## Increasing Student Engagement

Today I’m giving a presentation on Increasing Student Engagement. Here are some links I refer to during my session:

## Video composition ideas (Michelle So, Hiya Ganju, Sophia Kim and Joyce Liu)

#exploremaths

After brainstorming through several concepts, our group decided to use the mathematical concept found in the novel “The Da Vinci Code”, written by Dan Brown. The novel inspired us as it contains the mathematical concepts of encryption and the golden ratio which we had discussed during one of our lessons in class. One of the most interesting topics we have learnt in class is encryption as codes and methods of cracking them are highly fascinating. In addition, we found that because this mathematical concept appealed to all the members of our group, meaning the entire class would engage with our video composition.

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## The Stigma of the Enigma [Adam Tan]

1. What is the flaw in the Enigma Machine?
In an Enigma coded message, a letter cannot appear as itself, nor the same corresponding letter twice (unless it appears 26+ times). There where also certain words or phrases (eg. Heil Hitler) that would appear often in a message. By recognising these phrases, codebreakers could eliminate/investigate the possibilities of certain letters.

2. What did the Allies do to crack it?

They created a device – a ‘Bombe’ – that would crunch through every Enigma possibility until it found a setting in which no letter would appear the same twice. When a letter was entered, it as aligned with 25 letters – all except for itself. Alan Turing was the mastermind behind this operation, and many German messages were decrypted using his ‘Bombe’.

#exploremaths

## Cryptanalysis of Enigma (Novin Noori)

What was the flaw Enigma Had?

The problem in which enigma had was that when a specific letter was typed into the machine, the letter would be matched up with 25 other letters except for itself. This was a huge flaw as it would eliminate the possibilities how the message was encrypted making enigma easier to crack when the flaw is recognised. The allies recognised this having ‘Alan Turing’ able to this and continued to do so until the war with the Germans was over.

What did the allies do to break Enigma?

The allies recognised this flaw having to create a mechanical machine known as ‘The Bomb’ which was constructed and made in Bletchley park. The mother of computers (The Bomb) would be tweaked towards specific setting having the letters be matched up with 25 letters except for itself. This huge flaw eliminated the very possibilities towards how the message was encrypted. Alan Turing was able to crack this and continued to use this information along with a device called ‘The Bomb’ which cracked the German plans leading to the allies victory. The making of the bomb, shortened the war by less than 2 to 4 years.

By Novin Noori

#exploremaths

## Substitute Cipher (Novin Noori)

What is the weakness of the substitution cipher?

The substitution cipher is weak in today’s standard, meaning that it is very easy to crack. Not only that but every letter is ALWAYS encoded by the same symbol, which makes frequency analysis a very effective tool.

Another problem: knowing context of the message is very useful (for instance, if you know that the text is about the types and number of airplanes in the enemy’s army, you should expect words “airplane”, “aircraft”, “weapon”, and so on)

Guesses also help: for instance, if you deciphered a part of the sentence “A cat drinks …”

you would guess that the last word is “milk” (although it could be “lemonade”)

Suggest a solution towards this?

One solution towards this is to make the code more complicated instead of being lazy having to add an specific encryption to the keys. It would take more time for the enemy to decipher it meaning more time to crack it. Using different languages or unusual languages  will also make cracking the code more difficult as it is harder for people to guess the start or end of the sentence.

By Novin Noori

#exploremaths

## Cracking the Enigma- Terrence Wong

The Enigma was considered to be the Unbreakable Code of WW2. But there were a few flaws with the code with one being that the letter could not be coded with the same letter. This eliminated a few thousand possibilities on how you could crack the Enigma Code.

The Allies saw this mistake and constructed a machine called “The Bomb”, which was an electromagnetic device which was held in Bletchely Park. The prime purpose of this machine was to crack the German Enigma code. It would do this by pairing up letters with a the 25 letters but itself. This would eventually eliminate the possibilities for the code and in the end, the Allies cracked the code.

#exploremaths

## Enigma (By Joyce Liu)

#exploremaths

What is/are the weakness that Enigma has?

As the enigma is changed daily, the code is hard to solve, but there are some obvious flaws. Since the enigma is a machine, it is programs a letter to never be itself and by using educated guesses, the enigma will eventually be solved. Also since it was built by the Germans, they always write “Hiel Hitler” giving away several letters already.

How did the allies crack it and get around this sophisticated machine?

Some of the forms of cracking the code were mentioned above, but also by using educated guesses and English letter frequency, Alan Turing and several others were able to build a machine called The Bomb, which matched up letters of a message with the 25 other letters in the alphabet, eventually decoding the message.

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