Substitution Codes Changes

Substitution Codes

By Sarah Bonnell

History of Codes Throughout history, codes have been used to hide or keep messages secret. There are many different types of codes that have been invented and used, although lots have been broken after a while. A famous type of code that was used and eventually broken, was the ENIGMA CODE used by the German army during the Second World War. An Enigma Machine, used to generate this code, can be seen on the next slide.

This is an Enigma Machine. It generates codes by substituting each letter typed for another. However, the code is made harder to break as the same letter can be substituted to any random letter, unless the machine is used in the same setting as when the message was first typed. For example, A could come out as C the first time, and F the second.

Other Types of Codes Not all codes are substitution codes. Codes can be broken by using objects, like the Spartans did 2500 years ago. A long strip of any material was used to wrap around a piece of wood. A message was written, that could only be decoded by using exactly the same size wood. This code was good, but it was eventually broken. One example is shown below:

The code can only be broken when the right size stick is used

There are many other types of codes that have been used throughout history, and for many different purposes. purposes

The Problem The Problem we were given was a substitution code, whereby we had a number of symbols which substituted for each letter in the alphabet. The problem was, we didn’t know what symbol corresponded to what letter.

Our Method       A

b

c

d

e

f

    h

I

j

k

l

m

 o

p

q

When we saw the problem we were given, we decided to try gand see if it was written in Wingdings, a coded font. We typed out the Wingdings n alphabet (left) and realised that the symbols matched up. We deciphered the message, which you can see on the next slide.

rs

   t

u

v

w x

y

z

The Solution The message we deciphered was: The Substitution Cipher was originated by Julius Caesar, so it is said. Julius Caesar was born in 100 BC, and was Emperor of the Roma Empire. He invaded France in about 55 BC, and used a lot of codes to communicate with his generals. The Caeser Cipher was the first substitution cipher to be used for military purposes.

More Methods 

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Although it was easier for us to break the code because we knew where to find the answer, we decided to try to use the symbols as clues to breaking the code. When we first broke the words “Julius Ceaser,” we could easily see the symbol order of this name and see if it came up any more in the symbolized text. As you could see from the solution slide, it did. Also, looking for symbols that occurred frequently in the text, gave us a clue to what they might be. For example, a symbol that appears on its own in a sentence is either an ‘a’ or an ‘I.’ Also, the numbers were not substituted, which helped us to recognize the symbols behind them could either have been : “AD” or “BC.”

Our Second step  We

became more interested and decided to look at other challenges; Brailer and Guesswork we found very easy.  Then we came across the Knapsack challenge and found this an interesting challenge . Here is what we came up with. This seems interesting.

How did we solve the knapsack challenge?

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Once we all went through the challenge on our own, we discussed what the best and easiest way would be to decode the message. One member from our group suggested the best way would be for some of us to sit around the computer solving the first half while the others were writing the solution on paper.

1cm

We had the following numbers to decode: 33,18, 20, 1, 31, 20, 30, 31. We first worked out each number using the sticks which meant we had to see what sticks add up to make the number.

3cm

5cm

10cm

20cm

The solutions  So

using the stick 1, 3 , 5, 10 and 20, we thought that we should use 3, 10 and 20 to make 33 so our binary code is 01011 because we didn’t use 1or 5 which meant we had to use 0 to replace them with their number. We got the number 1 because we used the sticks 3, 10 and 20 once. 01011 represents k in the chart we was given. ( shown on the next page). So went on using the same the method through out task one and ended up with KNAPSACK.

LOOK UP TABLE TO DECODE THE MESSAGE. Binary Letter Letter Binary Reference Reference a 00001 n 01110 b 00010 o 01111 c 00011 p 10000 d 00100 q 10001 e 00101 r 10010 f 00110 s 10011 g 00111 t 10100 h 01000 u 10101 i 01001 v 10110 j 01010 w 10111 k 01011 x 11000 l 01100 y 11001 m 01101 z 11010

PROBLEM 2 The next problem was using the same method to decode the message but there was more than one solution. The sticks we were given were 1, 2, 3, 4,5. The numbers we had to decode were 1, 5, 14 ,4 ,5, 8, 10, 5, 4 ,7,9. The challenge was that there was more than one answer which meant that some numbers had two different ways of adding the sticks. Like for example; 2+3=5 and so does 4+1=5 so this meant that there was more than one binary code. So we all thought how the best way to work out the problem was and some of us decoded the message and some of us wrote all the different ways the solution will be.  This is how we decoded the messages: 

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Method of working out the solution: To decode the number 1 the binary code was:10000 which is P. To decode 5 the binary code is either 10010 or 01100 which is either R or L. To decode 14 the binary code is: 01111 which is O. To decode 4 the binary code is either: 10100 or 00010 which is either T or B. As you may have realized we went on using the same technique and ended up with many possibilities some of them didn’t make sense but the solution looked like the word PROBLEM. Next we had to find the ending meaning what ending fitted in with problem this was really confusing at first but we soon realized that some endings did not make sense like: RTI, RBI , ABIU. It took us quite some time on the ending and we fitted each ending with problem and the answer was:PROBLEMATIC which made sense to us.

 Can

you explain why super increasing series are so much easier to decode?

Super increasing series are easier to decode because there are many different possibilities to make a word. We as a group found knapsack very challenging especially problem 2 but we found it really interesting to do. The most difficult part was to find which one made sense and that was the method. While solving this KNAPSACK we really enjoying the task it took us a lot of time but we enjoyed each and every minute of the problem.

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