Questions tagged [probability]

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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
33 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
102 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
24 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
69 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 ...
6
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2answers
407 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
41 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
58 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
70 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
498 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
175 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
2k 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
77 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% ...