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Cryptography-One Time Pad Revisited

Natasha Y JeppuNational Public SchoolBangalore, Class 10

What is cryptography?

Cryptography is the science of sending secret messages. People often use the term ‘secret

code’ to mean a method for changing a message into a secret message.

In Boston in 1776 a simple code was used to

show how the British were coming. The code involved the number of lanterns hung in the church bell tower: “one if by land, two if by sea.”

Cryptanalysis

• Simple substitution– Every character in plaintext is represented by

an alphabet which is shifted by a definite integer(n). • Example : Shift of 3

‘a’ in plaintext is represented by ‘D’ in cipher text.This is followed for other characters.

Cipher wheel

Cryptanalysis

• Drawback– The code becomes very easy to solve if the

shift key is known.

Navajo – Code Talkers

• The Navajo “code talkers” developed a secret code based on Navajo language.

• They first made up simple English words to represent military words and translated them into Navajo. This way ‘submarine’ became ‘iron fish’ which was translated to ‘besh-lo’.

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Dancing men

Sir Arthur Conan Doyle, the author of the Sherlock Holmes mysteries developed a substitution cipher made from stick figures of dancing men. Above is an example of a substitution cipher made of symbols instead of letters.

The symbols correspond to letters as shown below and the flags are added to indicate the end of words.

Cryptanalysis

• Decoding method– Frequency analysis

• Encryption methods– Double transposition– One time pad

Frequency analysis

• In this method the frequencies of the occurrence of each alphabet of the plain text and cipher text is made and then matched. The cipher character having the highest frequency is likely to be ‘E’ and so on.(refer to graph)

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A C E G I K M O Q S U W Y

Study on frequency analysis

A frequency analysis of three different books was made.

– The lost symbol, Dan Brown– The chariot of the gods, Erich Von Daniken– Dynamics of flight, Bernard Etkin

• A soft copy of the book in word format was used and each character replaced by #. Word indicates the number of replacements thus providing a count.

Results

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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

Series1

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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

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The lost symbol Dan Brown

The chariot of the gods Erich Von Daniken

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Results

Dynamics of flight Bernard Etkin

These results show that the three books indeed have an alphabet distribution that is similar. This can now be used to a decode simple cipher codes.

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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

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One Time Pad

One Time Pad

A miniature paper one-time padTapir conversion table

My idea

This is based on the one time pad concept.

• A unique character in the plaintext will be represented by different characters in the cipher text.

• This makes the code difficult to break.So even if you do a frequency analysis of the cipher characters, it is not necessary that they will represent the same plaintext character.

Demonstration

757 706 823 438 489743 31 694 381 445392 276 317 765 646655 46 950 795 709

171 97 34 186 754

This demonstration has been

made using Matlab.• This is a simple 5/5 grid

having numbers from 1 to 1000 arranged randomly.

• This is the known to both the sender (A) and the receiver (B).

Demonstration

• ‘A’ saves the original grid using a unique password (in this case 1234) which is added to every number in the original grid. (as shown)

• Similarly ‘B’ saves it using another password (in this case 4321)

• The password is known only to the users (A) and (B)

1991 1940 2057 1672 17231977 1265 1928 1615 16791626 1510 1551 1999 18801889 1280 2184 2029 19431405 1331 1268 1420 1988

Grid as saved by A

5078 5027 5144 4759 48105064 4352 5015 4702 47664713 4597 4638 5086 49674976 4367 5271 5116 50304492 4418 4355 4507 5075

Grid as saved by B

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Demonstration

Example:

‘This is a message.’

• Every alphabet has an unique ASCII code. The message to be sent is first written in ASCII code.

T I M G

H S E E

I S

S A S

A

84 105 109 103 32

104 115 101 101 32

105 32 115 46 32

115 97 115 32 32

32 32 97 32 32

ASCII code for this message.

Demonstration

• The ASCII codes are then added to the original grid. The resultant grid is displayed below.

841 811 932 541 521847 146 795 482 477497 308 432 811 678770 143 1065 827 741203 129 131 218 786

• This is then sent to ‘B’ who then decodes the message.

• For this the original is got back by subtracting the password from the grid that is saved. The message grid is subtracted from the original. This will give us the ASCII code of the message which is then used to display the message.

Image cryptography

• As mentioned earlier , we can use images to send coded messages.

This is the original image that both the sender and the receiver know. Each square represents a pixel

This is the image that represents the message. The dark blue boxes at the end represent empty spaces.

Message: ‘This is a message’. Blue indicates spaces

This image is the coded message that is sent. The same principle can be used in sending secret messages using pictures where every pixel will have different colors.

This method makes decoding very difficult.

Improvising on it

• The message is stretched to fit the one-time pad by adding random number of non spaces (eg.#).

• Random spaces before and filler spaces after the message are added to make the message equal to one time pad.

Eg. ‘This is a message.’“ T###########h###i###########s####### #####i#######s ###########

#######a#### #####m###e#####s###s###########a###### g#e#####.########### ”

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Improvising on it

• The spaces before and after are allotted random numbers between 200 and 8,000,201.

• The non spaces or # are allotted random numbers between 8,000,201 and 16,000,201.

• Other characters are allotted their respective ASCII numbers.

• Modulus function is used to wrap the numbers and limit between 0 and 16777216.(2^24)

• The one time pad has numbers between 0 and 16777216.

• There is a 6 digit password to save and retrieve the one time pad.

Conversion to image

• The 16,000,000 number is converted to an RGB color value by converting it into a 24 bit digit.

• This is divided into three parts. The first 8 are assigned to R. The next 8 bits to G and the last 8 to B.

• The image is stored as a tiff file.• A reverse process is done to

to get the 16 million value

VB application

• This algorithm has been made into a VB application for the PC.

One time pad

VB application

MessageLength of

the messsage

Password

VB application

Encrypted image

Future work

• Investigate increase in complexity by using a Vigenere square

• Convert this into an Android code for a mobile application.

• Investigate methods to make the saving of one time pads more secure.

• Investigate methods to send one time pads via Email securely

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References

• D. Rijmenants, “Is One-time Pad History?”, Cipher Machines & Cryptology © 2010 –http://users.telenet.be/d.rijmenants

• http://users.telenet.be/d.rijmenants/en/onetimepad.htm

• Janet Beissinger and Vera Pless, “The Cryptoclub, using mathematics to make and break secret code”

Thank you