What is Cryptography?

The process or skill of communicating in or deciphering secret writings or ciphers.

Symmetric Ciphers

They have some problems

Caesar Cipher

Input: Hello Team!
Output: Khoor Whdp!

Book cipher (Ottendorf cipher)

(Using War and Peace, [page#-word#])

Input: Hello Team!
Output: 285-32 120-5

Asymmetric Ciphers

You make two keys:

A, B

And a process where...

process(A, your_message) => garbage

process(B, garbage) => your_message

the inverse is also true

A        B

?

Let's get clever

Ensures that it came from Blue, and only Orange can open it

Ex1. Only Orange can open

Ex2. Came from Blue

Let's put both together

( )

Time to get mathy

message^{public key} \textbf{mod} \;standard = garbage

message^{public key} \textbf{mod} \;standard = garbage

garbage^{private key} \textbf{mod} \; standard = message

garbage^{private key} \textbf{mod} \; standard = message

the public and private key are very special in that they have this relationship.

Two Methods:

RSA

Elliptical Curves

Modular arithmetic is weird.

= 2 + 13 mod 12
= 15 mod 12
= 3

Every every prime number, there exists two numbers where this is true:

anything^{A} \textbf{mod} \; prime = anything^{B} \textbf{mod} \; prime

anything^{A} \textbf{mod} \; prime = anything^{B} \textbf{mod} \; prime

anything^{5} \textbf{mod} \; 71 = anything^{29} \textbf{mod} \; 71

anything^{5} \textbf{mod} \; 71 = anything^{29} \textbf{mod} \; 71

These two numbers are your keys

Public Key: Point A + Point E

Private Key: Number of hops from A to E

There exists special curves where...

y^2 = x^3 + ax + b

y^2 = x^3 + ax + b

That's all I got.