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wildtopology.com | ||
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dominiczypen.wordpress.com
Let $latex \omega$ denote the first infinite cardinal - that is, the set of non-negative integers. Let $latex p_0 = 2$ be the smallest prime number, and let $latex (p_n)_{n\in\omega}$ enumerate all prime numbers in ascending order. Let $latex \mathcal{U}$ be a free ultrafilter on $latex \omega$. We consider the field $latex F = \big(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z}\big)/{\mathcal... |
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fabricebaudoin.blog
Exercise 1.Solve Exercise 44 in Chapter 1 of the book. Exercise 2.Solve Exercise 3 in Chapter 1 of the book. Exercise 3.Solve Exercise 39 in Chapter 1 of the book. Exercise 4.The heat kernel on $latex \mathbb{S}^1$ is given by $latex p(t,y) =\frac{1}{2\pi}\sum_{m \in \mathbb{Z}} e^{-m^2 t} e^{im y} =\frac{1}{\sqrt{4\pi t}} \sum_{k \in \mathbb{Z}} e^{-\frac{(y... |
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xorshammer.com
An arithmetic statement is one made up of quantifiers ``$latex \forall n\in\mathbb{N}$,'' ``$latex \exists n\in \mathbb{N}$,'' the logical connectives ``and,'' ``or,'' ``not'', function symbols $latex \times$, $latex +$, constants $latex {0}$, $latex 1$, and variables $latex n$ which are bound by the aforementioned quantifiers. It is known that there is no algorithm which will decide... |
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www.jeremykun.com
In this article I'll cover three techniques to compute special types of polynomial products that show up in lattice cryptography and fully homomorphic encryption. Namely, the negacyclic polynomial product, which is the product of two polynomials in the quotient ring $\mathbb{Z}[x] / (x^N + 1)$. As a precursor to the negacyclic product, we'll cover the simpler cyclic product. All of the Python code written for this article is on GitHub. |
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