Atbash Cipher How the code works: Reverse the alphabet so a becomes Z, b becomes Y, c becomes X, and so on. Decode this message: SV DZH Z EVIB XOVEVI NZM The Enigma Project Historical Footnote: Atbash was originally used in Hebrew. The name comes from the first and last letters in Hebrew, aleph and tav, and the second and second to last letters, beth and shin. Some Hebrew religious texts use atbash to turn words into other words. For example, in English the word ‘hold’ becomes ‘slow’, and ‘grog’ becomes ‘tilt’. The Atbash Cipher in Hebrew תתתתתתתתתתתתתתתתתתתתתתPlease do not write on this worksheet
Transcript
Atbash Cipher
How the code works: Reverse the alphabet so a becomes Z, b becomes Y, c becomes X, and so on.
Decode this message:
SV DZH Z EVIB XOVEVI NZM
The Enigma Project
Historical Footnote: Atbash was originally used in Hebrew. The name comes from the first and last letters in Hebrew, aleph and tav, and the second and second to last letters, beth and shin. Some Hebrew religious texts use atbash to turn words into other words. For example, in English the word ‘hold’ becomes ‘slow’, and ‘grog’ becomes ‘tilt’.
The Atbash Cipher in Hebrew
ת ש ר ק צ פ ע ס נ מ ל כ י ט ח ז ו ה ד ג ב אא ב ג ד ה ו ז ח ט י כ ל מ נ ס ע פ צ ק ר ש ת
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Homophonic Cipher
Historical Footnote: This code hides how common the letters are. The most common letter in English is e, so if we give it the most symbols we can then use any of those symbols in place of e. The code makers of King Louis XIV of France used a code like this. It was known as The Great Cipher and was thought to be unbreakable. When it fell out of use, a lot of messages in the French archives became entirely unreadable! The Great Cipher was finally broken 250 years later by a codebreaker called Étienne Bazeries over a period of three years! All the symbols for a given letter are called ‘homophones’ because they all represent the same ‘sound’.
The Enigma Project
Decode this message:
How the code works: Some letters in this code have more than one symbol:
Historical Footnote: This code goes back to the 18th century. In particular, it has been widely used by certain organisations, such as the Freemasons, to keep their secrets. Some tombstones can be found that use the code as part of the inscription.
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Decode this message: Use the diagrams above to find these symbols.
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Caesar Shift
How the code works: This code uses two alphabets that wrap around in a circle. The alphabet in the centre can shift clockwise or anti-clockwise.
In this example, the alphabet in the centre has been shifted 7 places anti-clockwise (that’s equal to 19 places clockwise). So the message hello becomes OLSSV.
Break this code: I used a different shift for this message. What does it say?
BYLUT TKHYDW JXU DYDJX SUDJKHO
Historical Footnote: This code was used by Julius Caesar, a Roman general who led the first invasion of Britain in 55BC and became leader of Rome in 49BC until his assassination five years later. This is an easy code to break because there are only 26 ways to shift the alphabet, but it worked for Julius Caesar because his enemies did not realise he was using a code at all!
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Make sure you collect the Caesar Wheel that comes with this code.
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Knapsack Cipher
How the code works: To send a letter, look up its instructions in the table below:
Instructionsa 11000 h 00101 o 00011 v 01111b 10011 i 01100 p 01101 w 11001c 01110 j 11010 q 11101 x 10111d 10010 k 11110 r 01010 y 10101e 10000 l 01001 s 10100 z 10001f 10110 m 00111 t 00001 space 00100g 01011 n 00110 u 11100
For example, j = 11010. Write these instructions beneath the following numbers:
667 334 335 670 3401 1 0 1 0
These instructions tell you to add the numbers 667, 334, and 670 (and to not add the numbers 335 and 340) to make the secret code 1671. This method is called the public key.
To decode the message, you could reverse the public key – but that would be quite difficult. Instead we multiply the code by the secret number 3.
