Questions tagged [probability]

Questions about the branch of mathematics concerned with modeling and analyzing random phenomena.

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Can we determine a security parameter in the hybrid argument where the number of hybrids is polynomially bounded but not known?

Let $\lambda$ be a statistical security parameter. Consider a security proof that is based on hybrid argument, where there are polynomially many (say, $n = p(\lambda)$) hybrids, $H_1, ..., H_n$. Any ...
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3answers
155 views

Can you have perfect secrecy with countable message/key spaces by dropping countable additivity?

This classic paper by Chor and Kushilevitz shows that if the key space and the message space are both countably infinite, then it is impossible to have a perfectly secure private-key encryption scheme....
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2answers
76 views

On The Next Bit Test

I would like to know what $O(v(n))$ really means in detailed and simple words please. I found it everywhere in the literature I am reviewing but I cannot find what the intuition of it (especially if ...
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1answer
64 views

Explaining the reason of radically more accuracy while using different set of hash functions instead of same set of hash functions on some operations

So I am looking for an explanation of an experiment. In this experiment, I took a set of k hash functions. Say the total number of data points I am working on is d. Call an algorithm A which used that ...
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1answer
75 views

Laplace Inequality

I am trying to prove that if $r_i \sim Lap(0,1/\varepsilon)$ where $\varepsilon >0$ then: $$Pr[r_i \geq 1+r^*] \geq e^{-\varepsilon}Pr[r_i \geq r^{*}]$$. I know that for $r*>0$ it satisfies ...
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0answers
19 views

Probability that length of shortest nonzero vector is less than a number

Let $\Lambda\subset \mathbb{Z}^n$ be an $n-$ dimensional lattice with determinant $d$. We know that the probability that a uniformly random integer vector $x$ is a point in $\Lambda$ is given by $\...
3
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1answer
149 views

Likelihood of signature collision with EdDSA

Taking EdDSA as an example, given the length of a signature is 512-bits for a given data payload, what is the probability of a collision where there is another 512-bit value that is also a valid ...
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1answer
69 views

Probability that rank of a square matrix, whose each element is uniformly random from a ring of integers modulo prime p, is not full

I am currently reading a paper from CRYPTO, which is a top conference in cryptology. In the paper, the authors use a thereom like the one given below without a rigorous proof: the probability that $...
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1answer
519 views

Is it possible to construct a PRNG where the output numbers have a certain distribution of hamming weights?

I am in need of a non-uniform random number generator where each n-bit output has a hamming weight with a certain binomial distribution. For example, I would like a non-uniform PRNG which generates ...
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2answers
93 views

Random Oracle to prove an Authenticated DH protocol

I am trying to understand how they use the random oracle to solve the CDH. For example, in the security proof on page 7 of the following paper; A Lightweight Message Authentication Scheme for Smart ...
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1answer
38 views

How to have a bound (upper or lower) of Gaussion distribution over lattice based crypto>

In lattice-based crypto, we always need to sample 'noise' from Gaussian distribution, but how to measure the bound the noise? For example, if the Gaussian distribution is D_{u,\sigma}, where u is the ...
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41 views

Primal and dual attack against NTRU

I am looking at the primal attack against schemes in the second round of the NIST Post-Quantum Standardization Project. The cost of primal attack usually comes from an estimate described in NewHope ...
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1answer
130 views

Statistical distance in distributions

I have two questions regarding to statistical distance in distributions. 1: If $Z$ is uniform random variable over $N$ consecutive integers and $m < N$ then $Z$ mod $m$ has statistical distance ...
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1answer
71 views

Compute statistical distance between two distributions over tuples

Let $X$ denote one distribution. Let $f,g, \text{ and } h$ denote three functions. If we have the results: $g(X)$ is within a negligible statistical distance of $h(X)$. Is it possible to prove $$(f(...
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0answers
101 views

How do I calculate the conditional probability of a Caesar cipher?

I have a frequency distribution of letters for the plaintext and the ciphertext. I'm trying to determine the conditional probabilities to identify the plaintext/ciphertext pairings. If I encrypt ...
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1answer
82 views

$X_ {i_1}, . . . , X_{ i_ k} $ are IID random variables or not?

