1. Cryptography Programming Lab
Mike Scott

2. Why Cryptography? Astrachan’s Law: Secrets are interesting
“Do not give an assignment that computes something that is more easily figured out without a computer. ... Show off the power of computation.”
Secrets are interesting
Practical applications
Is it safe to use my credit card to purchase something via a website?
Fascinating history
Mary Queen of Scots, Alan Turing
Application of mathematics and programming

3. Plan for today Look at four different ciphers
Complete program involving each
Caesar
Columnar
Random Substitution
Vigenère

4. Definitions Cryptography Cipher Encryption Decryption
The art and study of hiding information
Cipher
Algorithm for performing encryption and decryption
Encryption
Converting plain text (or information) to unintelligible text (aka cipher text) that cannot be understood without knowing how the information was converted
Decryption
recovering the original plain text from the cipher text

5. Caesar Cipher Named after Julius Caesar Also called the shift cipher
Example of a substitution cipher
Each letter (or character) is replaced by another letter in the alphabet

6. Caesar cipher
Example with a shift of 5 ABCDEFGHIJKLMNOPQRSTUVWXYZ Plain FGHIJKLMNOPQRSTUVWXYZABCDE Encrypted COMPUTER SCIENCE Plain HTRUZYJWXHNJSHJ Encrypted Assume all non letters removed.

7. Variations
Using computer could simply apply shift to all characters, not just upper case letters
Printable ASCII characters space to ~ (32 – 126)
Maintain or remove non letters?
lower case to upper case?

8. Breaking Caesar Cipher
Brute force
With only letters try all 25 possibilities
Still not hard if all ASCII

9. Caesar Programming Problem
Log in
Go to
Click on link to Crypto Resources at bottom of page
Download Caesar.java to desktop
Start Eclipse (or other IDE if you prefer)
Create project
Add file
Complete method printAllShifts(String msg)

10. Columnar Cipher Example of a Transposition cipher
The characters from the original message are used, but put in a different order, based on the cipher
Hook ‘em Horns! We bleed orange! Plain
Pick a number of rows for the cipher
Fill in the grid in column major order

11. Columnar Encryption H ' o l e r W ! m n a k s d b g
Hook ‘em Horns! We bleed orange!
Read off rows to create message
H’o loeoerWer!omneeak s dn H!b g H ' o l e r W ! m n a k s d b g

12. Columnar Programming Problem
Download Columnar.java
Complete the method printColumnar(String clear, int rows)

13. Random Substitution Cipher
How strong is the Caesar cipher?
Pick a secret word with no repeat letters, computery
ABCDEFGHIJKLMNOPQRSTUVWXYZ Plain
COMPUTERYABDFGHIJKLNQSVWXZ Encrypted

14. Example
ABCDEFGHIJKLMNOPQRSTUVWXYZ Plain COMPUTERYABDFGHIJKLNQSVWXZ Encrypted THE ANSWER FOR NUMBER THREE IS A THEANSWERTONUMBERTHREEISA Plain NRUCGLVUKNHGQFOUKNRKUUYLC Encrypted

15. Random Substitution Ciphers
Instead of picking a keyword randomly pick letters
Must share the whole key, but lots of possibilities
26! possible keys = × 1026
Assume we could check a billion keys a second
It would take × years to check them all.
About the age of the universe

16. But ...
But substitution ciphers turn out to be relatively easy to solve
Why?

17. Letter Frequency

18. Cracking the Substitution Cipher
Given an encrypted message count how often each character occurs
If only letters, assume most frequent letter is e, next most frequent is t, next most frequent is a, and so forth
Apply the potential key
Look for clear words
Alter key as appropriate

19. Substitution Programming Problem
With a computer a key can easily be created that uses all printable characters not just the letters.
Download DecryptSub.java
Complete the method int[] createFreqTable(String encrypted)
The method returns an array of length 128. All ASCII chars are counted.
The index of the array maps to the ASCII value of the char

20. Substitution Programming Problem
When run the program:
converts a hard coded file (which I have encrypted with a randomly generated substitution key) to a String
creates a frequency table (using your method)
creates an initial key based on the frequency table and the “normal” frequency of printable ASCII chars
applies the initial key to the encrypted message and displays it
prompts for change in key, applies it and displays new decrypted message (A bit of an art)

