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www.jeremykun.com | ||
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qchu.wordpress.com
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| | | | | In this post we'll describe the representation theory of theadditive group scheme$latex \mathbb{G}_a$ over a field $latex k$. The answer turns out to depend dramatically on whether or not $latex k$ has characteristic zero. Preliminaries over an arbitrary ring (All rings and algebras are commutative unless otherwise stated.) The additive group scheme $latex \mathbb{G}_a$ over... | |
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andrea.corbellini.name
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| | | | | [AI summary] The text provides an in-depth explanation of elliptic curve cryptography (ECC), covering fundamental concepts such as elliptic curves over finite fields, point addition, cyclic subgroups, subgroup orders, and the discrete logarithm problem. It also discusses practical aspects like finding base points, cofactors, and the importance of choosing subgroups with high order for cryptographic security. The text emphasizes that ECC relies on the difficulty of solving the discrete logarithm problem on elliptic curves, which is considered computationally hard and forms the basis for secure cryptographic protocols like ECDH and ECDSA. | |
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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loup-vaillant.fr
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| | | Despite advice to the contrary, I have implemented my own crypto for serious use. Here's how. | ||