In this paper secret sharing is to distribute information (the secret) over a set of participants such that the secret can only be reconstructed if certain authorized combinations of participants join ...
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1answer
64 views

Can anybody please explain why is the probabilty of finding a desired message for random chaining values equal $2^{-224}$?

Can someone explain why does probability is equal $2^{-224}$ in the following piece of paper? The length of messages blocks in Hamsi is equal 32 and the length of chaining values is equal 256.
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0answers
37 views

decrypting a one-time-pad that outputs 0,1 in preknown probabilities

assuming a two users want to use a one time pad ciphersystem, and they are using a program that was developed by a third party that was supposed to create random undependable bits, but for some reason ...
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3answers
294 views

Derivation of birthday paradox probability

I am trying to come up with an explanation of the probability of birthday collision. $P$(no collision among t people) = $(1− \frac{1}{365}) · (1-\frac{2}{365}) ··· (1-\frac{t-1}{365})$ For one ...
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0answers
31 views

Again on discrete gaussians over lattices [duplicate]

Define $$\rho_{s,c}(x) = exp(-\pi \cdot \frac{\|x - c\|^2}{s^2})$$ and $$\rho_{s,c}(L) = \sum_{x \in L} \rho_{s,c}(x)$$ Then Discrete Gaussian over $L$ with center $c$ and standard deviation $s$ is ...
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2answers
100 views

Is there only one formula for the statistical difference between a pair of distribution ensembles?

Statistical closeness implies computational indistinguishability was recently posed. It revolves around a numeric value $\Delta(n)$ of the statistical difference between a pair of distribution ...
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2answers
564 views

Statistical closeness implies computational indistinguishability

This is so trivial that authors usually don't bother to give an explicit proof. But for me there is some vagueness. We say that two ensembles $X_n$ and $Y_n$ are statistically close, if $$ \Delta(n) ...
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1answer
66 views

What is / How would I calculate the number of bits(?) I need to make the probability of a collision very small?

If I wanted to create a TOTP-esque algorithm that generated a string n characters long, with each character being a base64 character, generated from a user secret <...
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2answers
85 views

What's the meaning of probabilities in differential privacy formula?

I don't understand what does it mean by "The probability is taken is over the coin tosses of K." Does it mean, the probability distribution is generated based on exactly same data but only the ...
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1answer
29 views

Can randomness protect a list of signatures against forgery attacks?

Suppose we have a list of signatures $S = [s_1, .., s_n]$ for a list of messages $M = [m_1, .., m_n]$, and we want to verify that $S$ is a valid signature of $M$, so each $s_i$ should be valid for ...
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0answers
109 views

What is the probability equation of rotational cryptanalysis on modulo multiplication?

The answer in this question defined how to calculate the probability of rotational cryptanalysis on modulo multiplication $\odot$. This paper defined an algebraic equation of how to calculate the ...
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2answers
990 views

Why the definition in $\epsilon$-differential privacy is multiplicative rather than additive?

According to its mathematical definition, a random algorithm $M: D\rightarrow R$ satisfies $\epsilon$-differential privacy if the adjacent datasets $x, y \in D$ where $D$ is a whole dataset and ...
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2answers
219 views

Meet-in-the-middle probability of success

In page 358 of Bruce Schneier's Apllied Crypto, when explaining the meet-in-the-middle attack, he states that the success probability is «1 in $2^{2m - 2n}$» with two plaintext/ciphertext pairs, and «...
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2answers
4k views

Using a hash function as a random number generator

Using MD5 or SHA1 for instance, and applying integers (as seed so to speak) to the hash function, in sequence, and only keeping, say, the first 64 bits of the resulting hash, do we always have a ...
2
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1answer
86 views

Is there a rule of thumb for ZK protocols?

There's always a small chance for many zero knowledge protocols that the prover had a lot of luck to prove something to the verifier. Take the Ali Baba cave as an example: The prover has a 50% ...