21. Vigenère Cipher Named after Blaise de Vigenère
“The Unbreakable Cipher”
A poly-alphabetic substitution cipher
Each letter in the plain text can encrypt to multiple letters

22. Vigenère Cipher All 26 Caesar Ciphers Pick a secret word
Repeat secret word over the plain text
The secret word letter gives the row, the plain text gives the column
The letter at the intersection is the cipher text

23. Vigenère Cipher Example
Secret word: TEXAS
Plain text: MEET AT THE TOWER
TEXASTEXASTEXA
MEETATTHETOWER
1st letter, row T, column M -> F
2nd letter, row E, column E -> I
3rd letter, row X, column E -> B
FIBTSMXEELHABR

24. Large Vigenère Example

25. Frequencies In Cipher text
Longer Secret Words with more of the letters flattens it more!

26. Breaking the Vigenère Cipher
Given a long enough sample of cipher text it is possible to break the Vigenère cipher
Assume the secret word is TEXAS which has a length of 5.
Notice then there are 5 ways to encode the plain text word “the”
Some words show up a lot in regular language
So let’s look for 3 letter sequences that are repeated in a cipher text

27. Cipher Text
BLXDLAMPSLHVVFJHQLNWPLLHSWRLBMLMKEKLXLTWEPFTLHQBOJMSXNQHXEEJBQXYUKIAILMLBSWWYZTAOIFNXEYBNUXSCAFHPAVAGXXGWNTLNLAIKAJKEQOJYSOTZXFBGAGRFNYHJFTSGHJYGPRPKWIXFCSEMKCJXHRLAMCAUJBRDTZXHXYKMLXTXHPIOOXHCOJMLBBSEEKCWHJQHWLXOAFZIQADXAEEFFCZOFOMSISELLSLWMPCGOIOEVMLXTZXLXDLHPAMWLSJUUAEK DLAEQIOTWMRGGIQOVHYYTXNPKEKL

28. 3 Letter Repeated Sequences
DLA [270] EKL [265] HPA [165] KEK [265] LAM [159] LXD [255]
LXT [70]
MLB [125]
MLX [70]
OJM [145]
TZX [50, 130, 80]
XDL [255]
Numbers are distances between the repeated 3
letter sequence

29. Using Repeated Sequences
Some repeated sequences will just be random.
But, some will be due to the same word being encoded with the same parts of the secret word!
If this is the case the secret word is a factor of the distance between the repeated sequences

30. Factors of Distances
DLA: [2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270] EKL: [5, 53, 265] HPA: [3, 5, 11, 15, 33, 55, 165] KEK: [5, 53, 265] LAM: [3, 53, 159] LXD: [3, 5, 15, 15, 17, 51, 85, 255] LXT: [2, 5, 7, 10, 14, 35, 70] MLB: [5, 25, 125] MLX: [2, 5, 7, 10, 14, 35, 70] OJM: [5, 29, 145] TZX: [2, 5, 10, 25, 50] TZX: [2, 5, 10, 13, 26, 65, 130] TZX: [2, 4, 5, 8, 8, 10, 16, 20, 40, 80] XDL: [3, 5, 15, 15, 17, 51, 85, 255]

31. Frequency of Factors 2 - 6 3 - 5 4 - 1 5 - 13 6 - 1 7 - 2 8 - 2 9 - 1
10 - 6
11 - 1
13 - 1
14 - 2
15 - 6
16 - 1
17 - 2
18 - 1
20 - 1
25 - 2
26 - 1
27 - 1
29 - 1
30 - 1
33 - 1
35 - 2
40 - 1
45 - 1
50 - 1
51 - 2
53 - 3
54 - 1
55 - 1
65 - 1
70 - 2
80 - 1
85 - 2
90 - 1

32. Secret Code Word Strong evidence the code word is length 5
So start with first character and do frequency analysis on every 5th character. Will just be a simple Caesar shift
Repeat starting at second character and every 5th
5 frequency analysis problems

33. Simon Singh Vigenère Cracking Tool

34. Slide for Best Fit
First Letter of Secret Word is V in this example

35. Vigenère Programming Problem
Download FindSecretWordLength.java
Complete the printFactors(String repeatedSection, int distance) method that prints all factors of distance in order
If you finish add a method to find the most frequent factor. Feel free to change printFactors to return the factors found.