In this case we get 3 × 1671 = 5013 – we are only interested in the last two digits of the result, the number 13. Finally, find the instructions to make 13 using the following numbers:
1 2 5 10 201 1 0 1 0
Notice these numbers are much smaller and easier to use! Also notice the instructions are 11010 – the same instructions to make the letter j. The letter is decoded!
Historical Footnote: It is called the Knapsack Cipher because you can use the numbers above as weights in a bag, which means you can send a secret message by how heavy the bag is. In practice, you would make this code much harder to reverse by using even bigger numbers. This sort of idea is used to send codes on the internet. For example, a bank will publish a public key. If you want to send the bank a message you will use its public key. This key is very hard to reverse, so no one can read the message. Only the bank can decode the message using its secret private key.
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Railfence Cipher
How the code works: Make a block of letters by writing the message in rows. The number of rows is your key. The columns of the block are your coded message.
Example: I will form a block of letters by writing this is a railfence cipher in two rows.
t h i s i s a r a i lf e n c e c i p h e r
I can now mix up the letters by taking the columns as my code: TFHEINSCIESCAIRPAHIELR
Break this code: I made this code in the same way, except I used more than two rows. What does it say?
TCEOSHORUCEDWSISEAMEEBSUNCRASTREFLIEAAISTKMMT
The Enigma Project
Historical Footnote: There are two types of cipher. There are substitution ciphers (when you replace one letter for another), and there are transposition ciphers (when you rearrange the letters like an anagram). The Railfence Cipher is a transposition cipher.
You can also use a mixture of both (change the letters of the message and rearrange them). One of the advantages of mixing the two types of cipher is that it doesn’t matter which order you apply them. Applying the substitution cipher first then rearranging the letters will give you the same answer as rearranging the letters first then applying the substitution cipher.
When you use two rows this code is called a railfence cipher. It is called that because of the way it zigzags up and down on two lines, like the bars of a picket fence.
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Affine Cipher
Example: Let’s send the word ‘camels’ using the numbers A = 3 and B = 10:
plaintext: c a m e l sas numbers: 2 0 12 4 11 18Ap + B: 16 10 46 22 43 64remainder: 16 10 20 22 17 12ciphertext: Q K U W R M
Break this code: I sent this code using A = 15 and B = 4. Find C and decode the message:
TEQFXEXMathematical Footnote: When A = 1, this is the same as the Caesar Shift. When choosing A, it’s important that the number should be coprime to 26 – this means there are no numbers that exactly divide both A and 26 without remainder. So A cannot be 13 or any even number.
The Enigma Project
How the code works: To send a message, first turn all the letters into numbers using this:
a b c d e f g h i j k l m n o p q r s t u v w x y z0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
The code multiplies each letter by a number A, then adds a number B. In other words;
ciphertext = (A × plaintext) + B
Plaintext is what you call the message before you write it in code. Ciphertext is what you call the message after you write it in code.
Finally, make the result less than 26 by finding its remainder after division by 26.
To decode the message, we need to find a number C such that;
plaintext = C × (ciphertext - B)
The number C is a whole number, not a fraction, such that A × C - 1 is a multiple of 26.
For example, to decode the message above use C = 9, because (3 × 9) - 1 = 26.
ciphertext: Q K U W R Mas numbers: 16 10 20 22 17 12C(c – B): 54 0 90 108 63 18remainder: 2 0 12 4 11 18plaintext: c a m e l s
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Frequency Analysis
How the code works: Below is a clue to a secret codebreaker. It is written using a substitution code – one letter written for another. However, the underlying frequencies of the message do not change, so we can break the code using frequency analysis.
³ The most common letters in English are e, t and a.³ The most common pairs in English are th, er, and on.³ The most common triplets in English are the, and, and tha.
