TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been...
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Transcript of TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been...
![Page 1: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/1.jpg)
TMAT 103
Supplemental Chapter
Cryptography
![Page 2: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/2.jpg)
Cryptography
• Sending messages that cannot be read if stolen– Been in use for centuries (wars)– Used to transmit data securely over a network– Hundreds of techniques
• Utilizes mathematical functions and operations• Requires a key• Encode – uses corresponding function and key• Decode – uses inverse of the function and key
![Page 3: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/3.jpg)
TMAT 103
Method 1
Sir Francis Bacon’s Code
![Page 4: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/4.jpg)
Sir Francis Bacon’s Code
• Algorithm to encrypt a message using Bacon’s code1. For each letter, find the corresponding binary code
1. Determine the corresponding decimal number (a = 0, b = 1, c = 2, …, z = 25)
2. Convert the decimal number to binary
2. Concatenate the binary codes for all letters3. Create the encoded message
1. The message must have the same number of characters as 0s and 1s in the concatenated binary codes
2. Key: Choose how to distinguish 1s from 0sExample: Use uppercase for 1s and lowercase for 0s
![Page 5: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/5.jpg)
Sir Francis Bacon’s Code
• Encode ‘DISCRETE’ using Bacon’s code
00011 01000 10010 00010 10001 00100 10011 00100OREGO NISAS TATEI NTHEU NITED STATE SOFAM ERICA
Message sent:
oreGOn Is a sTatE in thE uNiteD stAteS of AMerIca
• Example: Encode ‘TECHNOLOGY’
![Page 6: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/6.jpg)
Sir Francis Bacon’s Code
• Reverse the process to decode• Example – decode the following
WilLiAm iS A FaMous auTHOR from tHE SixteeNth cEntuRY
Key: Lowercase stands for 0, uppercase stands for 1
![Page 7: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/7.jpg)
TMAT 103
Method 2
Substitution Code
![Page 8: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/8.jpg)
Substitution Code
• Algorithm to encrypt a message using the Substitution code1. Choose a key (a word with no repeated letters)
Example: DESTINY2. Correlate alphabet characters according to the key
3. Create the encoded message by substituting the corresponding letters
![Page 9: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/9.jpg)
Substitution Code
• Example: Encode ‘DISCRETE’ using a substitution code with the key ‘DESTINY’
• Message sent:
TBPSOIQI
• Example: Encode ‘TECHNOLOGY’ using this scheme
![Page 10: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/10.jpg)
Substitution Code
• Reverse the process to decode• Example: The following message was sent using a
substitution code
Decode the message:
D M W I M L C U L R F I R D E W E E H E L K
Key: BASKET
![Page 11: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/11.jpg)
TMAT 103
Method 3
Transposition Code
![Page 12: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/12.jpg)
Transposition Code
• Permutation Function
• Can also be written as a cycle
1 2 3 4 5 6 7 8 9 10
3 9 7 4 6 1 2 5 8 10
1,3,7,2,9,8,5,6
![Page 13: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/13.jpg)
Transposition Code
• Algorithm to encrypt a message using the Transposition code1. Choose a key (a permutation function)
2. Change the order of the characters in the message according to the key
![Page 14: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/14.jpg)
Transposition Code
• Example: Encode ‘DISCRETE’ using a Transposition code with the key (1, 3, 7, 8, 2, 6)
Message sent:
EEDCRIST
• Example: Encode ‘TECHNOLOGY’
![Page 15: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/15.jpg)
Transposition Code
• Reverse the process to decode• Example – decode the following
OICLPCYIGULSOYRRVTTEA
Key: (16, 15, 6, 1, 3, 7, 11, 2) (8, 13, 4, 5, 19) (14, 10) (21, 20, 17)
![Page 16: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/16.jpg)
TMAT 103
Method 4
Keyword Columnar Transposition
![Page 17: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/17.jpg)
Keyword Columnar Transposition
• Algorithm to encrypt a message using the keyword columnar transposition1. Create a matrix (rows and columns) using the
letters in the key as the column labels
2. Fit the message into the matrix (left to right, top to bottom) – pad with Xs if necessary
3. Form the new message by taking the columns in alphabetical order by the column labels
![Page 18: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/18.jpg)
Keyword Columnar Transposition
• Example: Use a keyword columnar transposition with the key ‘JONES’ to encrypt:
THE FIFTH GOBLET CONTAINS THE GOLD
Result:FGTAHDTFBONGEHETTLHTLNSOIOCIEX
![Page 19: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/19.jpg)
Keyword Columnar Transposition
• Example: Use a keyword columnar transposition with the key ‘JONES’ to encrypt:
ALL DIFFICULT MATHEMATICAL PROBLEMS ARE CHARACTER BUILDING
![Page 20: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/20.jpg)
Keyword Columnar Transposition
• Decoding a keyword columnar transposition – reverse the process– Algorithm to decrypt a message using the keyword
columnar transposition1. Create a matrix (rows and columns) using the letters in
the key as the column labels2. Count the characters in the message, and divide that
number by the number of characters in the key3. Starting from the beginning of the encrypted message,
group the letters according to the calculation in step 24. Fit the message into the matrix5. Read the message from the matrix (left to right, top to
bottom)
![Page 21: TMAT 103 Supplemental Chapter Cryptography. Sending messages that cannot be read if stolen –Been in use for centuries (wars) –Used to transmit data securely.](https://reader036.fdocuments.net/reader036/viewer/2022070409/56649e735503460f94b727c5/html5/thumbnails/21.jpg)
Keyword Columnar Transposition
• Reverse the process to decode• Example – decode the following
AAK7ENWHRSOER9SAETOELNNWIDYELXBO1DXKTI3R
Key: BASEBALL