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首页LVH密码学基础教程：深入理解Crypto101

LVH密码学基础教程：深入理解Crypto101

Crypto101

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" Crypto101 密码学教程是LVH（Laurens Van Houtven）在2013年至2017年期间创作的一份基础加密学教育资源，它遵循Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) 许可协议。这个教程的目的是提供一个易于理解的密码学基础知识概览，而不是商业用途的替代品。根据许可协议，用户可以自由地： 1. 分享：可以在任何媒体或格式下复制和分发这些材料，包括但不限于文本、博客文章、课堂讲义等。 2. 适应：允许对内容进行修改、改编和扩展，只要保持原始作者的荣誉，并且表明所做的更改，但不能暗示许可方对你的使用表示支持。 3. 非商业使用：禁止将这些材料用于商业目的，这意味着它们主要用于教育、研究或其他非盈利性质的活动。 4. 无额外限制：你不得添加法律条款或技术措施来限制他人按照许可协议规定的权利行事。请注意，对于公共领域内的元素或者许可明确允许使用的部分，你不需要遵守此许可证。这是一份鼓励知识共享和传播的教育资源，旨在帮助学习者理解和探索密码学的基本原理和概念，如加密算法、哈希函数、公钥/私钥系统、数字签名等。对于希望深入了解密码学的人来说，这是一个宝贵的起点。"

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CHAPTER 4. ACKNOWLEDGMENTS 16

Following the public release,many more people contributed changes.

I’d like to thank the following people in particular (again, in no partic-

ular order):

• coh2, for work on illustrations

• TinnedTuna, for review work on the XOR section (and others)

• dfc, for work on typography and alternative formats

• jvasile, for work on typefaces and automated builds

• hmmueller, for many, many notes and suggestions

• postboy (Ivan Zubo ), for many reported issues

• EdOverow, for many contributions

.. as well as the huge number of people that contributed spelling,

grammar and content improvements. ank you!

Part II

Building blocks

Exclusive or

5.1 Description

Exclusive or, often called ”XOR”, is a Boolean

binary

operator that is

true when either the rst input or the second input, but not both, are

true.

Another way to think of XOR is as something called a”programmable

inverter”: one input bit decides whether to invert the other input bit, or

to just pass it through unchanged. ”Inverting” bits is colloquially called

”ipping” bits, a term we’ll use often throughout the book.

In mathematics and cryptography papers, exclusive or is generally

represented by a cross in a circle:

⊕

. We’ll use the same notation in

this book:

Uses only ”true” and ”false” as input and output values.

Takes two parameters.

CHAPTER 5. EXCLUSIVE OR 19

e inputs and output here are named as if we’re using XOR as an

encryption operation. On the left, we have the plaintext bit

. e

is just an index, since we’ll usually deal with more than one such bit.

On top, we have the key bit

, that decides whether or not to invert

. On the right, we have the ciphertext bit,

, which is the result of

the XOR operation.

5.2 A few properties of XOR

Since we’ll be dealing with XOR extensively during this book, we’ll

take a closer look at some of its properties. If you’re already familiar

with how XOR works, feel free to skip this section.

We saw that the output of XOR is 1 when one input or the other

(but not both) is 1:

0 ⊕ 0 = 0 1 ⊕ 0 = 1

0 ⊕ 1 = 1 1 ⊕ 1 = 0

ere’s a few useful arithmetic tricks we can derive from that.

CHAPTER 5. EXCLUSIVE OR 20

1. You can apply XOR in any order: a ⊕ (b ⊕ c) = (a ⊕ b) ⊕ c

2. You can ip the operands around: a ⊕ b = b ⊕ a

Any bit XOR itself is 0:

a ⊕a = 0

. If

is 0, then it’s

0 ⊕0 = 0

;

if a is 1, then it’s 1 ⊕ 1 = 0.

Any bit XOR 0 is that bit again:

a ⊕ 0 = a

. If

is 0, then it’s

0 ⊕ 0 = 0; if a is 1, then it’s 1 ⊕ 0 = 1.

ese rules also imply a ⊕ b ⊕ a = b:

a ⊕ b ⊕ a = a ⊕ a ⊕ b (rst rule)

= 0 ⊕ b (second rule)

= b (third rule)

We’ll use this property often when using XOR for encryption; you

can think of that rst XOR with

as encrypting, and the second one

as decrypting.

5.3 Bitwise XOR

XOR, as we’ve just dened it, operates only on single bits or Boolean

values. Since we usually deal with values comprised of many bits, most

programming languages provide a ”bitwise XOR”operator: an operator

that performs XOR on the respective bits in a value.

Python, for example, provides the

(caret) operator that performs

bitwise XOR on integers. It does this by rst expressing those two

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图书：Crypto 101，有关密码学的入门书籍

加密101：这本书这是的源代码库，这是有关密码学的入门书籍。执照请参阅文件。笔译目前，crypto101仅提供英语，但。建筑在存储库的根目录中运行make book ，以将源文件转换为所有受支持格式的呈现版本。依存关系由于存在大量依赖关系，强烈建议使用docker： docker build -t crypto101 docker/ docker run --rm -it -v " $( realpath . ) " :/repo -u " $( id -u ) " crypto101 ./make-lang YOUR_LANGUAGE_CODE html latexpdf epub YOUR_LANGUAGE_CODE必须为有效的，例如en ， fr ， ko或zh_CN 。您可以在专用的dockerfiles中找到和依赖项的安装过程。

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