Seven Kings High School presents

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Seven Kings High School presents
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After the first video conference

• We went back to our classrooms and
• decided to
• Look at the Caesar shift,
• Look at the frequency of the letters,
• Look at Binary codes and then
• Make our own codes.

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• Here are the results

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Frequency
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Frequency graphs for the English text

• We found a small article in English from a
  newspaper and analysed the frequency of each
  letter.
• We could then compare these results with the
  results from the frequencies from the codes.

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After receiving the article, the students
involved in the maths conference split up the
piece of text into equal sections and recorded
the frequencies of the letters for their passage.
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We then put all the frequencies from all the
divided text together and presented them in a
table on excel.
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• We totalled the frequencies and used excel to
  calculate the percentages of how frequently each
  letter occurred.
• For example, the frequency of A in the passage
  is 109.
• The total frequency was 1105.

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• The person in charge of this graph then presented
  a bar graph showing the frequency of each letter
  in the small paragraph of English.

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Here is the frequency table followed by the graph
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• The graph shows that E T will be the most
  frequent letters
• and
• Q Z will be the least frequent.

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We changed the bar chart so that the percentages
were in order starting from the smallest.
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Here the bar graph showing the percentages of the
frequencies of each letter in order.
q z j x k m v y b f p u
c w d g l r n o h I s
a t e
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Frequency Graphs for the coded text
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• We worked out the percentages of the
  frequencies of the letters for each of the four
  codes

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• We could then draw the bar graphs.

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Here is the bar graph for Code 1
G I Q W X F E D N C J
R T B M Z S K O P U Y H
V A L
LETTER
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Comparing the two similarities and differences

• In the first code, the bar graph shows that L
  is the most frequent letter.
• This means that it is more likely for the letter
  L in the first code to be E because the
  frequency graph for the paragraph in English
  showed that E was the most frequent letter.

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Here is the bar graph for Code 2
D K M W T O C I P S Z Q
J X H Y L E U V F A B N
G R
LETTER
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• In the second code, the bar graph shows that R
  is the most frequent letter.
• This means that it is more likely for the letter
  R in the second code to be E.

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Here is the Bar Graph for Code 3
F U Y J T Q W B C E G K V Z
A H L N Q P I M X D R S
LETTER
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• In the third code, the bar graph shows that S
  is the most frequent letter.
• This means that it is more likely for the letter
  S in the third code to be E.

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Here is the Bar Graph for Code 4
I S Z H E G T K O V D L M F Y
P U A J X Q B N R C W
LETTER
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• In the fourth code the bar graph shows that W
  or C is the most frequent letter.
• This means that it is more likely for the letter
  W or C in the fourth code to be E or T.

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• All four graphs had roughly the same shape.
• We used the results of our frequency analysis to
  help us to crack the 4 codes.

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• Code frequencies compared with the English
  frequency
• The most frequent letter in code 1 is L and the
  most frequent letter in English is E. In code 1,
  L is E so code 1 follows the graph data.
• The most frequent letter in code 2 is R and the
  most frequent letter in English is E. In code 2,
  R is E so code 2 follows the graph data.

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• There are two codes in code 3. The most frequent
  letter in code 3 is S and the most frequent
  letter in English is E. In code 3, S is O in the
  first code of code 3 so the frequencies in
  English and code 3 do not correspond with each
  other. S is T in the second code of code 3.

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• Again, the frequencies do not correspond because
  the most frequent letter in English does not
  equal the most frequent letter in code 3. Code 3
  does not follow the graph data.

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• The most frequent letter in code 4 is W and the
  most frequent letter in English is E. In code 4,
  W is N so code 4 does not follow the graph data
  because W does not equal E.

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Top tips for deciphering any code

• As our studies in frequency analysis have shown,
  one way to crack a code is to tally the
  frequencies of the different characters and work
  out which is the most frequent letter.

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• As the most frequently used letter in the English
  language is E, this is probably that character.
• The next most frequent character will be T or H.

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• If the characters are still grouped in their
  natural form, then look for recurring patterns of
  small groups-
• these will probably be ECWs
• words like the or and.
• extremely common words

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• Other members of our group used the Caesar Shift
  to crack the code.

