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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Elliptic curves and zero-knowledge constructions are not shown over non-prime finite fields. Why?
What are the reasons that cryptography-related constructions -- such as featured in excellent explainers on elliptic curves on RareSkills and Practical Cryptography for Developers, and all the ...
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What background is needed to understand lattices?
I'm trying to read the paper Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known but the subject matter is over my head.
I have an academic background in Applied ...
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What does "a key is uniform" mean in cryptography?
In the lecture on Coursera platform, the inequality below was shown: there exists an algorithm $A$ such that
$$\underset{{k \overset{R}{\longleftarrow} \mathscr{K}}}{\operatorname{Pr}}\left[\left.A(G(...
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What does $\mathbb{Z}_2^3$ mean? [closed]
What does $\mathbb{Z}_2^3$ mean? Is the subscript $2$ a modulo and the superscript $3$ dimensions of each element? I am studying lattice cryptography and set theory and I would like to know the how ...
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Finding the period of the BBS sequence
Let $n=pq$, where $p,q$ are primes and $p \equiv q \equiv 3 \mod 4$. Choose an integer, $x_0$, such that $x_0$ and $n$ are co-primes. We define the sequence:
\begin{align}
x_i = x_0^{2^i} \mod n
\end{...
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Unexpected Result from Finite Field Calculations in GF(2^8)
I'm performing calculations within the finite field $GF(2^8)$ and I can't seem to get the expected results. This is my first time working with finite fields, so my understanding is quite basic. I ...
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Distinct derivations of polynomial over finite field
I am a student studying algebra and cryptography.
I wonder below question is possible.
Can I make some polynomials $f(x)$ over finite field that all derivations $f^{(k)}(x)$ are distinct when x is ...
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Prove that if $e.d \equiv 1 \bmod (p-1)(q-1)$ then it’s impossible to have $e.d \equiv 1 \bmod pq$
I am studying R.S.A. cryptosystem and here is the question that came to my mind. Let’s pick $p, q$ to be two primes and $n = p * q$. From that we calculate Euler’s totient function:
$$
\phi(n) = (p - ...
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Time to Find an Elementary Antiderivative of an Elementary Differential Form?
So, in encryption theory, a basic principle is that one has an operation that can be computed in a "forward direction" relatively quickly but for which computing in the "reverse ...
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Testing a Pseudo-Random Number Generator Algorithm
I created a pseudo-random number generator that creates random bits from given numbers. For better visualization, suppose that we have inputs "a", "b", "ab", "abc&...
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About calculating isogeny between two elliptic curves
I'm trying to understand Vélu formulas for calculating isogenies. I took an elliptic curve $E: y^2 = x^3 + 3x + 5$ over $GF(7)$. So I've got the following points on this curve:
\begin{equation}
\{\...
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Binary multiplication in Galois Field GF(2^8)
I am working on a project (high school), and I need to explain the process of AES MixColumns for one of the parts.
I am trying to show an example of the matrix multiplication in MixColumns that uses ...
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Are high-dimensional versions of NTRU cryptosystem more secure?
The basis for this question is a 1-dimensional NTRU cryptosystem.
After some literature inspection I have found out it can be also generalised into higher algebras: quaternions (QTRU) and octonions (...
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ElGamal signature scheme problem and unsure whether my calculations are wrong or that's the answer.
Trying to solve problem with verifying a message through the ElGamal signature scheme and I end up getting two different values.
I'm given a prime number $p = 881$, $e_1 = 3 d = 60$, random value $r = ...
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Clarification on Multiplication in $GF(2^3)$ vs. Boolean Algebra
While experimenting with finite fields, specifically $GF(2^3)$, I stumbled upon a puzzling situation when comparing multiplication operations to those in Boolean algebra.
Let's take two elements $A$ ...
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