Cryptology Kylie Brown Outline Introduction What is Cryptology

Cryptology Kylie Brown

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

Introduction • What is Cryptology • Confusion and Diffusion • History

What is Cryptology � � � � 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

Confusion and Diffusion � 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.

History � 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

History � 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

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

Single Key � 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

Substitution: Monoalphabetic Cipher � Caesar Cipher: Shift the alphabet A B C D E F G H I J K L M N O P Q R S T U V WX Y Z A B C › DOG = GRJ � Keyword: keyword then fill in alphabet A B C D E F G H I D I J K L M N O P Q R S T U V WX Y Z C T O N A R Y B E F G H J K L M P Q S U V WX Z › COMPUTER SCIENCE = CJGKSQOM PCYOHCO

Substitution: Playfair Polyalphabetic Cipher � Charles Wheatstone in 19 th Century England � 5 X 5 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

Playfair � 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

� Key: Dictionary � Message: Computer Science D I/J C T O N A R Y B E F G H K L M P Q S U V W X Z � CO MP UT ER SC IE NC EX � TD PQ XD GN PO DF RD HU � What is this? ODMCQZ

Problems with Monoalphabetic � 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)

Substitution: Vigenere � Polyalphabetic � How Cipher it works 1. Choose a key 2. Write the key for the length of the message 3. (p+k)mod 26 C O M P U T E R S C I E N C E D I C T I O N A R Y D I C T I G X P J D I S S K B M N W W N A B C D E F G H I J K L M N O P Q R S T U V WX Y Z 1 2 3 4 5 6 7 8 9 1 1 1 1 1 2 2 2 2 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6

Substitution: Autokey � 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

Transposition: Route Ciphers � Rail Fence: stagger plaintext between X rows � Ex: Computer Science with rail fence 2 C M U E S I N O P T R C E

Route Ciphers �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)

Example I LIKE TO PLAY WITH MATRICES E N C R Y P T 2 3 1 5 7 4 6 I L I K E T O P L A Y W I T H M A T R I C E S Z Z Z IAAZIPHELLMSTIIZKYTZOTCZEWRZ

Product Cipher: ADFGVX � Uses a 6 X 6 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

ADFGVX Example � Message: Computer Science, Key: Dictionary A D F G V X A D I C T O N D A R Y B E F F G H J K L M G P Q S U V W V X Z 0 1 2 3 X 4 5 6 7 8 9 � AFAVFXGAGGAGDVGFAFADAVAXAFDV

Stream vs. Block Cipher �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

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

DES Algorithm � Cycles are repeated 16 times � Split the plaintext into 64 bit 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

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

Overview of Rijndael 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

Rijndael

Problems with Single Key � 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

Solution: Public Key � 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

Background for RSA � 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

RSA Algorithm � 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

RSA Encryption and Decryption � Encryption: C = En, e(M) = Me mod n � Decryption: M = Dn, d (C) = Cd mod n

Cryptanalysis Overview � � � � 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

Ethics and Cryptology � 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

References Pell, Oliver. Cryptology. http: //www. ridex. co. uk/cryptology/ � Arup Guha’s class lectures http: //www. cs. ucf. edu/~dmarino/ucf/cis 3362/lect ures/ � Pfleeger, Charles P. Pfleeger, Shari Lawrence. Security in Computing. 4 th Edition. Pearson Education. 2007 � Falk, Courtney. The Ethics of Cryptography. http: //www. cerias. purdue. edu/bookshelf/archive/ 2005 -37. pdf �