# Questions tagged [entropy]

Entropy is a measure of how predictable the outcome of a random process is, or how much uncertainty one has about an unknown quantity in one's state of knowledge, defined in terms of the probability distribution on possible outcomes or quantities.

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### How should I calculate the entropy of a password?

If part of the password is a whole regular English word, does the entropy of that part depend on the number of English words in existence, the number of English words known by the choosing algorithm, ...
965 views

### How to interpret the entropy results for a NIST test file?

There is test data derived from pi that is supplied by NIST for validating their entropy measurement formulae listed in NIST's Recommendation for the Entropy Sources Used for Random Bit Generation. ...
939 views

### Entropy when iterating cryptographic hash functions

Consider a cryptographic hash function that maps $n$-bit strings to $n$-bit strings:  \DeclareMathOperator{\H}{H} \DeclareMathOperator{\SHA}{SHA-256} \H(x) : \left\{0,1\right\}^{n} \mapsto \left\{0,...
2k views

### The effect of truncated hash on entropy

Suppose I have a 128-bit random binary string (128 bits of entropy), then I hash it using SHA-256, then I take the first 128 bits of the output hash. Does the taken bit string still have (almost) 128 ...
6k views

### Should I use the first or last bits from a SHA-256 hash?

I have the need for a hexadecimal token that is smaller than the normal length of the hexadecimal representation of a SHA-256 hash. Should I take the first bits or the last bits? Which of them ...
8k views

### How is the One Time Pad (OTP) perfectly secure?

The Wikipedia entry on One Time Pads (OTPs) states that if this cipher is used properly; ie, the keys are truly random and each part of the key is independent of every other part, it's uncrackable, ...
2k views

### If a SHA256 hash with high entropy is then hashed with one made from low entropy, is the resulting hash higher/same/lower entropy?

If one were to create a SHA256 hash using 256 coin flips converted to hex (which, as I understand it, is as "entro-phized" as one can capture in SHA256) then take that hash as a string, combine that ...
324 views

### Why does entropy halve during its extraction?

It is common to use cryptographic hash functions to extract randomness from entropy sources. One of the quantitative criteria for this is that if 2n bits of entropy are put through a hash, n bits of ...
327 views

### What is the relationship between entropy conditioning and final output bias in a TRNG?

This question concerns the conditioning and output of true random number generators. It refers to NIST Special Publication 800-90C, Recommendation for Random Bit Generator (RBG) Constructions. It ...
3k views

### 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 ...
27k views

### What is entropy?

We discuss a lot of topics and use measures of entropy to determine how difficult it is for an attacker to be successful. What does entropy mean in the context of cryptography? How is entropy ...
7k views

### Estimating bits of entropy

I know there are different statistical tests out there (NIST, Dieharder, etc), which all do different ways of analyzing entropy. What I'm having a hard time finding is any particular literature ...
6k views

### Why is ciphertext from low entropy plaintext not compressible?

This comes following a discussion with a colleague. My plaintext file plain consists of a about 100,000 lines of "all work and no play...". It's size is: 2.2 MB. ...
768 views

### Why is Min-entropy significant in cryptography?

Let $H_{min}$ = Min-entropy and $H$ = Shannon entropy. Unless you're gaming the system or deliberately trying to be obtuse, very rarely is $\frac{H} {H_{min}} > 10$ from any conceivable ...
299 views

### Conditioning Component in Entropy Source

Given a sample of random bytes, how to determine if Entropy Source (source of random bytes) includes a Conditioning Component or not, with respect to NIST SP 800-90 B)? Thanks
1k views

### Will hashing over and over eventually give the same hash?

There are many cases in maths where doing the same thing over and over again will bring you closer to a value. Derivation of polynomials is the striking example: no matter what you start with, you end ...
2k views

### Mixing Entropy Sources by XOR?

Assume that I have two sources of entropy (say, a hardware RNG and a CSPRNG) and that the two sources are independent (do not know anything about the internal state of the other RNG). Can I mix them ...
6k views

### If you hashed a hash an infinite number of times would you end up with a unique hash?

If you took a hashing algorithm for example MD5 and repeatedly passed the output hash back into the algorithm an arbitrarily large number of times would you eventually end up with one unique hash? My ...
1k views

### Estimated entropy per bit given P-value of a statistical test, and number of bits tested?

Assume that a certain statistical RNG test (say from the NIST Statistical Test Suite, Dieharder, etc..) gives us a certain P-value (per the definition [*] used in NIST Special Publication 800-22), ...
1k views

### How many bits of entropy does an elliptic curve key of length n provide?

A FAQ for an open source project makes the claim: Indeed, an elliptic curve key of length n provides $n/2$ bits of security. I have two questions: What is the practical difference between "bits ...
203 views

### Why should one model an entropy source in order to build a TRNG?

Some assert that a theoretical model of the unconditioned source must be created when building any TRNG. It's believed to be a fundamental requirement. So a few related questions arise:- What is a "...
1k views

### Why do “nothing up my sleeve numbers” have low entropy?

As a preface, forgive me for some of the links being from Wikipedia. I realize that academia frowns upon this. I came across this article about "nothing up my sleeve numbers". In it, it says: In ...
2k views

### Entropy of two concatenated random values

In this Intel blog posting, the author claims: The amount of work required to brute-force predict a random value that has n bits of entropy is $O(2^n)$. If you concatenate two values together, the ...
5k views

