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Introduction › What is Cryptology › Confusion and Diffusion › History Methods › Single Key › Public Key Cryptanalysis Overview Ethics

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What is Cryptology Confusion and Diffusion History

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The use and study of methods of hiding information Plaintext: The message (not encrypted) Cipher text: The encrypted message Encryption: The process of converting the plaintext into cipher text Code: Rule for replacing a piece of the plaintext with something else Key: Known only b the transmitter and receiver, used to encrypt/decrypt the message Cryptanalysis: The science of code breaking

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Confusion: The interceptor should not be able to predict the effect of changing one symbol of plaintext will affect cipher text. Diffusion: Information from plaintext should be spread throughout the cipher text so that changes to the plaintext will cause changes throughout the cipher text.

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Spartans in Ancient Greece › First documented use of cryptography › Used a tapered baton called a scytale › The message could only be read when the parchment upon which the message was written was wrapped around the scytale 4 th Century BC: first treatise › Written by Aeneas Tacticus › In the book: On the Defense of Fortifications

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WWI › Most famous cipher was the German ADFGVX fractional cipher WWII › Rotor Cipher Machines › Most famous Cipher Machine: Germany’s Enigma Cracked by the British using the Turing Bomb

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Single Key Monoalphabetic Ciphers Polyalphabetic Ciphers DES AES Public Key Key Distribution RSA

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Key for encrypting and decrypting are the same Monoalphabetic Cipher: Each letter in the plaintext will always be replaced by the same letter/symbol › Ex: Caesar Cipher Polyalphabetic Cipher: Each letter in the plaintext may not always be replaced by the same letter/symbol › Ex: Playfair Cipher

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Caesar Cipher: Shift the alphabet › DOG = GRJ Keyword: keyword then fill in alphabet › COMPUTER SCIENCE = CJGKSQOM PCYOHCO ABCDEFGHIJKLMNOPQRSTUVWXYZ DEFGHIJKLMNOPQRSTUVWXYZABC ABCDEFGHIJKLMNOPQRSTUVWXYZ DICTONARYBEFGHJKLMPQSUVWXZ

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Polyalphabetic Cipher Charles Wheatstone in 19 th Century England 5X5 grid, fill in the key at the beginning and then add the rest of the alphabet (in order) › I/J are in the same box Pair the letters of the message into digrams. › If there is an odd number, add X to the end › If there a digraph is made up of identical letter, separate them with a different letter

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Rules for exchanging letters 1. If the columns and rows are different New letter is the row of the current letter and the column of its pair 2. If the rows are the same New letter is the one to the right 3. If the columns are the same New letter is the one below

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Key: Dictionary Message: Computer Science CO MP UT ER SC IE NC EX TD PQ XD GN PO DF RD HU What is this? ODMCQZ DI/JCTO NARYB EFGHK LMPQS UVWXZ

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Monoalphabetic ciphers are easy to break (think cryptoquip) › Find most commonly used letters (E, T, A, O, N, I, R, S, H) › Find most commonly used digrams and trigrams (ex: the, st) › Then the most common trigrams, etc. › Spacing makes it even easier (so don’t carry over spaces)

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Polyalphabetic Cipher How it works 1. Choose a key 2. Write the key for the length of the message 3. (p+k)mod26 COMPUTERSCIENCE DICTIONARYDICTI GXPJDISSKBMNWWN ABCDEFGHIJKLMNOPQRSTUVWXYZ

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Repetition was Vigenere’s undoing How to use autokey 1. Write key once 2. Fill in the rest with either the plaintext or cipher text

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Rail Fence: stagger plaintext between X rows Ex: Computer Science with rail fence 2 CMUESINE OPTRCEC

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A better method: 1. Create a matrix with a keyword across the top row. 2. Fill the Matrix from left to right with the message 3. Take the letters from top to bottom by alphabetic order of the keyword (do not take keyword)

