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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Does hashing a secret/seed make it effectively 2X less secure?

In many cryptocurrency projects I noticed that 32-byte seeds/secrets are hashed to arrive at new 32-byte keys. The reason why is because you can then, with the addition to an index, use the same seed ...
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Password entropy requirements for online dictionary attacks on OPAQUE?

My understanding is that for PAKE protocols such as OPAQUE (https://eprint.iacr.org/2018/163.pdf), the the adversary has no choice but to just do online attacks on the password. If this is true, I ...
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How to calculate entropy of a specific cryptosystem?

I want to calculate the entropy of a specific cryptosystem such as the Caesar cipher or Vernam cryptosystem etc but I don't quite understand how to do so. Any help?
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What are the key difference between Shannon entropy and Guessing Entropy?

Any body can explain, what are the key differences between Shannon entropy and Guessing Entropy? In some research I got entropy uses binary search or balanced Huffman tree. Guesswork uses linear and ...
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For any numbers $a, b$, what are the operators $X, Y$ such that revealing $a\ X\ b$ and $a\ Y\ b$ doesn't reveal info about $a,b$?

Previously I thought about a pair of 8-bit uniformly distributed random numbers $(a,b) \in \{0,1\}^8$, and $X$ to be bitwise XOR, $Y$ to be 8-bit addition. But it turned out that revealing $a \text{ ...
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What does $(a+b) \bmod{256}$ and $a$ XOR $b$ reveal about $a, b$?

Say $a$ and $b$ are some uniform random $8$ bits so that the entropy of $a$ and $b$ is 8 bits each. If I show you $(a+b) \bmod{256}$ and $a$ XOR $b$, then what can you tell about $a$ and $b$? Or how ...
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What is the methodology for selecting symbol bit length and window size when performing Shannon Entropy Analysis?

When performing Shannon Entropy analysis on something like an RNG or a file, you must: Select a symbol bit length and number of samples would will perform analysis on at a time (IE: windows size) ...
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Mapping number into number with big algorithmic entropy - how to do it?

I need to parameterize some PRNG, let's assume I need 32-bit numbers. But when numbers doesn't look very random it gives bad results. The creators of SplitMix had similar problem (note that from what ...
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Extractor and Min-Entropy proof

I'm following a course that speaks about cryptography. In this course we talked about Min-Entropy ($H_{\infty}$) and Extractor. To show that an extractor $Ext:\{0,1\}^n \rightarrow \{0,1\}^l$ that ...
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Which hashing function is good enough for session IDs?

Background I'm building a URL shortener, and the URL to shorten may contain a SessionId. For the URL shortener to not compromise the security of the SessionId, I must use a shortening strategy that ...
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Where did Whitfield Diffie say "If you can make random numbers, you can have a private conversation"?

I've seen the following (alleged) quotation on this site and other places:- If you can make random numbers, you can have a private conversation. -Whitfield Diffie. Yet we (Google & me) can't ...
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Could anybody help by applying a secure multiparty secret sharing scheme?

Suppose that we have a multi-secret sharing scheme as it is described in the literature Let there be $I$ agents and say that $S$ is the space of the (uniform) random variables $s=(s_1,s_2,\cdots,s_I)\...
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Is the Secret sharing scheme thresholds of variable of interest shared related with the entropy of the variable?

Is the $t$ out of $n$, namely $(t,n)$, threshold in the secret sharing scheme related to the entropy of the random variable that is shared according to the scheme? What changes in the secret sharing ...
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Why Entropy to be defined as Joint Probability Distribution Sum?

From Stinson's book, during the demonstration of the following Theorem which says: $H(X,Y) \leq H(X) + H(Y)$, with equality if and only if $X$ and $Y$ are independent random variables. The author ...
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How can a generate a key with defined key size with a hash function with its security/internal state shorter than the key?

