Questions tagged [cryptography]

Questions on the mathematics behind cryptography, cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.

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What a hash function is [closed]

What does a hash function represent? How do we define it mathematically and why is it so important? What are the properties of a hash function? (for example is it injective etc.) I would appreciate ...
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Secret sharing scheme of a polynomial function of degree $t$ and how $s$ is calculated after the reconstruction?

Suppose that we want to share a secret $s\in S$ in $t$ parts and we use a secret sharing scheme to do it. Suppose that $|Y|\geq |S|$ is a field sufficiently large with cardinality $p$ and a polynomial ...
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Explain RSA in a math language that I can understand

Having not a super high-level background in math, I can't understand several parts of RSA. I know that you select a number n, and two numbers e and d. Then you have ed= mod(φ(n)), which looking it up ...
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Secret sharing schemes without cryptograpy? [closed]

Are there any details about secret sharing schemes where without cryptographic tools using only some tools of linear algebra and group theory?
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If we re-define this function could it be bijective?

According to this paper in page $4$ where it describes the encryption scheme where a cipher function is defined as it follows $$\rho:T\times Y \to X$$ such that $|Y|\geq |T|$, where $y\in Y$ is the ...
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Proving modular equivalence of sum with noises [closed]

I'm trying to prove the following let $x \xleftarrow{$} \mathbb{Z}_{R'}$be uniformly sampled from$\mathbb{Z}_{R'}$. Let$R = N(R' - 1) + 1$. Now let$ y \xleftarrow{$} \mathbb{Z}_R$. Now let there ...
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How did we discover that this quadratic residue oriented PRNG generates unique numbers in a sequence?

Question (tl;dr) How do we know that even for extremely large numbers like even far past $32^{15}$ (any bigint, or any number really), that as you increment the sequence from $0$ to $n$, $n$ being the ...
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Could someone tell me how such a secret sharing scheme could work?

Taking into account a post here which is the following, I want to make some questions. A secret sharing scheme is a method of distributing finite pieces of information (called shares $\alpha_i$) among ...
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Intuition behind entropy requirements in information theoretic structures

Let $X$ be a random variable that takes values in a finite set $\mathcal{X}$. For any $x\in\mathcal{X}$, let $p(x) = P[X = x]$ be the probability that $X$ takes the value $x$. The entropy of $X$ is ...
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What is the formula for determining how many errors a generator matrix can correct?

I am wondering whether or not there is a generic formula for determining how many errors a generator matrix is able to correct if also provided the field the code is in. For example, given the ...
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Determine if a generator matrix G' also generates the same code C (generated by generator matrix G)

I am asked that if I know that a binary code $C$ is generated by a matrix $G$, how to show that another matrix $G'$ does or does not generate that same code $C$. I have deduced the parity matrix $P$ ...
51 views

Why is the complexity of N=pq for RSA considered as exponential time?

I'm studying about RSA algorithm for 16-bits and noticed that the complexity of N=pq is considered as exponential time. In the algorithm, p and q are two random and distinct strong primes. All the ...
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Cryptography books?

Not sure if this is the correct place to post. If not, maybe someone knows where I should go :) I am curious about cryptography and have taken some related courses through my studies. However I was ...
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Stochastic independence and linear combination of uniform random variables

The following theorems are part of this paper Suppose that $(X_1,\dots,X_k)$ is a family of i.i.d. uniform random variables in $\mathbb{F}^{n}$ (why do we assume that the exponent of the field/set/...
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Encrypting plaintext into ciphertext using RSA.

Good Day, I am attempting to curate ciphertext using RSA encryption given values for the message to encrypt using the encryption algorithm: $c = m^e Mod N$ I understand the elements that go into ...
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Inverse with Extended Euclidean Algorithm

I'm solving a task from https://www.coursera.org/learn/crypto/, particularly the following question: I know that 3x - 5 = 0 and since "ax + b = 0" that implies "x = -b * a^-1", ...
36 views

Infinite Sequence vs. Indexed Set

I'm having a look at this provable cryptography tutorial and early on there is a definition of something called a "probability ensemble" which I haven't come across before. A probability ...
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What is the probability of an attacker winning the following cyber attack scenario?

An attacker with a high hash rate is playing against a network in a proof of work situation. 10% of hashes open up a vulnerability for the attacker, his goal is to find such hashes and broadcast it ...
27 views

Crytpographic theory books?

I was reading a paper in communication mechanisms, and the tools that are used from the authors have been taken from cryptograpgy. If anyone have some time to check the paper nd see the proof of ...
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Location-privacy-preserving protocol for finding relative direction?

Sorry if this is a silly question, but: imagine there are two agents on a finite 2d plane. Each agent knows her location but not the other's, and they want to find the relative directions between them ...
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Is factoring primes $pq$ eqivalent to discovering $p+q$, thus binding $q$ and the search for $(p+q)$ when $(q/p) < 4$?

Background Some crypto algorithms rely principally on the difficulty of factoring two prime numbers $p$ and $q$. For the purpose of this discussion, assume $p<q$. (The top of this article is ...