Questions tagged [probability]
Questions about the branch of mathematics concerned with modeling and analyzing random phenomena.
60
questions
2
votes
0answers
37 views
What's the probability distribution of 3DES keys' key check values?
Do the key check values of two-key 3DES keys have a uniform distribution? If not I'm curious as to what the distribution is.
I ask because I want to know how safe it is to use a key's KCV as an ...
3
votes
1answer
104 views
Mathematical formulation for a cryptosystem
I will try to define easily the cryptographic system of this paper. The author designs a communication game for $N$ players. The private information of every player is denoted as $t_i\in T_i$ and ...
1
vote
1answer
33 views
Differential Privacy with Outliers
To use the Laplace mechanism, we have to get the global sensitivity of a query function. What do we do in the case where there is one huge outlier(or multiple outliers) in the dataset such that the ...
0
votes
1answer
39 views
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 ...
1
vote
0answers
21 views
Secret sharing scheme combined with probability theory results?
As a sequel of my previous post I am writing a new one with respect to the secret sharing scheme. I will only cite here the answer because I want to make a question on it.
$\textbf{Answer:}$ To be ...
0
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0answers
20 views
How to design such a secure multiparty computation scheme with the players using a majority rule
Suppose that $y$ is a uniform random variable that is defined over the field (or group or abelian group) $Y$. Let us suppose that there are $N=\{1,2,\cdots,i\cdots,N\}$ agents and only one of them, ...
0
votes
1answer
43 views
Could this be a secure multiparty secret sharing scheme?
Suppose that $y$ is a uniform random variable that is defined over the field (or group or abelian group) $Y$. Let us suppose that there are $N=\{1,2,\cdots,i\cdots,N\}$ agents and only one of them, ...
1
vote
2answers
68 views
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 ...
1
vote
0answers
57 views
Understanding notation of probability of algorithm equal to 1
I would like to understand what the following notation means:
let $A$ be a polynomial-time algorithm and say $X(a,n)$ is a probability ensemble where $a\in\{0,1\}^*$ and $n\in\mathbb{N}$.
What does ...
1
vote
1answer
75 views
What are the expected values of a particular rotational-XOR property of a sequence of random bitstrings?
Assuming that $x$ is a sequence of $l$ bits and $0 \le n < l$, let $R(x, n)$ denote the result of the left bitwise rotation of $x$ by $n$ bits. For example, if $x = 0100110001110000$, then $$\begin{...
1
vote
1answer
195 views
How are probabilities combined in the game hopping proof technique?
I'm currently studying a paper (Sequences of Games: A Tool for Taming Complexity in Security Proofs) on proving semantic security using the Game Hopping technique by Victor Shoup.
On pages 9-11, he is ...
1
vote
0answers
81 views
One time pad, Proof for a problem
We know 2 plaintexts of length L and 2 ciphertexts of length L(we don't know which one belongs which), assuming each given ciphertext is generated by encrypting one of the given plaintexts by XOR'ing (...
1
vote
0answers
34 views
What is the success probability of a single exploitation attempt for these scenarios
Consider an architectural security measure intended to prevent stack buffer overflow attacks where, instead of storing the return address on the stack, the CPU stores the difference of the stack ...
1
vote
1answer
57 views
Differential Privacy: Gaussian Mechanism when $\epsilon >1$, Laplace Mechanism when $\epsilon = 0$
In Differential Privacy resources, the limiting cases of $\epsilon, \delta$ are not justified well enough.
For example, on Wikipedia, it is said that Gaussian mechanism only works when $\epsilon < ...
1
vote
1answer
45 views
Is the collision chance 2^(n/2) of an n-bit tag τ unchanged if reduced to (n/2)-bits using a reduction of τ to some 2^(n/2) order group element?
If $H(k, Μ) = τ$, in the context where $τ$ is an $n$-bit tag produced as a mac on a key, $k$, and a message, $M$, through a keyed-hash function, $H$, is there a function $F(τ) = T$ that transforms $τ$ ...
1
vote
1answer
36 views
How was the adversary's success probability calculated in this 2002 paper by Dodis, Katz, Xu, Yung about key-insulated signature schemes?
In this paper ("Strong key insulated signature schemes" by by Dodis, Katz, Xu, Yung (2002)), I understand most of the proof for Lemma 1 (pg. 9); I struggle with how some of the probability ...
0
votes
2answers
188 views
What are the fastest algorithms that sample from the uniform distribution?
