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| | pfzhang.wordpress.com
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| | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers....
| | blog.lambdaclass.com
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| | Elliptic curves (EC) have become one of the most useful tools for modern cryptography. They were proposed in the 1980s and became widespread used after 2004. Its main advantage is that it offers smaller key sizes to attain the same level of security of other methods, resulting in smaller storage
| | www.jeremykun.com
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| | 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.
| | ropmann.wordpress.com
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