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% Imports
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\usepackage{amsmath}
\usepackage{multicol}
\usepackage{ragged2e}
\usepackage{blindtext}
\usepackage[english]{babel} %this is the dictionary you will use
\usepackage{graphicx,mathdots,chemarr,fancyvrb,comment} %some more packages
\usepackage{tikz} %some more packages
%the packages from here on will help with creating a graph
%tikzpicture
\usepackage[many]{tcolorbox}
\usepackage{wrapfig}
\usepackage{scalerel}
\usepackage{pict2e}
\usepackage{tkz-euclide}
\usepackage{scalerel}
\usepackage{pict2e}
\usepackage{tkz-euclide}
\usepackage{listings}
\usepackage{color}
\usepackage{xifthen}
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	before skip = 0.2cm,    % add extra space before the box
	after skip = 0.5cm      % add extra space after the box
}                           % setting global options for tcolorbox
\makeatletter


%My Custom Commands
\newcommand{\mnewline}{\newline\newline\newline}
\newcommand{\mline}{\rule{0.5cm}{0.5pt}}
\newcommand{\proj}[1]{\text{Proj}_{#1}}
\newcommand{\st}{\ni:}
\newcommand{\evaline}[2]{\Big|^{#1}_{#2}}
\newcommand{\nulli}[1]{\text{Null }{#1}}
\newcommand{\ran}[1]{\text{ran }{#1}}
\newcommand{\col}[1]{\text{Col }({#1})}
\newcommand{\re}[1]{\text{Re}({#1})}
\newcommand{\im}[1]{\text{Im}({#1})}
\newcommand{\spa}[1]{\text{span}\{{#1}\}}
%\newcommand{\neproof}[3]{$\text{Let } \epsilon > {#2} \text{ be given}$\\\text{Choose $N = {#1}$\text{ Suppose $n > N  > {#3}$}}}
\newcommand{\neproof}[3]{ %The first one is without the 3rd argument and the second one is
	\ifthenelse{\isempty{#3}}{$\text{Let } \epsilon > {#2} \text{ be given}$\\\text{Choose $N = {#1}$\text{ Suppose $n > N$}}}
	{$\text{Let } \epsilon > {#2} \text{ be given}$\\\text{Choose $N = {#1}$\text{ Suppose $n > N  > {#3}$}}} 
}
\newcommand{\infobox}[2]{\begin{InfoBox}
		\smash{\raisebox{-5pt}{\includegraphics[width=0.77cm,height=0.68cm]{information}}}{\bf #1}\newline\newline
		{#2}
\end{InfoBox}}
\newcommand{\warningbox}[2]{\begin{WarningBox}
		\smash{\raisebox{-6pt}{\includegraphics[width=0.70cm,height=0.70cm]{warning}}}
		{\bf #1}\newline\newline
		{#2}
\end{WarningBox}}
\newcommand{\theorybox}[2]{\begin{TheoryBox}
		\smash{\raisebox{-6pt}{\includegraphics[width=0.70cm,height=0.70cm]{theorem}}}
		{\bf #1}\newline\newline
		{#2}
\end{TheoryBox}}
\newcommand{\notebox}[2]{\begin{NoteBox}
		\smash{\raisebox{-6pt}{\includegraphics[width=0.55cm,height=0.70cm]{reminder}}}
		{\bf #1}\newline\newline
		{#2}
\end{NoteBox}}
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
	\hskip -\arraycolsep
	\let\@ifnextchar\new@ifnextchar
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	leftrule = 6pt % left rule weight
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	leftrule = 6pt % left rule weight
}
\newtcolorbox{TitleBox}{
	boxrule = 2pt,
	rounded corners
}
\makeatother
\usepackage[letterpaper,left=6mm,includemp=true,marginparwidth=12mm,marginparsep=1mm,reversemarginpar,right=19mm,
includefoot=true,top=19mm,nohead,footskip=12mm,bottom=6mm]{geometry}
% Here are the custom commands I have created. They are increadibly retarded
% mnewline: creates 3 newlines
% mline: Creates a horizontal line
% proj: Creates a Proj with a suitable subscript - Takes an argument
% st: creates a ni and a : as the 'such that'
% evaline: creates a vertical line for evaluated definite integrals. First argument is upper limit, second is lower. - Takes two arguments
% nulli: creates a Null (with a whitespace) - Takes an argument
% col: creates a Col (with a whitespace) - Takes an argument
% ran: creates a ran (with a whitespace) - Takes an argument
% re: creates a Re() - Takes an argument
% im: creates a Im() - Takes an argument
% sp: creates a span{} - Takes an argument
% neproof: Creates a cookie cutter N-epsilon proof. First argument set's N's value and second argument sets epsilon greater than value and the third (optional) argument sets the n > N > value. IF YOU DO NOT WANT THE THIRD ARGUMENT YOU NEED AN EMPTY CURLY BRACKET
\begin{document}
	\setlength{\parindent}{1cm}
	\begin{center}
		{\bf \Large CSCD27}
	\end{center}
	\begin{TitleBox}
		\begin{center}
			{\bf 09/10}
		\end{center}
	\end{TitleBox}
	{\bf Big Definitions}\\
	Safety is defined as reasonable input for reasonable output, or correctness, or the program does what is intended.\\
	Security is defined as unreasonable inputs get reasonable outputs.\\
	Threat -- Possibility of damage, can be tangible, possible, whatever. A threat can be accepted or not accepted. Rejected threats are ones that are not cost-effective or low possibility.\\
	Vulnerability -- A weakness in the system, but not necessarily something that can be exploited or no exploit has been discovered yet.\\
	A vulnerability enables a threat, and an attack/exploit takes advantage of a vulnerability. There is a clear differentiation between an attack and a vulnerability. An attack realizes a threat.\\
	Countermeasure -- something done to disable an attack, limit the possibility or consequences of damage. So this can be like a patch or workaround. It mitigates a thread or removes/reduces a vulnerability\\
	CIA -- An acronym for the three pillars of security, confidentiality, integrity and availability. For example, confidentiality means only the student can see their own grade, integrity is only the professor can enter a grade, availability just refers to keeping important systems online like 2FA. There are sub properties, see slides for Venn diagram.\\
