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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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Presentation Transcript


Kylie Brown


  • Introduction

    • What is Cryptology

    • Confusion and Diffusion

    • History

  • Methods

    • Single Key

    • Public Key

  • Cryptanalysis Overview

  • Ethics


What is Cryptology

Confusion and Diffusion


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.


  • 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


  • 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


Single Key

Monoalphabetic Ciphers

Polyalphabetic Ciphers



Public Key

Key Distribution


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


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


  • 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



  • 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)




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


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


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


  • Pell, Oliver. Cryptology.

  • Arup Guha’s class lectures

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

  • Falk, Courtney. The Ethics of Cryptography.

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