1. THE SCIENCE, MATHEMATICS, AND ART OF PRIVACY BASIC STUFF 1 CRYPTOGRAPHY

2. THE BIG QUESTION Who is the world’s largest employer of mathematicians (and a significant number of computer scientists) Click for the Answer Need More Encouragement?

3. THE CENTRAL PROBLEM Secure communication over an insecure medium Alternatively: “Cryptography is about communication in the presence of an adversary” (Goldwasser & Bellaire) Two aspects: Designing and building cryptosystems—the emphasis in CPSC 453 Breaking cryptosystems

4. SOME CRYPTO BASICS Key cryptograpic problem Terms Three simple ciphers Kerchoff’s Principle Four classic ttacks Five cryptographic problems and protocols

5. KEY CRYPTOGRAPHIC PROBLEM Sending a private message over a public network Alice Wants To Send Message Bob Wants to Receive Message Eve Wants to Listen To The Message

6. CRYPTOGRAPHIC SOLUTION msg Encrypted msg Encrypted msg Decrypted msg Eve listens (but can’t understand)

7. BASIC TERMS Plaintext or P: the message to be hidden Ciphertext or C: the hidden message Encrypt: the process of turning plaintext into ciphertext Decrypt: the process of turning ciphertext back into plain text Cryptosystem: the combined system for encryption and decryption Cipher: sometimes used interchangeably with cryptosystem Key: a piece of information used in the encryption/decryption process

8. TWO MAJOR CLASSES OF CRYPTOSYSTEMS Symmetric Key Systems: Same key is used for encryption and decryption Public Key Systems: Encryption key is public, Decryption key is private

9. TRANSPOSITION CIPHERS Rearrange the letters of the message, generating an anagram Scytale: Oldest known military cipher Rail Fence: Generalization of Scytale

10. SCYTALE: SPARTA 5 TH CENTURY BCE Ingredients: Two blocks of wood Carve n flat surfaces of the same size Encrypt: 1. Wind a strip of leather around the scytale 2. Write out the message horizontally 3. Unwind the strip 4. Send it on its way Decrypt: 1. Wind the strip of leather around a scytale of same size as the one that 2. Read the message horizontally

11. RAIL FENCE Sonnet 29: Like to the lark at break of day arising 1.Drop every other letter down a row (rail) L K T T E A K T R A O D Y I E O H L R A B E K F A 2.Append the bottom row to the top LKTTEAKTRAODYIEOHLRABEKFA 3. C an be extended to n rails: 1 st letter on 1 st rail, 2 nd letter on second rail, etc. 4. Problem: Key space (number of rails) is small.

12. SUETONIUS (C. 69 -- AFTER 122 CE) BIOGRAPHERS OF THE CAESARS “If he [Julius Caesar] had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others.”

13. SHIFT (OR SUBSTITUTION) CIPHERS Each alphabetic character is substituted for another in a regular fashion The Caesar cipher is a shift/substitution cipher

14. FORMALIZING AND GENERALIZING THE CAESAR CIPHER To encrypt a character: 1.Determine its position in the range [0..25] 2.Add a shift to that value (Caesar added 3) 3.Mod the result by 26 enc(ch) = (pos(ch) + shift) % 26 To decrypt a character: Determine its position in the range [0..25] Subtract a shift amount in the range [0..25] Add 26 Mod the result by 26 dec(ch) = ((pos(ch) – shift) + 26) % 26

15. KERCHOFF’S PRINCIPLE: THE KEY IS THE KEY Scytale: key is the number (and size) of the surfaces carved into the cylinder Rail Fence: Key is the number of rails Shift Cipher: key is the number of positions shifted Kerchoff’s Principle: Assume that every aspect of the cryptosystem is known except the key