	Anonymity vs Pseudonymity -- Pseudonymity is like hiding behind a username or pseudoname, like a Reddit account. But as you make posts, people can begin tracing stuff back to you. True anonymity eliminates this.\\
	The properties of CIA can be conflicting or even undesirable.\\
	An example of where properties are conflicting, voting is an example.\\\\\\
	{\bf Classical Cryptography}\\
	Two kinds of cryptography fields, one is the pure mathematical side building the individual tools. Then there is a technical side that utilizes these tools to build crypto protocols.\\
	Caesar Cipher -- Oldest cryptosystem. It is a {\bf shift cipher} where you shift the alphabet by a fixed offset.\\
	Interception -- Attacker obtains and reads the message. (Confidentiality)\\
	Modification -- Attacker changes the message (Integrity)\\
	Fabrication -- Attacker injects a message (Integrity)\\
	Interruption -- Attacker disrupts communications (Availability)\\
	Cryptography only addresses confidentiality. Secure messages/channel over an insecure medium.\\
	Plaintext -- Original message intended for author and recipient.\\
	Ciphertext -- Encrypted message.\\
	Encryption -- Turning plaintext into ciphertext.\\
	Decryption -- Turning cipertext into plaintext.\\
	Cryptographic algorithm -- Method to do encryption and decryption.\\
	Cryptographic key -- Input used by algorithm to perform the actions. For example case of Caesar cipher the key is the shift offset.\\
	N-Bit security entropy -- The measure in which we measure the strength of the algorithm. It is the number of bits to encode the number of possible keys. So for example in the Caesar cipher, with 25 possible rotations (not counting a full rotation which is dumb) you need 5 bits.\\
	100 bits is the minimum threshold to not be considered a weak key.\\
	In the example big picture, an integrity attack can be where Mallory takes the message and sends it to someone else other than Bob, or resends it to Bob later.\\
	Kerckhoffs' Principle -- ``The enemy knows the system'', or in other words, there is no security by obscurity. A cryptography algorithm should not rely on the fact the algorithm itself is secret. This only doesn't apply to the key.\\\\
	Types of ciphersystem attacks:\\
	Brute force: for $n$ keys it takes on average $n/2$ attempts to crack.\\
	Ciphertext Known: (you are given) One or more random ciphertexts are known.\\
	Known Plaintext: (you are given) You know a plaintext with it's associated ciphertext.\\
	Chosen Plaintext: (you get to interact with the system) You feed the cipher a plaintext and get the associated plain text.\\
	Chosen Ciphertext: (you get to interact with the system) You have the ciphertext and you can decode to get the plaintext.\\\\
	So Ciphertext Known for Caeser Cipher, you can try can try to reverse engineer the cipher by analysis, as opposed to brute forcing. So if you know something about the nature of the plaintext, you can do this.\\
	Chosen Plaintext and Ciphertext are really just mirrors. So for Caesar cipher for chosen plaintext, you input a plaintext character and count the offset. For Chosen Ciphertext you do the same but with the ciphertext character (so basically in this case it looks identical).\\\\\\
	Monoalphabetic Cipher -- A cipher that does not change the frequency of letters in a message. This is generally a bad idea. They are vulnerable to statistical analysis.\\
	Substitution is an example of a monoalphabetic ciper (along with Caesar). It is more resilient against brute force, but is vulnerable still to the other four attacks.\\ You can combine known plaintext with bruteforce, it is common to mix them.\\\\
	Polyalphabetic Cipher. Our example is a Vigenere cipher. Instead of a fixed permutation, we have a phrase or word as our key instead of a number or set of permutations.\\
	A big enough $n$ makes brute force not possible for Vigenere. Statistical analysis is also dependent on length and the quality of the key. In an attack what you could do is try to reduce the search area to make brute force more viable. The other attacks are still possible if not easy.\\
	OTP is the best cipher eva. The key is an infinite random string. The reason why its called One Time Pad, you can only use the key once. In this case we use XOR to compute the ciphertext. Using the random string, we eliminate statistical analysis. And since we use the key only once, known plaintext is no good. Problem with this is that we have to constantly exchange keys. Many ciphersystems base themselves on OTP.\\
	Transposition Cipher is where we have a message of a fixed size, and each message we shuffle around characters in the messages. The key is the set of permutations. Brute force again depends on the entropy. You can still do some analysis if you have a known ciphertext. Known Plaintext you can reduce size, Chosen you send the alphabet and match the letters.\\\\
	The pillars of modern cryptography are: Diffusion, Confusion and Randomization. Confusion and Randomization are good enough by themselves and are used to build a stream cipher. Diffusion and Confusion can be mixed together to build a block cipher.\\\\
	Random Keys with high entropy are best.\\\\
	\end{document}