# Cryptology - PowerPoint PPT Presentation

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Cryptology. Kylie Brown. Outline. Introduction What is Cryptology Confusion and Diffusion History Methods Single Key Public Key Cryptanalysis Overview Ethics. Introduction. What is Cryptology Confusion and Diffusion History. What is Cryptology.

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Cryptology

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## Cryptology

Kylie Brown

### Outline

• Introduction

• What is Cryptology

• Confusion and Diffusion

• History

• Methods

• Single Key

• Public Key

• Cryptanalysis Overview

• Ethics

### 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

• 4th 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 Key

Monoalphabetic Ciphers

Polyalphabetic Ciphers

DES

AES

Public 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

• DOG = GRJ

• Keyword: keyword then fill in alphabet

• COMPUTER SCIENCE = CJGKSQOM PCYOHCO

### Substitution: Playfair

• Polyalphabetic Cipher

• Charles Wheatstone in 19th 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

### Playfair

• Rules for exchanging letters

• If the columns and rows are different

• New letter is the row of the current letter and the column of its pair

• If the rows are the same

• New letter is the one to the right

• If the columns are the same

• New letter is the one below

• 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

### 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 Cipher

• How it works

• Choose a key

• Write the key for the length of the message

• (p+k)mod26

### Substitution: Autokey

• Repetition was Vigenere’s undoing

• How to use autokey

• Write key once

• 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

### Route Ciphers

• A better method:

• Create a matrix with a keyword across the top row.

• Fill the Matrix from left to right with the message

• Take the letters from top to bottom by alphabetic order of the keyword (do not take keyword)

### Example

I LIKE TO PLAY WITH MATRICES

IAAZIPHELLMSTIIZKYTZOTCZEWRZ

• 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

• Message: Computer Science, Key: Dictionary

### 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 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

• 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

### 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/cis3362/lectures/

• Pfleeger, Charles P. Pfleeger, Shari Lawrence. Security in Computing. 4th Edition. Pearson Education. 2007

• Falk, Courtney. The Ethics of Cryptography. http://www.cerias.purdue.edu/bookshelf/archive/2005-37.pdf