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• We used the same coded text that we used for the
  frequency analysis which was taken from the
  website Motivate Maths.
• The code was quite hard to crack, but we managed
  it in the end.
• This is how

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• We used 2 strips of paper with the alphabet
  written on each one.
• One of the strips was stuck to the table.
• The second strip was not stuck down as that strip
  would need to be moved around.
• This system is known as the Caesar shift.

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• We looked for words in the text
• which had only two or three
• letters as that would be a good
• start because they would be easy
• to check.

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• For example, if we had A and F together, we would
  know that it could only be a small word like it
  etc.
• We then found the letter on the movable strip and
  put it against the top strip which was stuck to
  the table.

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If we put the letter A next to the letter I then
the letter F will automatically be next to the
letter N. If this works out to be correct, we
can stick the movable strip down to the table in
that position and we will be able to crack the
code for that piece of the text.
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• Using this method we were able to crack the codes.

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We found that the 1st code was the easiest to
crack. Codes 2 4 were more difficult as letters
were grouped in fives rather than actual
words. Code 3 appeared to change the shift half
way through.
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The codes read-

• Code 1 Each letter had moved on a shift of 7
• We will attack at dawn. Legions X and XI should
  move round to the right under the cover of
  darkness to attack the enemy from the rear.
  Legions II and IV should move round to the left
  under the cover of darkness to attack the enemy
  from the left. Legions VII and IX will start the
  attack from the front.

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Code 2 Each letter had moved on a
shift of 13 places.

• We have been betrayed there are spies in our
  midst. You must search everywhere and everyone.
  Find out who is passing on all our plans to the
  enemy. When you find the traitors make sure they
  tell you all they know. If they can be turned so
  that we can pass on false information they may
  live otherwise they will die.

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Code 3 T The code moved on a shift of
22 then changed to a shift of 1

• The Queen will be travelling from London to York
  next week. She is due to leave on Monday at first
  light. She will be accompanied by armed troops.
  However this is our best chance to kill her. Send
  your best men. They must not fail.

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Code 4 Each letter had moved on a
shift of 17 letters

• Send word to all your spies the King needs
  information urgently about the intentions of his
  brother in France. Where is he going. Who is he
  meeting. What is he planning to do on his return.
  The King knows that his brother is planning
  against him and that he will stop at nothing to
  bring him down. For this reason it is vital that
  we discover as much as we can about what Philip
  is doing so that we can prevent the success of
  his plans.

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Codes using binary systems

• This the decoded version of the binary code.
•  This sentence has been coded using the ASCHI
  system and binary numbers.

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• This is a code that we were set to decode by
  working out what the binary numbers totalled to.
• We were provided with a sheet that told us what
  the binary numbers stood for and the denary that
  they represented.

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• For example -
• capital numbers 65 to 90,
• lower case 97 to 122,
• spaces 32, full stops 46, etc.

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• After filling in the sheet we started looking at
  the binary code.
• Then by matching up the total binary number to
  the denary number on the sheet we worked out
  where the spaces were in the text.
• From there we worked out the letters from the
  beginning to the end.

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• Finally we worked on devising our own code.

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• Here are our messages using
• our own codes
• Try to decipher them!

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Message 1

• 0001 0101 001T 00UH 00K0 0S01 0E01 0B0D
  0FR1 001L 0001 00Q0 011Z 0MS1 001G 0PVX
  0Y01 0NC1 01WT 01ZP 001A 0UQ1 0111 0101
  001K 0JF0 0KZH 0R00 0D00 0101 0E1E 001A
  0111 0R0V 01JE 011L 0100 00X0 0010 0AB0

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Message 2

• PVKITBCDKH, ILUIFFITUI GTB AHHAVJQTKJS. JDKC KC
  AQV MAJJA GJ CIXIT YKTWC DKWD CUDAAF. EI NIFKIXK
  KT PGKVTICC GTB IOQGFKJS PAV IXIVSATI. JDKC
  CUDAAF KC G MQFJKUQFJQVGF CAUKIJS GTB IXIVSNABS
  DIFHC IXIVSATI IFCI AQJ.
• Good Luck!