Here are the full frequencies:
Break this code:
ZRB ABNIBZ NQLBMIBYFBI KYA Y CBIP NGBCBI HYJ SJLBBL. RB AZXLSBL Y GQZ QT AXMDBNZA SJNGXLSJU HYZRBHYZSNA.
Historical Footnote: Frequency Analysis has been used by codebreakers for hundreds of years. The code makers could make it more difficult by removing the spaces, misspelling words on purpose, and occasionally using dummy letters that didn’t mean anything. More sophisticated methods of hiding the underlying frequencies include using more than one symbol for each letter (homophones), using more than one code (polyalphabetic substitution), and substituting pairs or triplets instead of individual letters (polygraphic substitution).
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Playfair Cipher
How the code works: I have filled a 5 × 5 square with a secret mixed alphabet. The letters I and J are combined:
P L A Y FI R C H EB D G K MN O Q S TU V W X Z
Write your message into pairs of letters.
For example, the message some mammoth becomes so me ma mx ot hx. We added an x to the double m to make it a pair, and another x to the unpaired letter h at the end.
To send a code there are three rules:
³ If two letters in a pair are in the same row move each letter one place to the right. So so becomes TQ. Letters at the end of the row wrap back to the start, so ot becomes QN.
P L A Y FI R C H EB D G K MN O Q S TU V W X Z
³ If two letters in a pair are in the same column move each letter one place down. So me becomes TM. Letters at the bottom of the column wrap back to the top, so hx becomes KY.
P L A Y FI R C H EB D G K MN O Q S TU V W X Z
³ Otherwise, a pair will form two corners of a box. Each letter will become the other corner in the same row. So ma will become GF, while mx will become KZ.
P L A Y FI R C H EB D G K MN O Q S TU V W X Z
So altogether, the message some mammoth became TQ TM GF KZ QN KY.
Decode this message: Use the same grid above to decode the message:
YI RP QT NL EI HVHistorical Footnote: The code was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair who promoted its use. It was initially rejected by the British Foreign Office because of its complexity. Wheatstone offered to show that three out of four boys in a nearby school could learn to use it in 15 minutes. The Foreign Office responded, "That is very possible, but you could never teach it to attachés". The code was used during the Boer War, World War I and World War II. To break this code you can perform frequency analysis on all 600 possible pairs of letters (called digraphs) which requires a much longer message than usual.
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Historical Footnote: This code was devised by the author Sir Arthur Conan Doyle for his Sherlock Holmes story ‘The Adventure of the Dancing Men’. In the story, Holmes is approached by a man whose wife is being terrified by a series of mysterious notes containing stick figures. Holmes deduces it is a code and breaks the cipher using frequency analysis. When the code is broken he realises his client is in danger and rushes to his house, only to find him shot dead with his wife seriously injured. Holmes decides to send a message using the same code. When a man arrives at the house it confirms he was the villain as only the murderer could have read the message. Holmes examining the drawing
The Enigma Project
How the code works: Each letter is replaced with a stick figure:
a b c d e f g h i j k l m
n o p q r s t u v w x y z
A flag means ‘end of word’.
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Dots and Pinpricks
Find the secret message: In this Victorian advert the words “Brooke’s Soap” are written in the staircase. Can you find another secret message hidden in the article below the picture? Read the historical footnote for more information.
Historical Footnote: In Victorian times, posting a letter cost a shilling for every hundred miles – but newspapers could be post for free! So instead of writing a letter, the cunning Victorian could send a message using dots or pinpricks above the letters of a newspaper article. This is an example of a hidden message. It is not a code but another form of secret message.
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Semaphore
How the code works: This code is a way to send messages over large distances using flags:
Break this code: I was stood behind the flag waver and this is what I saw. What is the message?
Historical Footnote: Semaphore flags are used by the navy to send messages between ships. It has proved to be useful during battle, most famously at the Battle of Trafalgar during the Napoleonic Wars. The downside is there is no secrecy because everyone within visual distance can see the message.
