $z$. I have a fixed secret value $x$. I mask ...
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### Does an encrypted random sequence conserve its “randomness”?

If you have a random uniform sequence of bits $A$ generated by a TRNG with good performance of randomness tests (eg Dieharder, NIST, Kolmogorov complexity, chi-square, etc) and perform an encryption (...
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### Raw /dev/random output for keymat [duplicate]

Noob question: It is my understanding that the raw output from non-blocking /dev/random (where the kernel's entropy_avail estimate is equal to or greater than the number of random bits required) ...
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### Why do we require a CSPRNG's output to be indistinguishable from true random?

Everywhere I read, indistinguishability of output from true random is stated as a requirement for CSPRNGs. However nobody bothered to give the rationale for such a strong requirement. Specifically, ...
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### use the same pad reversed

Suppose I have a random number (eg 625 467 921). I use it once to encrypt a message OTP style, and when I want to use them again, I reverse them (eg to ...
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### Whitening and randomness extraction

The Von Neumann randomness extractor is explicitly mentioned in the randomness extractor page of Wikipedia, but strangely enough that page does not contain any reference to whitening the results of an ...
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### How many bits of entropy can I expect from /dev/urandom in iOS?

Apple's latest security documentation indicates that it now uses CTR_DRBG for generating pseudo-random numbers (previously Yarrow instead of CTR_DRBG), using "timing variations during boot" and "...
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### In $\mathbb Z/p\mathbb Z$, is $(a+b\cdot r)$ a random value for fixed $a,b$ and random $r$?

Let $p$ be a prime number. Consider two fixed values $a,b\in\mathbb Z/p\mathbb Z$, where $b\neq0$, and a uniformly random value $r\leftarrow \mathbb Z/p\mathbb Z$. Is $v=a+b\cdot r$ a uniformly ...
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### Pseudo Random Function

The definition of pseudo randomness that leads to pseudo random function talks about indistingishability of a key-ed function and a random function. i.e. The key-ed function family $\{F_k\}$ is PRF ...
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### How useful is NIST's Randomness Beacon for cryptographic use?

NIST have just launched a new service called the NSANIST Randomness Beacon. It has been met with some initial skepticism. Perhaps the cryptography community would have used it before June 2013 when ...
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### Mathematically / statistically “safe” way to differentiate between crypto and random blob?

I assume the United Kingdom will impose (as opposed to just talk about it) restrictions on crypto software that may be used within it's borders. Me, quite the border clown (yes, I always bring a up ...
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### How to generate a large random number from smaller ones?

I'm using a function randInt that takes as input two integers as upper and lower bounds (inclusive) and outputs a pseudorandom number in that interval. ...
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### Better lower bound on min-entropy

In “Randomness Condensers for Efficiently Samplable, Seed-Dependent Sources” by Dodis, Ristenpart, and Vadhan (PDF), I have seen the statement that: any tuple of distributions $(X,Z)$ is $ε$-close ...
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### If you have a file and XOR every bit with a random bit, can you extract any information?

Say you have a file that is not random, and you XOR every bit with a random bit (not pseudo, but really random). Can someone who sees only the result extract any information from it? Obviously, it won'...
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### Generating PGP key *without* random generator? (using fixed input only)

I understand why in general, a strong random generator or source of entropy is used when generating PGP keys. However, I have a use case where I want to generate PGP keys deterministically, i.e. ...
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### Difference RSA keypair creation openSSL and openPGP?

Creating a 2048bits RSA keypair I figured that doing this using openssl takes as an input 32bytes of "randomness" from ...
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### Meaning of entropy of a bitstring in NIST SP 800 - 90A

From NIST SP 800 - 90A from January 2012 (see http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf), page 6: For the purposes of this Recommendation, an n-bit string is said to have ...
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### Turning data into seemingly random noise

I am currently working on a python script that does image steganography, altering the least significant bit on each channel of the image. Now imagine encrypting a file with a bunch of null bytes, or ...
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### Why use randomness in digital signature algorithms?

