25 docs tagged with "basic"

抽象代数（Abstract algebra），又名近世代数，是现代数学的重要基础之一，它研究群、环、域这三种基本的代数结构的结构理论。zk理论中大量使用到了抽象代数的概念，因此学习者应该熟悉抽象代数的基础知识。

作为零基础的零知识证明教程，我们将从最基础的整数运算开始学习。相信大部分人在中学时已经学过，会非常轻松。我们还将用python复现整数运算，新手也可以很快上手。

欢迎来到 WTF zk 教程的第2讲！在这一讲中，我们将探讨质数的基础知识。质数在密码学中扮演着关键角色，理解它们对于学习零知识证明至关重要。

这一讲，我们将学习最大公约数和计算它的欧几里得算法，它们在密码学中有广泛的应用。

在本讲中，我们将深入研究欧几里得算法的一种扩展，这一算法不仅可以计算最大公约数，还能找到满足贝祖等式（Bézout equation）的整数解。

这一讲，我们将探讨模运算（Modular Arithmetic），我们在密码学领域会经常用到。

模运算的除法和普通整数的除法有很大区别，理解它非常重要。这一讲，我们将介绍模运算除法，模逆，和计算逆元的方法。

之前我们介绍了模运算中的加减乘除，这一讲，我们介绍模幂和小费马定理。

这一讲，我们将介绍剩余类和著名的中国剩余定理，它可以用来解同余方程组。

给定一个整数 $n$，小于等于 $n$ 的正整数中有多少和 $n$ 互质的数呢？这一讲，我们将研究这个问题，知识点包括单元集和欧拉函数。

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

欧拉定理是数论中的基本定理，表明在模运算中，对于任意整数与模数互质的情况下，该整数的欧拉函数次幂与模数同余于1，为RSA等加密算法提供了数学基础。这一讲，我们将介绍离散对数问题，单元阶，以及欧拉定理。

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been relearning Solidity, consolidating the finer details, and also writing a "WTF Solidity Tutorial" for newbies to learn. Lectures are updated 1~3 times weekly.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.

Recently, I have been revisiting Solidity, consolidating the finer details, and writing "WTF Solidity" tutorials for newbies.