### What happens to entropy after hashing?

What happens to entropy after hashing? Suppose you have a key with entropy $k$. Can entropy $k$ be increased by hashing the key?
580 views

### Tactics available to help prove security of a new system?

I believe that the accepted tactic to "prove" a system as secure is to allow the crypto-community to review it and if no vulnerabilities are found over a long period of time (5 or 6 years), then a new ...
328 views

### Enumerating the bias of NIST and Pearson randomness extractors

The following is an extract from a paper about using your mobile phone as a true random number generator (TRNG). The mobile phone bit is incidental to this question though. I'm interested in the ...
5k views

### How to calculate the entropy of passwords? [duplicate]

Here is a cartoon about password entropy. http://xkcd.com/936/ I dont quite understand how the entropy is calculated in the cartoon assuming they are calculate correctly. But in general, I dont have ...
151 views

### Can an attacker exploit the nonuniform distribution of letters in a diceware password to improve a brute force search?

I use some diceware pass phrases in some places but I have one question that I can't find the answer to. Let's say I roll the dice and get $N$ words with a total of $M$ letters and that I don't put ...
2k views

### What happens to the entropy of a password when you hash it?

For example, if the entropy of a password is 30 bits, what is the entropy of the password when you hash it with MD5?
789 views

### Entropy of system data - use all and hash, or trim least significant bits?

I'm working on a background entropy collector for key generation that monitors hardware and produces an entropy pool. Here's my list of sources: Mouse position Keyboard timings (i.e. time between ...
15k views

### Password cracking: What if attacker is lucky? [closed]

We have always measured password or private key strength by the amount of entropy it contains, but what if the attacker who cracks it is lucky. Consider the following simple scenario, we have 1 bit [...
8k views

### Can Shannon's entropy be used to determine if a file is encrypted?

If we have to determine a file is encrypted or not, can we use Shannon's entropy algorithm on the file? As discussed here, the entropy (in bits per byte) being closer to 0 is considered as more ...
1k views

### Is this a good entropy collector and whitening technique?

I'm just reviewing a program someone wrote to provide high quality random data using an entropy collector and a hash based whitening technique. I'll try summarize the process: Collect entropy from ...
444 views

### NIST 800-90B /Non-IID track - min-entropy result > 8 for 8-bit symbol

I'm conducting an analyisis of noise sources based on the NIST 800-90B Non-IID track. Accordingly, I applied the non-iidmain.py script on a datarecord, which delivered the following output: ...
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### Brute forcing CRC-32

I'm working on a cryptosystem which uses IDEA. The designer made the mistake of including a CRC-32B hash of the password unencrypted in the header, so that the system can quickly reject bad passwords....
553 views

### Feedback on rolling my own entropy gatherer

First of all, I don't recommend doing this. This was something I created when I didn't know better and didn't have a solution available to me. Long ago I created my own entropy gather for a ...
301 views

### Detecting steganography by analysing non-significant data entropy?

I am not thinking only steganography in images, I think it is also possible to encode data for example into the length of spaces of a clear html text. I suspect, the steganography changes (elevates) ...
1k views

### How to calculate entropy of a combined key

I know how to calculate the entropy of a key that relates to its selection process. For example if the key space is $1000$, entropy of a randomly chosen key is $1000$. Suppose now you have two keys $X$...
6k views

### How does generating random numbers “remove entropy from your system”?

In a previous question, I quoted the --gen-random entry in the GPG Man Pages. At the end it says: PLEASE, don’t use this command unless you know what you are ...
2k views

### Are picture files “random enough” to be usable as a one-time pad?

Say you have a picture with 1 megapixels taken at random and with $2^{24}$ possible colours per pixel (RGB-24). That image would be unique and the possible combinations $(2^{24})^{10^6}$ immense. ...
651 views

### Is it safe to generate two 256-bit ECC keys from 128 bits of entropy?

Apparently it is perfectly safe to use 128 bits of entropy to generate a single 256 bit ECC key. Can I use 128 bits of entropy and a KDF to make a 256-bit ECC key? I assume this is because 256 bit ...
2k views

### 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 ...
2k views

### Entropy calculation

I calculated the entropy for "variable", "property" and their concatenation "variableproperty" (with e.g. the Shannon Entropy) and got $2.75, 2.5$ and $3.33$ respectively. These are all entropy per ...
837 views

### Quality test for an hardware source of randomness

Say that I developed an hardware source of randomness, which I would like to use to seed a cryptographically secure random number generator. How would I go about testing it? Are there standardized ...
313 views

### Post-Quantum Primitives' Object Sizes

1. Alternative Cryptographic Primitives For quite a while, I've been thinking is it possible to "craft" a cryptographic primitive (like ECC) suitable for the purposes of post-quantum cryptography, ...
752 views

### Do the NIST tools on GitHub measure entropy reliably? [closed]

There is a supposed NIST tool called SP800-90B_EntropyAssessment on that Git thing. It's designed to be used in accordance with NIST's Recommendation for the Entropy Sources Used for Random Bit ...
2k views

### Measuring entropy for a ciphertext only attack

When bruteforcing a password (e.g. the common attacks on DES), where you have ciphertext only, you need a way to assess whether a decrypted plaintext is the right one. I believe the EFF DES machine ...
2k views

### Deterministically combine more than one source of entropy

What is the proper/canonical way to do this? For example, $0 < r1 < 1$ and $0 < r2 < 1$. Presuming uniformly distributed probabilities for the two, combining/averaging them is going to ...