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Pocket Enigma
How the code works: To decode a message you need to know which rotor to use (there is a different rotor printed on each side) and the starting position (where the big arrow starts).
1. Follow the connections to change one letter into another2. After decoding each letter, move the rotor one place clockwise
In the example above, we are using Rotor I and starting position W. The word ok becomes QL.
Break this code: This code was sent using Rotor I.
This time we don’t know the rotor starting position, but we think the first three letters of the message is the word ‘the’. Use this as a clue to decode the rest of the message:
ZCCZRTVBLBBJKPA
Historical Footnote: The Pocket Enigma works like an Enigma Machine because the code is different each time you move the rotor. The real Enigma Machine uses three rotors, otherwise the pattern would repeat every 26 letters. Like the Pocket Enigma, the real Enigma Machine turns the 26 letters of the alphabet into 13 pairs, making it easy to code and decode. Clues like we used here are called ‘cribs’.
The Enigma Project
Make sure you collect the Pocket Enigma CD case that comes with this code.
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Vigenère Cipher
How the code works: To use this code you need a keyword and the following table:
To send a message: Find the first letter of the keyword (down the left side) and the first letter of the message (along the top). Where they meet in the middle is the first letter of the code. Continue in this way for each letter of the message. Repeat the keyword if necessary.
Historical Footnote: This code is named after a sixteenth century French diplomat called Blaise de Vigenère. Because it was so difficult to break, the code became known as ‘le chiffre indéchiffrable’ (French for ‘the indecipherable cipher’). It was first broken by the famous English engineer Charles Babbage in 1854. He realised that if substitution codes are broken by looking for the most common letters, the Vigenère code could be broken by looking for the most common words.
The Enigma Project
Example: Let’s send the message ‘shaken not stirred’ using the keyword BOND. Use the table to find where B and s meet in the middle – this is the first letter of the code. It is the letter T.
The rest of the message looks like this:
B O N D B O N D B O N D B O N Ds h a k e n n o t s t i r r e dT V N N F B A R U G G L S F R G
Complete this code: Work out the keyword and complete this message:
N I N A N I No s i i s m t e i i
J N U U G S F E Q Z U S L Z I Z T E Q N B O O I E A
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World War I Cipher
How the code works: The code maker fills a 5 x 5 square with a secret mixed alphabet. The letters i and j are combined. The rows and columns are labelled with the letters A, D, F, G and X.
A D F G XA q a z w sD x e d c rF f v t g bG y h n u i/jX m k l o p
Step 1: Coordinates: ADFGX are used like coordinates to give the position of each letter (always rows first, columns second). For example, this is how to write the message ‘hello world’;
h e l l o w o r l dGD DD XF XF XG AG XG DX XF DF
Step 2: Write in a grid: The code maker writes the coordinates above, in rows, into a grid. At the top of the grid he writes a keyword. For example, he might decide to use the keyword dawn:
d a w nG D D DX F X FX G A GX G D XX F D F
Step 3: Swap the columns: Finally, the code maker swaps the columns of the grid. He does this by putting the letters of the keyword in alphabetical order:
a d n wD G D DF X F XG X G AG X X DF X F D
Reading across, the code becomes: DGDDFXFXGXGAGXXDFXFD
The Enigma Project
Decode this message: Reverse the procedure to decode the message below. It was sent using the same secret square of letters at the top of the page, but this time the keyword was tiger.
GXXDFXFGFXXADFADGDDFFFFGGGXDAG
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Historical Footnote: This code was used by the German army during World War I. The letters A, D, F, G, and X were used because they sound very different in Morse Code, thus reducing mistakes. Later the letter V was added to make a 6 x 6 grid that included the whole alphabet and the numbers 0 to 9. The Germans thought the code was unbreakable. Eventually it was broken by a man in the French army called Georges Painvin.
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Historical Footnote: Messages sent by mobile phones or computers include error correcting codes to fix mistakes made in transmission, without the need for the sender to transmit the message again. American mathematician Richard Hamming created the first error correcting code in 1950.