I understand why randomness has to be employed in encryption, because deterministic ciphers are not IND-CPA. I don't understand why digital signature schemes that employ randomness, like RSA-PSS, are ...
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### Benefit of using random key in Shamir's Secret Sharing

I am implementing Shamir's Secret Sharing, and I find that in (t,n)-threshold scheme, the shares are just using 1,2,3...,n as the key to form the shares ...
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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?
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### Random Galois fields

Note: I have now answered this by my own research and can generate random fields up to G(2^9) in reasonable time. I would need to find more speedups for larger fields. At this time G(2^8) takes a few ...
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### Is there a kind of OS entropy pool on Windows systems? [closed]

I am wondering if Windows provides an equivalent of /dev/urandom from linux ? Or any kind of system entropy pool ?
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### What is the difference between CSPRNG and PRNG?

What is the difference between CSPRNG and PRNG? Is there performance differential between them? For example: We use PRNG for key generation which is very expensive and CSPRNG for IV/nonce in block ...
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### PRNG determinism (and java.security.SecureRandom)

Looking at getDefaultPRNG() in java.security.SecureRandom makes me very unsure about how to use it. On my desktop, it uses sun.security.provider.NativePRNG, which reads from ...
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### Looking for a secure PRNG that I can implement in hardware

I'm trying to implement a (sort of) simple PRNG in hardware for fun. My idea would be to allow a user to enter a key using a keypad (or some dip switch settings that can be set and hidden) and to ...
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### Statistical properties of hash functions when calculating modulo

When using SHA-1 to hash an input, the result is a pseudo-random number in the numeric ID space $\{0\dots2^{160}-1\}$. Do I loose any statistical property in the result if I use modulo to restrict the ...
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### Issue about randomness : what if random looks “human” ? [closed]

I read a lot of stuffs about entropy/randomness. But what if a random generator (either digits or strings) once output a "human" patern ? I know it is very unlikely to happen, but if a random code ...
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### Is there a Javascript and Java implementation of a good CSPRNG [closed]

I need to use a cryptographically secure pseudo random number generator in my client running Javascript and in my server running Java. Is there a well-known implementation of a good CSPRNG in both ...
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### Random Permutation polynomial

I need to know, please: (1) Is there anyway to pick uniformly at random permutation polynomial in a field of prime order? (2) Are there many permutation polynomials in a field? (3) In a finite ...
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### Is a die implemented in a physics engine truly random?

So, a fair die throw is really random, not pseudo. So, would a RNG implemented as the result of a die throw in a physics engine (say, Newton, Havok, Nvidia's PhysX) be regarded as both ...
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### How good is middle cube method with jumbled digits?

I had to make my own prng for a stream cipher for an inter school science project (I am mentioning that a lot). So I thought of cubing the seed instead of squaring it (like in the middle square method)...
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### How can a good pseudo-random number generator be made?

I am trying to make a pseudo-random number generator so that I can use it in a synchronous stream cipher for encrypting plain text. I want it to generate numbers which are as random as possible. What ...
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### How do you test randomness?

Suppose I receive a list of 1 million coinflips, and I want to know how likely it is that the list was randomly generated. My first thought would be to count the number of heads and tails, which ...
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### To prove $r_2$ is a uniformly at random value in $Z_n$, where $r_2=r_1 . m$

$m$ is arbitrary value in $Z_n$, where n is RSA modulo. Then we do: $r_2=r_1 . m (modn)$, where $r_1$ is a random value such that $r_1\in Z^*_n$. ** Question(1): is $r_2$ a uniformly at random ...
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### What's causing the poor randomness in this program: the LCG, or the program logic itself?

(Crypto Gods, I should begin by stressing that I haven't lost my mind: I'm not doing this in real life, I'm just trying to understand the theory behind what's happening. With your help, hopefully I ...
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### Is there some way to generate a non-predictable random number in a decentralised network?

Is there a way to generate a random number with given restrictions: It will be used in a decentralised network with a big number of peers (no central authority to generate it) Its generation should ...
Suppose a $1000$-bit key used in the one-time pad is not randomly and uniformly generated. Suppose that the values of the first $5$ bits are $0$, and the other $995$ bits are randomly generated and ...