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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

Cryptology

Kylie Brown

outline
Outline
  • Introduction
    • What is Cryptology
    • Confusion and Diffusion
    • History
  • Methods
    • Single Key
    • Public Key
  • Cryptanalysis Overview
  • Ethics
introduction
Introduction

What is Cryptology

Confusion and Diffusion

History

what is cryptology
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 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
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
history1
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
Methods

Single Key

Monoalphabetic Ciphers

Polyalphabetic Ciphers

DES

AES

Public Key

Key Distribution

RSA

single key
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
Substitution: Monoalphabetic Cipher
  • Caesar Cipher: Shift the alphabet
    • DOG = GRJ
  • Keyword: keyword then fill in alphabet
    • COMPUTER SCIENCE = CJGKSQOM PCYOHCO
substitution playfair
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
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
slide13

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
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
Substitution: Vigenere
  • Polyalphabetic Cipher
  • How it works
    • Choose a key
    • Write the key for the length of the message
    • (p+k)mod26
substitution autokey
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
Transposition: Route Ciphers
  • Rail Fence: stagger plaintext between X rows
  • Ex: Computer Science with rail fence 2
route ciphers
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
Example

I LIKE TO PLAY WITH MATRICES

IAAZIPHELLMSTIIZKYTZOTCZEWRZ

product cipher adfgvx
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
ADFGVX Example
  • Message: Computer Science, Key: Dictionary
  • AFAVFXGAGGAGDVGFAFADAVAXAFDV
stream vs block cipher
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
Data Encryption Standard
  • Developed by IBM, based on an encryption algorithm called Lucifer
  • Proper name: Data Encryption Algorithm
des 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
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
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
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
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
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
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
RSA Encryption and Decryption
  • Encryption: C = En,e(M) = Me mod n
  • Decryption: M = Dn,d (C) = Cd mod n
cryptanalysis overview
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
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
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
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