How the code works: This code is in binary. Here is the alphabet in binary (also called Baudot).
a 11000 h 00101 o 00011 v 01111b 10011 i 01100 p 01101 w 11001c 01110 j 11010 q 11101 x 10111d 10010 k 11110 r 01010 y 10101e 10000 l 01001 s 10100 z 10001f 10110 m 00111 t 00001 space 00100g 01011 n 00110 u 11100
The number at the end of each row (or column) is the sum of the digits in that row (or column). Digits are added in the normal way, except 1 + 1 = 0.
The extra row and column allow us to find mistakes. If they don’t add up then there is a mistake.
For example, if we changed one of the red digits in the third row we would get a different letter. Notice the digits of the third row, and the second column, no longer add up correctly. The intersection of this row and column helps you find which of the red digits has been changed.
How the code works: Morse code turns letters into dots and dashes. The length of each letter is counted in dots, such that;
1. A dash is equal to three dots.2. A gap between dots and dashes is equal to one dot.3. A pause between two letters is equal to three dots.4. A space between two words is equal to seven dots.
Example: In Morse Code the distress signal SOS is:
5 dots 11 dots 5 dots
S is equal to 5 dots. O is equal to 11 dots. Including pauses, SOS is equal to 27 dots
Break this code: The message below was lost on transmission.
We know the length of each letter, and that the total message was equal to 71 dots.
Use this information to work out the message below.
Historical Footnote: Morse Code is a way to transmit messages using light or tones. It is a code but it is not a secret code. It was invented in 1844 by three Americans, Samuel Morse, Joseph Henry and Alfred Vail. Morse Code was vital in World War II. Notice common letters like ‘e’ are short, while rare letters are the longest.
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RSA
Example: Let’s use x = 2 and y = 5. So m = 2 × 5 = 10. Then E may be any number coprime to (x-1)(y-1) = 1 × 4 = 4. Let’s use E = 3. So:
Original message: b a d c h e fWrite in numbers: 1 0 3 2 7 4 5Raise to the power E = 3: 1 0 27 8 343 64 125Find remainder after division by m = 10: 1 0 7 8 3 4 5
Break this code: We know the message below was sent using the public key E = 27 and m = 55. Work out the original prime numbers and use them to find D to decode:
18 9 23 5 15 24 2 7 41
Historical Footnote: This method is widely used today for internet encryption. The public key is published for anyone to use, but only the person who made the public key knows the secret private key - so only they may decode the message. This code relies on the fact that making the public key by multiplying two prime numbers is easy, but breaking the code by factorising the public key is hard. The larger the prime numbers, the more difficult it is to break. In reality, the letters of the message are combined to form blocks that hides the frequencies of individual letters. RSA stands for Rivest, Shamir and Adleman, who first publicly described the method in 1978.
The Enigma Project
How the code works: To send a message you need two prime numbers x and y.
We also need their product m = xy, and a number E that is coprime* to (x-1)(y-1).
The numbers E and m are your public key.
To send a message:
³ First, replace the letters for numbers, (a=0, b=1, c=2, …, z=25)³ Raise all numbers to the power E³ Find their remainder after division by m
*two numbers are coprime if they share no common factors (except 1).For example, 15 and 24 are not coprime because they are both divisible by 3, but 15 and 26 are coprime.
To decode the message we perform the exact same procedure, but with a number D to replace E such that (E × D) − 1 is a multiple of (x-1)(y-1). The number D is your private key.
For example, to decode the message above we can use D = 7 because (3 × 7) – 1 = 20, which is a multiple of 4.
Code, in numbers: 1 0 7 8 3 4 5Raise to the power D = 7: 1 0 823543 2097152 2187 16384 78125
Find remainder after division by m = 10: 1 0 3 2 7 4 5Original message: b a d c h e f