Let's suppose I took a high resolution photo full of entropy and I want to convert in a key with 2048-bits of security. Practically all the known hash algorithms have maximum 512-bits of security. Is ...
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Entropy of SIM PIN code

Each mobile SIM card has a four-digit number ($b_1$,$b_2$,$b_3$,$b_4$) called PIN code. Each digit $0 \le b_i \le 9$ (for i = 1, 2, 3, 4) is generated using a random 16-bit sequence as follows: $b_i=(...
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Difference between Non-uniformly random and Uniformly random

I am reading up on Key Deriving Functions (KDF) and in a section of the Real-World Cryptographic book by David Wong, a comparison is being made with Pseudorandom number generator (PRNG). And one of ...
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Signature of low-entropy data: can they be faked?

I am working on an application where I have a physical product identification label containing a block of public, low-entropy data (~50 bytes) such as serial number and other info, all readily ...
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To what degree does a high PKBDF-HMAC-SHA1 iteration count compensate for a weak passphrase entropy?

Lost a LUKS-encrypted laptop at the end of 2019 and now trying to figure out the odds of a very sophisticated attacker being able to break in. The LUKS container was created mid-2017 with LUKS1 ...
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What can chaos provide to cryptography?

Chaos-based cryptography is facing a lot of criticism, however, some people argue that it can provide many cryptographic primitives, such as stream ciphers, block ciphers, hash functions, public-key ...
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Estimation of the entropy of keys derived from truly random numbers

NOTE: This question is based on my assumption that $X$ is a "truly random number" if and only if it's length measured in bits is equal to its entropy measured in bits. In other words, when ...
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l-Diversity logarithm

I wanted to make a little example for anonymization evaluation using l-Diversity. For that I'm using the following formula for Entropy l-Diversity ($E$ is the equivalence class, $S$ are all possible ...
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Don't human generated passwords used with key derivation functions reduce the security of symmetric encryption?

The key size for AES is chosen as 256 because that's considered the minimum keysize which can protect against a brute force attack - i.e. $2^{256}$ tries. However, in practice, for a lot of ...
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Does grouping password characters for readability decrease entropy?

For example, for a randomly generated password of 28 lowercase letters, which is about 128 bits of entropy, how would adding a space after every four characters affect it? ...
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Randomness extraction on correlated data in TRNG

True random number generator (TRNG) designs I read about mostly consist of two digital stages: Low-frequency sampling (of a physical noise source) Randomness extractor The noise signal is sampled at ...
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Randomness extraction from a Santha-Vazirani (semi-random) source

In a quest to better understand randomness extractors (in the context of TRNG post-processing), I read some papers about the von Neumann Extractor and Santha-Vazirani (SV-) sources. The von Neumann ...
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Correlations in ring oscillator PUFs

A bunch of silicon Physical Unclonable Functions (PUFs) designs rely on variations of the propagation delay (due to process variation) of signals in different path. In many cases, a challenge selects ...
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Use of scrambler LFSR for randomness extraction of semi-random source

I am using a linear feedback shift register (LFSR) in a scrambler configuration as a randomness extractor for a weakly random source. This source is semi-random (aka. Santha-Vazirani source): the bits ...
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Why Entropy is low for Python Fernet Encryption

I am using Fernet encryption from python cryptography.fernet and generated the key as below ...
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How to compute the dataset size required by dieharder tests?

I am trying to use the dieharder random number test suite. However, this suite requires massive amount of data (this paper claims 228GB for no rewinding for every test) for most of the tests. I'd like ...
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Does watching Youtube generate entrophy

Does watching videos (either online videos such as off youtube or saved locally) generate enough (if any) entropy to create secure encryption keys? I understand that some activities such as memory ...
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Does applying a "PushEntropy"-function increase security of a private key?

I was just reviewing the source-code of the NBitcoin-package. As far as i can see when you create a new bitcoin-keypair Key privateKey = new Key(); (without passing ...
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How efficiently can an attacker forge parts of a fingerprint?

If two devices do not trust each other yet, you can't simply send the correct fingerprint across: you have to manually verify it. I am looking into the security of comparing only random parts of a ...
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Exercise applying Leftover hash Lemma

Say that X is a (k; n)-source if $X\in\{0,1\}^2$, and the min-entropy of X is at least k. Answer the following questions: (i) Suppose that $l=128$; what is the minimal amount of min-entropy needed in ...
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How to ensure that a cryptographic implementation is reasonably sound/robust?

