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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Finding key for Hill Cipher
Suppose a Hill cipher with block size 2 is given, with known plaintext and corresponding encryption
$E_K( ‘guns’ ) = ‘YGJC’$
What are the possibilities for the key $K$?
My initial thought was to setup:...
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the hardness of Conjugacy Search Problem in matrix groups
I learned that the Conjugacy Search Problem is considered as a mathematically hard problem to solve and can be used for cryptography.
Conjugacy search problem: Let G be a non-abelian group. Let g,h∈G ...
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Exact algorithms (e.g. in coding theory, cryptography) using the field of rational numbers
I noticed that most algorithms in coding theory or cryptography are based on the integers and some arithmetic results (e.g. RSA) or on the finite fields (e.g. Elliptic curve cryptography or BCH codes)....
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(How) can two words differ in fewer places than the minimum distance?
I'm working on an unassessed course problem (which I paraphrase for conciseness),
Let $C$ be the code over $\mathbb{F}_5$ with generator and parity-check matrices
$$G=\begin{pmatrix}2&3&4&...
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Given two public keys and $e$ to find a private key
I am taking a cyber security class recently. I was wondering if I was given two public keys, $n_1$ and $n_2$ (and $e$ the exponent)--how would one generate a private key for $n_1$? In this scenario, $...
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Recommendations for Papers on LLL Algorithm
Asked a professor who does research in cryptography for a project opportunity, and he told me to go read about Lenstra-Lenstra-Lovasz or LLL algorithm. I read the following paper and found the topic ...
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Can an algorithm prove that it produced its own output?
Apologies in advance for my ignorance. I am working on a research question in a different area, and it would be helpful to know the answer to the following question, or even a reference to any such ...
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If $x^e \equiv y^e \pmod N $, is $x \equiv y \pmod N$ where $\gcd(e,\phi(N))=1$?
Let $x,y,e,$ $p$, and $q$ be any integers where $N= pq$ and $e$ is coprime to $(p-1)(q-1)$ . I am wondering whether $x^e \equiv y^e \pmod N $ implies $x \equiv y \pmod N$, and if so how to show this. ...
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Existence of the shortest vector in a lattice [closed]
I am studying integer lattices in $\mathbb{R}^n$. I know that since there are no accumulation points in the lattice, the shortest vector always exists. Is there any way that one could prove it?
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Why do we use prime numbers with RSA? [closed]
I coded a small example of RSA in Python. When filling p and q, I mistakenly put in two numbers that were not prime numbers. And ...
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Distribution in the amount of roots of a randomised polynomial over the ring $\mathbb{Z}_{2^k}$.
I'm now trying to develop some protocols to work with cryptography over the ring $\mathbb{Z}_{2^k}$, and I tried to find a ring version of the Schwartz Zippel lema. The main idea is to work in a ring ...
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Proof of correctness of RSA sufficient? [duplicate]
In a lecture I am taking the following proof for the RSA cryptosystem is given:
$m^{ed} \equiv m^{ee^{-1}} \equiv m^1 \equiv m \pmod N$
where $N = pq$; $p$,$q$ prime; $2 < e < \phi(N)$; $e$,$\...
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Trouble detecting cyclic group order crossovers in elliptic curve additions
There's a problem in detecting whether the sum of public key addition has crossed the cyclic group order boundary
For this example, think of public keys $Pub$ as private keys $Priv$, (private scalars),...
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Schnorr signature variant with sum c and k instead of multiplication
I am reading about Schnorr signature and I though what if we calculate response as $r = \alpha + c + k$ instead of $r = \alpha + c*k$? Will it make scheme more insecure? Are there any name for this ...
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Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. And find the elements of a finite field with 9 elements.
Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. Using this fact construct a finite field $\mathbb{F}_9$ of $9$ elements. If $\alpha$ is a root of $f(x)$, then find ...
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