Cryptography

1. Zac Blohm & Kenny Holtz Cryptography

2. Importance of Algorithms Algorithms are the basis for cryptography • The basic idea of Cryptography in Computer Science is to run a message through an algorithm to receive an encrypted text which can safely be sent to be decrypted with another algorithm

3. Classical Cryptography • Monoalphabetic • Caesar Cypher • Polyalphabetic • Transpositional • Compositional

4. Monoalphabetic Cyphers • Simple substitutions • One of the earliest used forms of cryptography • Easily cracked by statistical analysis (ex. how many times each character occurs) and trial and error • Most famous example is the Caesar Cypher which simply replaces each character with one “K” places further in the alphabet

5. Example of a Caesar Cypher • If K=3, then A becomes C, B becomes D etc… • Therefore the plaintext “This is a message” • Is encrypted to say “Vjkuku c oguucig” • Notice that the number of characters and any patterns between them are shared (repeated characters, the standalone vowel etc…)

6. Polyalphabetic Cyphers • Multiple alphabets to disguise patterns • Biggest difference between them is how many alphabets and what determines a change of alphabet

7. Example key for a polyalphabetic cypher

8. Plaintext vs cyphertext for previous key Plaintext cyphertext Pjtobtoblwopoulcg The key changed alphabets after each character (spaces were incorporated into each alphabet to conceal word length) • This is a message

9. Failings of polyalphabetic cyphers • Still direct substitutions • The change of alphabets can be recognized, which then reduces the problem to a series of monoalphabetic problems

10. Transpositional Cyphers • Changes the arrangement of the plaintext to disguise the message • Immune to the frequency analysis that defeats substitution cyphers • Pure transpositional cyphers produce same amount of each letter as present in plaintext • A common example involves reading into a matrix one way, and reading out the other

11. Transpositional example

12. Transpositional plaintext vs cyphertext plaintext cyphertext Ti satsesghsietmsae # of t’s: 3 # of h’s: 1 # of i’s: 2 # of s’s: 5 # of spaces: 4 # of a’s: 2 # of e’s: 3 # of m’s: 1 # of g’s: 1 • This is a test message • # of t’s: 3 • # of h’s: 1 • # of i’s: 2 • # of s’s: 5 • # of spaces: 4 • # of a’s: 2 • # of e’s: 3 • # of m’s: 1 • # of g’s: 1

13. Failings of transpositional cyphers • The matrix example never changes the letter in the first position or the last, and requires the key to contain the size of the matrix needed for decryption • Creates an anagram (meaning some messages are easily decrypted just by rearranging the letters to make the most probable words, longer messages make this harder)

14. Compositions of substitution and transposition • Combining both makes a much stronger cypher as you can eliminate most of the apparent patterns in your cyphertext • An example would be taking “this is a test message” through the previously used polyalphabetic cypher to get “pjtobtoblwvpovkigcocra” and then reading it through a 2x11 matrix as before

15. Compositional transposition

16. Compositional plaintext vs cyphertext plaintext cyphertext “ptbolvokgorjotbwpvicca” No direct correlation between the position or frequency of each character • “This is a test message”

17. Questions?