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ENCRYPT ILIKETO PLAYWIT HMATRIC ESZZZZZ IAAZIPHELLMSTIIZKYTZOTCZEWRZ I LIKE TO PLAY WITH MATRICES

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Uses a 6X6 matrix and a key to encrypt the message into the letters A,D,F,G,V, and X Fill the matrix in with the keyword and then the rest of the alphabet in order, followed by the numbers 0-9 (no doubles) Replace each cipher text letter with the two letters that mark its row and column

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Message: Computer Science, Key: Dictionary AFAVFXGAGGAGDVGFAFADAVAXAFDV ADFGVX A DICTON D ARYBEF F GHJKLM G PQSUVW V XZ0123 X

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A stream cipher translates plaintext into cipher text symbol by symbol › Most of the methods discussed thus far are stream ciphers › Errors like skipping a symbol will corrupt the rest of the message A block cipher encrypts plaintext by blocks › Reduces corruption and risk of code breaking

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Developed by IBM, based on an encryption algorithm called Lucifer Proper name: Data Encryption Algorithm

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Cycles are repeated 16 times Split the plaintext into 64bit blocks Key is any 56-bit number with an extra 8 bits on the end Some people are uncomfortable with only a 56-bit key › Double DES: run twice with 2 different keys › Triple DES: 3 keys. Encrypt, Decrypt, Encrypt

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January 1997-August 1999, Encryption “Contest” Winner: Rijndael (RINE dahl) Combination of the names of the creators: Vincent Rijmen and Joan Daemen

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Plaintext split into 128-bit blocks Number of “rounds” based on key size › 10 for 128-bits, 12 for 192-bits, 14 for 256-bits Four Steps per cycle › Byte Substitution: Using a substitution box, substitute each bit according to a table › Shift Row: for 128 and 192: (n-1)bit left, for 256: row 2 by 1 bit, row 3 by 3 bits, row 4 by 4 bits › Mix Column: XOR bits together › Add Subkey: portion of subkey XOR with result

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Sender and Receiver must both hold a copy of the key › What happens if there are 100 people who want to communicate secretly › Each person has to remember 99 keys and must keep each key from being discovered › Number of keys required: 4950

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Also called two-key Each person has two keys › Public key for encrypting › Private key for decrypting › Keep your private key and give everyone else your public key

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Euler Totient: (n) › The number of integers in the set of real numbers less than n that are relatively prime to n › For a prime number, p, (p) = p-1 › For distinct primes p & q, (pq) = (p-1)(q-1) Examples › (8) = 4 {1,3,5,7} › (91) = (13)* (7) = 6*12 = 72

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Pick two large prime numbers (p & q) Calculate (n) where n= pq Find e such that e is relatively prime to (n) › gcd(e, (n)) = 1 Find d such that ed ≡ 1 mod (n) › d is the inverse of e mod (n) Public keys: e, n Private Key: d

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Encryption: C = E n,e (M) = M e mod n Decryption: M = D n,d (C) = C d mod n

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Method used is based on the amount of information Brute Force: try all possibilities Dictionary Attack: run through a dictionary of words trying to find the key or plaintext Cipher text only Chosen Plaintext: Have the ability to find the cipher text relating to an arbitrary plaintext Chosen Cipher text: can choose an arbitrary cipher text and know the plaintext Adaptive chosen plaintext: determine cipher text based on plaintext using iteration

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Is cryptology ethical? › “Technology has no intrinsic ethical nature” Wiretapping: Should encryption of digital communication be stymied in order to accommodate this practice? Proper usage of cryptology is all about individual responsibility Cryptology should not be withheld

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Pell, Oliver. Cryptology. Arup Guha’s class lectures 62/lectures/ 62/lectures/ Pfleeger, Charles P. Pfleeger, Shari Lawrence. Security in Computing. 4 th Edition. Pearson Education Falk, Courtney. The Ethics of Cryptography. chive/ pdf

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