I know from the bottom of my heart how bad the idea of custom-crypto is. I absolutely concur with the recommendation that it should only be done by professionals who specialize in implementing crypto ...
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Low Encrypted Entropy on PDF File

Thank you for the answers, I have edited my questions. It is a known fact that encrypting the files increases the file entropy. You can see the average entropy values of encrypted and non-encrypted ...
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Should I calculate SHA-256 hash of a raw bytes of a token or it's hex encoding?

I have a system where I should generate a secret token for a user. The presence of a token is sufficient to grant access to some user-related data. I am generating a 4096 bit token from a ...
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Measuring entropy of a uniform distribution source

What is entropy? I do not understand it at all. One article states: When there is an equal chance for all items to appear, we have a uniform distribution. In uniform distribution the entropy is high....
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Quantum key distribution using BB84 protocol

Quantum key distribution using BB84 protocol. The Secure key rate $R$, is given by $$ \quad R=1 - 2h(e_b) \tag{1}\label{q1}$$ where $e_b$ is the quantum bit error rate (QBER), $h(x)$ is the Shannon ...
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In my opinion a lot of encryption paper have small contribution in terms of security improvements [closed]

I used to saw a lot of encryption papers that have small significance in security improvements especially in terms of entropy, histogram and coefficient correlation especially in image encryption. Why ...
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How is it possible to prove that Shanon entropy does not change applying any bijective function to X? [duplicate]

I was wondering how is it possible to mathematically prove that Shannon entropy does not change when applying any bijective function to X? For instance H(X) = H(f(X)) assuming that f is invertible and ...
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How to prove that permutation and substitution ciphers satisfy H(X) = H(Y) in Shanon Entropy?

I was not able to mathematically prove that all permutation and substitution ciphers satisfy H(X)=H(Y) if we say that Y is the set of ciphertexts while X is the corresponding set of plaintexts in ...
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Recovery Passphrase Collission for BIP-39 and BIP-44

Referring to the standards of [BIP-39] and [BIP-44]: a 'master password' consisting of 12 words uniformly selected from a 2048-word dictionary corresponds to 128 bits of entropy, that is then used as ...
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Shannon information entropy value of 64 bit data?

So basically i have a set of float data, its value ranges from -1.3117 to 1.7956 and then i convert this data into 64 bit binary value(assuming it is originally 64 bit double float). After that, i ...
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What Permutation Entropy really is?

I was wondering about what is permutation entropy(PE). Then, I came to know this paper which describes PE. Now, let's assume that we have a pseudorandom permutation that is generated using an entropy ...
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How does the entropy of $r$ influence the security of the one-time pad $F_k(r) \oplus m$?

In an one-time pad scheme, $s \oplus m$ is uniformly random for any $m \in \{ 0,1 \}^\ell$ if $s$ is uniform in $\{ 0,1 \}^\ell$. By the security of PRF, it seems to be secure to replace the truly ...
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How to verify the claim of entropy available made by Linux 4.5?

The Linux kernel has an entropy source and it estimates its amount of bits in the device /proc/sys/kernel/random/entropy_avail. How can I verify that this number ...
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3 votes
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Formula for bits of entropy per bit, when combining bits with XOR

Assume that bits $A$ and $B$ each have .5 bits of entropy per bit. The two-bit result of the concatenation $A‖B$ has 1 bit of entropy total, and it retains the entropy density of .5 bits of entropy ...
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Where can I find a sample of data with a known entropy to see how well NIST SP 800-90B does on it?

I'd like a sample of true random data from a source that has a known entropy. It's not easy to even produce true random data in sufficient quantity --- much less know the entropy of the source. For ...
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Why does it make sense to use min-entropy for measuring cryptographic random data?

Comments on Cryptographic Entropy Measurement seems to challenge the heart of NIST SP 800-90B, which proposes min-entropy as a conservative measure of entropy produced by hardware source. [The idea ...
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