Questions tagged [probability]

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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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What is the probability to get all qubits as zeros with input of zeroes qubits [migrated]

question from exam: Bob built a quantum computer of 10 qubits. all qubits are set to zeroes. Bob performed on the system quantum fourier transform and then measured the system. what is the probability ...
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31 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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28 views

Probabilistic Symmetric Key Generation

Here is a brief description: We have two parties, Alice and Bob. Each party must choose either a positive key or a negative key. Subsequently, Alice will generate a 0 or a 1 at random and send it to ...
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1answer
51 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
45 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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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
61 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
63 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
36 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
148 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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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
79 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
469 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
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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
75 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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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
753 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
185 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
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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 ...
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1answer
85 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% ...