Lots of cryptography algorithms rely on pseudorandom number generators. Sometimes, given a plaintext, you need to generate a pseudorandom number from it. What are some fast algorithms that do so?
I've ...
1
vote
0answers
15 views
How hypergeometric sampling works in order preserving encryption?
According to https://crypto.stackexchange.com/a/8800/53007:
Start with the entire domain [M] and range [N]. Call y←N/2 our range
gap. Now using our key k we generate some pseudorandom coins and give
...
1
vote
1answer
36 views
Understanding this notation for the probability distribution of order preserving encryption
I'm reading this PDF: https://link.springer.com/content/pdf/10.1007/978-3-642-01001-9_13.pdf about order preserving encryption functions and there's this on page 9 (or 232):
It's describing the ...
2
votes
1answer
57 views
Checking Independence of combination of uniform random variables to use pilling up lemma
My question is very basic one. Suppose $a_0, a_1, a_2, a_3, a_4, b_0, b_1, b_2, b_3, b_4$ are $10$ uniform random variables from $\{0,1\}$ independent of each other. Now there are expressions of the ...
1
vote
0answers
36 views
Simple shift cipher probability exercise
This is a super simple probability exercise:
If we have a simple shift/ceasar cipher.
Let's say that there are only three messages encypted.
...
2
votes
1answer
99 views
trying to identify the key of a vigenere cipher via brute force
I'm working on a bit of an ARG game type thing that uses the vigenere cipher. what im wondering is the chance a player could brute force said cipher by simply checking all possible key sequences of ...
1
vote
0answers
47 views
If a different plaintext may produce the same ciphertext, is the system perfectly secure?
Define the injective map $\phi: \Omega\rightarrow \mathbb{N}$, such that $\Omega=\mathcal{A}^n$ denotes the set of all strings of length $n\in\mathbb{N}^*$ from an alphabet $\mathcal{A}$ of elements $...
9
votes
6answers
5k views
Is it possible that a SHA256 hash has the same hex character over and over again?
In theory, there are infinite inputs, that you can hash with SHA-256. So theoretically it would be possible that one hash string would read 0xaaaaaaaa...
But would ...
2
votes
2answers
76 views
What is the best way to accurately describe this statistical probability? [closed]
I am in the process of writing some information for an App. I need to express the probability of something happening but in a way that is correct but easy to understand. I'm confused on the actual ...
0
votes
1answer
239 views
Calculating minimum number of messages hashed a 50% probability of a collision (Birthday Paradox)
I encountered this while solving a crypto puzzle. This is the puzzle.
...
0
votes
0answers
22 views
Conditional probability being Constant in Threshold Cryptography
I am working on Threshold implementation of algorithms to prevent side channel attacks. I am not that much proficient in Statistics and Probability theory. I want to know what is the significance of ...
2
votes
1answer
88 views
GetModulus negligible probability
I have this textbook definition, I shall include below.
GenModulus denotes a ppt algorithm that, on input $1^n$, outputs $(N, p, q)$ where $N = p\,q$ and (except with negligible probability) $p$ and $...
2
votes
1answer
111 views
Cryptography Engineering - Design Principles and Practical Applications - Chapter 9 Generating Randomness - Section 9.4 The Generator
I'm currently reading "Cryptography Engineering - Design Principles and Practical Applications" written by "Niels Ferguson, Bruce Schneier, Tadayoshi Kohno" published by Wiley in ...
0
votes
1answer
77 views
How to deal with concrete security against lots of queries?
In general, $O(1/\epsilon^2)$ queries are required to distinguish between two distributions that are statistically close at most $\epsilon$.
This informal state deals with the required number of ...
1
vote
1answer
60 views
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 ...
4
votes
3answers
246 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....
1
vote
2answers
119 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 ...
-1
votes
1answer
112 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 ...
3
votes
1answer
97 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 ...
2
votes
0answers
31 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
votes
1answer
231 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 ...
1
vote
1answer
76 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 $...
5
votes
1answer
545 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 ...
0
votes
2answers
139 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 ...
0
votes
1answer
54 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 ...
1
vote
0answers
90 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 ...
2
votes
1answer
314 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 ...
1
vote
1answer
102 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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vote
0answers
196 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 ...
1
vote
1answer
95 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 ...
0
votes
1answer
65 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.
2
votes
0answers
42 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 ...
0
votes
3answers
568 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 ...
1
vote
0answers
40 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 ...
