Overview of Cryptographic Techniques, Lecture notes of Cryptography and System Security

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Overview of Cryptographic

Techniques

Some Basic Terminology

• plaintext - original message

• ciphertext - coded message

• cipher - algorithm for transforming plaintext to ciphertext

• key - info used in cipher known only to sender/receiver

• encipher (encrypt) - converting plaintext to ciphertext

• decipher (decrypt) - recovering ciphertext from plaintext

• cryptography - study of encryption principles/methods

• cryptanalysis (codebreaking) - study of principles/

methods of deciphering ciphertext without knowing key

• cryptology - field of both cryptography and cryptanalysis

Characteristics of Cryptographic Characteristics of Cryptographic

Techniques Techniques

• (^) Classified along three independent dimensions:
  • (^) The type of operations used for transforming plaintext

to ciphertext

• (^) The number of keys used
  • (^) symmetric (single key)
  • (^) asymmetric (two-keys, or public-key encryption)
• (^) The way in which the plaintext is processed

Symmetric Encryption

• or conventional / private-key / single-key

• sender and recipient share a common key

• all classical encryption algorithms are

private-key

Requirements

• two requirements for secure use of

symmetric encryption:

– a strong encryption algorithm

– a secret key known only to sender / receiver

• mathematically have:

Y = E K ( X ) [= E(K, X ) ]

X = D K ( Y ) [= D(K, Y ) ]

• assume encryption algorithm is known

• implies a secure channel to distribute key

Brute Force Search

• always possible to simply try every key

• most basic attack, proportional to key size

• assume either know / recognize plaintext

Key Size (bits) Number of Alternative Keys Time required at 1 decryption/ μ s Time required at 10^6 decryptions/ μ s 32 232 = 4.3  109 231 μs = 35.8 minutes 2.15 milliseconds 56 256 = 7.2  1016 255 μs = 1142 years 10.01 hours 128 2128 = 3.4  1038 2127 μs = 5.4  1024 years 5.4  1018 years 168 2168 = 3.7  1050 2167 μs = 5.9  1036 years 5.9  1030 years 26 characters (permutation) 26! = 4  1026 2  1026 μs = 6.4  1012 years 6.4  106 years

Caesar Cipher

• earliest known substitution cipher

• by Julius Caesar

• first attested use in military affairs

• replaces each letter by 3rd letter after

• example:

meet me after the toga party

PHHW PH DIWHU WKH WRJD SDUWB

Caesar Cipher

• can define transformation as:

a b c d e f g h i j k l m n o p q r s t u v w x 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

• mathematically give each letter a number

a b c d e f g h i j k l m n o p q r s t u v w x y z 0 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

• then have Caesar cipher as:

c = E( p ) = ( p + k ) mod (26)

p = D(c) = (c – k ) mod (26)

Playfair Cipher

• not even the large number of keys in a

monoalphabetic cipher provides security

• one approach to improving security was to

encrypt multiple letters

• the Playfair Cipher is an example

• invented by Charles Wheatstone in 1854,

but named after his friend Baron Playfair

Playfair Key Matrix

• a 5X5 matrix of letters based on a keyword

• fill in letters of keyword (minus duplicates)

• fill rest of matrix with other letters

• eg. using the keyword MONARCHY

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

Polyalphabetic Ciphers

• polyalphabetic substitution ciphers

• A set of related monoalphabetic substitution rules is used

• use a key to select which alphabet is used for each letter

of the message

• use each alphabet in turn

• repeat from start after end of key is reached

• make cryptanalysis harder with more alphabets to guess

and flatter frequency distribution

Key: deceptive 3 4 2 4 15 19 8 21 4

plaintext: wireless 22 8 17 4 11 4 18 18

ciphertext: zmtiaxao 25 12 19 8 26 23 26 39

Vigenère Cipher

• simplest polyalphabetic substitution cipher

• effectively multiple caesar ciphers

• key is multiple letters long K = k

1 k 2 ... kd

• ith^ letter specifies ith^ alphabet to use

• use each alphabet in turn

• repeat from start after d letters in message

• decryption simply works in reverse

Vernam Cipher and One-time

Pad

• Keyword is as long as the plaintext and

has no statistical relationship to it.

• Vernam system works on binary data with

ith bit of text exclusive ored with ith bit of

key to produce ith bit of cipher

• In one one-time pad key is used only once

• This scheme is unbreakable

Transposition Cipher

• Mapping is performed by some sort of

permutation on the plaintext letters.

• Example: Rail fence of depth 2

text : meet me after the toga party

m e m a t r h t g p r y

e t e f e t e o a a t

cipher: MEMATRHTGPRYETEFETEOAAT

Rail fence of depth 2