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### Cryptology

Kylie Brown

Outline

- Introduction
- What is Cryptology
- Confusion and Diffusion
- History
- Methods
- Single Key
- Public Key
- Cryptanalysis Overview
- Ethics

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

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

- 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)

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

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

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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