# Questions tagged [probability]

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

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### Statistics-heavy crypto papers

I'm currently taking a course in which we choose a stats-heavy paper and analyse it, summarising our work in the form of a written report and presentation. I have tried to find such a paper in crypto, ...
1 vote
44 views

### Unbounded distinguishers and statistical indistinguishability

In constructing a SHVZK simulator for a sigma protocol I am working on I have encountered some fairly basic questions, but ones which are not often discussed in textbooks and papers - consider the two ...
1 vote
64 views

### Biasedness of the XOR variable of two independent biased boolean variable

My question is very basic one. Suppose there are two independent boolean variable $X_1$ and $X_2$. It is given that $X_1$ is biased towards $0$ and $X_2$ is biased towards $1$ with same amount of bias....
79 views

### Where does the 8 come from? Generic Search Problem with Bounded Probabilities

I am working with lossy ID-schemes and their security in the QROM. Following the article of Kiltz et al. , I am at a loss of the number 8 appearing in most reductions throughout the article. I know it ...
73 views

### The second moment and fourth moment of $\mathcal{P}(V)$?

Backgroud: I am reading the paper "Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures". (here is the link). And I got stuck in understanding the computation of moment. ...
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### The different bounds of PRP/PRF switching lemma

The PRP/PRF switching lemma is usually denoted as follows: I understand the proof of this version of the bound $\frac{q(q-1)}{2^{n+1}}$ and the game-playing technique behind it. However, I came ...
76 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 ...
1 vote
134 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 ...
105 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 ...
48 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
1k 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
80 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
65 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 ...
177 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
319 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
128 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
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### 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
510 views

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### 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 ...
79 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 ...
1 vote