CryptologyKylie 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

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

D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

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

D I C T O N A R Y B E F G H J K L M P Q S U V W X Z

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 letters1. 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

CO MP UT ER SC IE NC EX TD PQ XD GN PO DF RD HU What is this? ODMCQZ

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

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

1. Choose a key2. Write the key for the length of the

message3. (p+k)mod26C 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 10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

Substitution: Autokey

Repetition was Vigenere’s undoing How to use autokey

1. Write key once2. 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 2C M U E S I N E

O P T R C E C

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

message3. Take the letters from top to bottom by

alphabetic order of the keyword (do not take keyword)

Example

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 Z Z

IAAZIPHELLMSTIIZKYTZOTCZEWRZ

I LIKE TO PLAY WITH MATRICES

Product Cipher: ADFGVX

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

ADFGVX Example

Message: Computer Science, Key: Dictionary

AFAVFXGAGGAGDVGFAFADAVAXAFDV

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

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

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/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