Public Key Exchanges

The videos below are for review only.  Watch them for help when developing protocols for the final challenge.  You can review Modular Arithmetic Here.

Summary:
1. What is the Diffie Hellman Exhange?
2. Why is this a good method?
3. Why is this called a public key exchange?

Diffie Hellman

RSA Exchange

Division Algorithm and Modular Arithmetic

Watch this video as many times as you need. WSQ in your notebooks.  

W = Work out any problems assigned during the video in your notes.

S = Summarize the video.  This can be done using bullets.  List at least 3 things you learned from this video or important things to remember about this lesson.

Q = Question you have or a question someone else might have about the information in the video. This can also be a question that sparks discussion or causes other to think about the topic more deeply.

Summary Questions:

1. How do you know there is a remainder when completing long division?
2. How would you describe modular arithmetic over the phone to a friend?
3. What operation does modular arithmetic use?
4. How does modular arithmetic affect the order of operations?

Ciphers

The earliest evidence we have of the use of cryptography dates back to around 1900 BC in a tomb in Egypt.  While many tombs had hieroglyphics written on the walls, this particular tomb used very unusual symbols in the place of those that are well known.  It is believed that the author was not trying to hide the message, rather project high status.  

Classic works from early civilizations describe espionage service,s particularly in India, where spies were given encrypted assignments.

It is presumed that the Egyptians as early as 1900 BC used cryptography in hieroglyphic writings to hide the meaning of a message.  The Greeks used a methods which involved a hexagonal prism shaped stick, called a scytale, wrapped in tape to write a message that, when unwound, had no meaning.  The recipient of the message would decrypt the message by re-wrapping the message around an identical scytale to read the message.  

Greek Scytale used to encrypt and decrypt messages.

Around 100 BC, Julius Caesar used encrypted messages to army generals during war times, giving us the most famous,  and uniquely named, substitution cipher, the Caesar Cipher.

A cipher is a secret way of sending a message by disguising the characters of your message with a code.

Substitution ciphers encrypt secret messages by switching one character for another.  For example, if a cipher was shifted by 4, the letter "A" would become "E" since it is 4 characters past "A" in the alphabet.  See the examples below:

The cipher above has been shifted by 2.  So, If you wanted to say "HELLO", you would write "JGNNQ"

This cipher split the alphabet so that each letter corresponds to another letter in the alphabet.

There are many more ways to create the key for a substitution cipher.

Decryption of a substitution cipher requires both the sending and receiving party to have a copy of the key.  Here in lies the problem.  Most keys throughout history have been compromised as a result of stolen keys.  In order to decrypt the message, you need to be told or given a copy of the key.  This leaves a lot of space for eaves droppers to overhear the key or physical copies left along for only a few moments can be taken by a thief.

Many people, have been able to crack the code by studying the encrypted message and looking for repeated characters.  Often the most common symbols substitute a space between words or most frequently used letters (think Wheel of Fortune's RSTLNE).  The ability to keep or crack codes have greatly altered the outcomes of wars, thus changing the course of history.

Explore a variety of ciphers we have today.

Try cracking theses Caesar Ciphers by examining repeated symbols. This applet only works when opened in Modzilla FireFox.  Warning:  Your computer must have Java installed.

Looking for something more challenging?  Check out this applet on Substitution Ciphers.  Can you crack these codes?  This applet only works when opened in Modzilla FireFox.  Warning:  Your computer must have Java installed.

Sources:                                                                            https://securityblog.redhat.com/2013/08/14/a-brief-history-of-cryptography/  http://www.studentpulse.com/articles/41/a-brief-history-of-cryptography 

What do you know about Cyber Security?

Take this quick pretest and survey before we get started.