# "Cryptography"

Essay by BrentMWHigh School, 10th gradeA, May 2004

INTRODUCTION

CRYPTOGRAPHY the science of the enciphering and deciphering of messages in secret code or cipher

cryptography is used everywhere it protects money transfers and credit card numbers used over the internet

but its main purpose is to keep secret documents secure from foreign governments

TERMINOLOGY

CRYPTOGRAPHY the science of the enciphering and deciphering of messages in secret code or cipher.

PLAINTEXT the original message before encryption or after decryption

CIPHERTEXT The encrypted form of the PLAINTEXT

ENCRYPTION The process of converting the PLAINTEXT into a CIPHER.

DECRYPTION The process of converting the CIPHER back into PLAINTEXT.

CRYPTANALYSIS The science of recovering information from ciphers without knowledge of the key.

CRYPTOSYSTEM a system for encrypting information.

KEY The secret information known only to the transmitter and the receiver which is used to encrypt and decrypt the message

HISTORY

cryptology has been used to conceal information in writing since writing was first developed, Egyptians are the first knowN to used CRYPTOGRAPHY.

Early Greeks also used cryptology, they wrapped a piece of cloth around a baton called a scytale and wrote the message on it. When it was unwrapped it looked like decorations and was worn as a robe by a servant and delivered to the receiver. When it was wrapped again around a scytale the message was easily read.

Another Greek Polybius invented the Polybius checkerboard which was a 5 x 5 grid containing all the letters of the alphabet, each letter was converted into two numbers such as A becomes 11

-

1

2

3

4

5

1

A

B

C

D

E

2

F

G

H

I/J

K

3

L

M

N

O

P

4

Q

R

S

T

U

5

V

W

X

Y

Z

ex. CAR is 131142

later the the 19th C. cryptodevices were invented

they used mechanical rotors to scramble messages

most famous were the German Enigma and Japanese PURPLE used in WWII

todays ciphers are far more advanced than any before due to the aid of computers, which can compute extremely large numbers and use cryptosystems that are impossible with pencil and paper

SUBSTITUTION CIPHER

one of the more basic cipher is the substitution cipher

a unit of plaintext (usually letters or numbers) is replaced with other symbols or groups of symbols, the order is not changed ex. B becomes C, C - D and so on

one of the most well know is the Caesar cipher which A becomes D and so on

these are easily broken by studying the letter frequency

the Playfair cipher

on a 5 x 5 matrix similar to the Polybius checkerboard

a keyword is placed first then the remaining letters of the alphabet after it

there are many rules to substituting different letters from the plaintext into a ciphertext

VigenÃÂ¨re cipher

in its simpliest form a phrase or word is reapeated over and over and is the key.

the ciphertext letter is found at the intersection of the column of the plaintext letter and the row of the repeating key.

to decrypt the plaintext letter is found at the head of the column determined by the intersection of the diagonal containing the cipher letter and the row containing the key

Plaintext SAINT JOHN NEW BRUNSWICK

Key HALIF AXHA LIF HALIFAXHA

Ciphertext ZATVY JLON YMB IRFVXWFIK

TRANSPOSITION CIPHER

very simple route cipher is the rail fence which just staggers the letters between two rows

Plaintext SAINT JOHN NEW BRUNSWICK

Cytosystem S I T O N E B U S I K

A N J H N W R N W C

Ciphertext SITONEBUSIKANJHNWRNWC

ciphertext is gotten by writing the letters down from each column following the order in which each letters in the key appear in the alphabet

this plaintext now becomes INUKJWWZTESZNNNZSOBIAHRC

PRODUCT CIPHER

letters of the plaintext are made into several letters on the ciphertext

one of the more well known Product Cipher was the ADFGVX Cipher used by the German Army during WWI

it is a fractional cipher

it used a 6 x 6 matrix to substitution-encrypt the 26 letters of the alphabet and 10 digits into pairs of the symbols A, D, F, G, V and X.

a keyword is chosen and then the rest of the matrix is filled in with the alphabet and 10 digits

Ex. The keyword is "subject"

Plaintext S E N D H E L P

Ciphertext AA AV FV DF DX AV FF GA

this ciphertext is then run through a transposition cipher

O

R

A

N

G

E

5

6

1

4

3

2

A

A

A

V

F

V

D

F

D

X

A

V

F

F

G

A

Z

Z

BLOCK CIPHERS

are what are used for modern encryption

translates blocks of plaintext (usually only 64 bit ) into ciphertext using a key and reversed when receiving the message

block size is becoming 128 bit due to faster processors

the iterated block cipher encrypts the same way only uses more stages

the more times this step is done the more secure the cipher is but it takes much longer to decipher

- DES

DES or Data Encryption Standard was up until a few years ago used to encrypt government documents

DES is symmetrical so both sender and receiver need the key

uses a 56 bit key to encode the data and is a friestal cipher which is very similar to a iterated cipher

the key is generated at random for each message from 72 quadrillion possibilities

a bit is a single unit of binary code either a 0 or a 1

there are over 72 quadrillion 56 bit combinations so chances of breaking it are remote

to break DES it would take 2^55 steps on average

DES was broken in 1997 by 16,000 computers running all the possible key until finally it was found after 18 quadrillion possibilities

Triple DES is now used which is DES done three times more until AES is completed

KEY DISTRIBUTION PROBLEM

there is a problem with these single key ciphers in that each member need a key to communicate with the next member

the equation is [n(n-1)]/2 so with 1000 members [1000(1000-1)]/2 = 499500

so this system becomes very impractical quickly

SOLUTION

the solution is a two key system or public key

with this the public key is used to encrypt and private to decrypt

now for a 1000 members there only needs to be 2000 keys 1000 public and 1000 private

up until 1976 a one key or symmetric system was used, the two key or asymmetric system is a relatively new invention as one key has been used for thousands of years

CRYTPANALYSIS

is the process of breaking a enciphered text

cryptanalysis is vital in wars most notably in WWII where the breaking of the Enigma and PURPLE ciphers was crutial in the winning of the war

the cryptanalysis of Enigma and PURPLE are one of the most celebrated triumphs of cryptanalysis

cIPHERTEXT ONLY ATTACKS

BRUTE FORCE ATTACK

an attack requires a lot of computing power and time to run

is basically just trying all the possibilities in a somewhat organized manner until the right one is found

this is a very impractical due to the large number of possibilities, such as DES which has 72 quadrillion

DICTIONARY ATTACK

this is a type of Brute Force Attack

essentially is running through all the words in a dictionary in hopes that the key is one of them

often uses for finding password because people often use easy to remember words as their passwords

PLAINTEXT ONLY ATTACK

PLAINTEXT ONLY ATTACKS ARE WHERE THE PLAINTEXT IS KNOWN AND IT CIPHERED VERSION AND YOU TRY TO FIND THE KEY

FREQUENCY TABLES

with single key cryptography usually some part of the original plaintext structure remains

for example with monoalphabetic substitution where plaintext letters are always replaced by different but always the same letters in the ciphertext ex. E will always be W in the ciphertext and so on

with a paragraph of jarbled letters there is a letter frequency which is how many times letters occur in that paragraph

in the normal English language there is a letter frequency, E occurs the most and has a frequency of .127 and T the next with .097

knowing this the letter frequencys can be overlapped for instance in this paragraph if W occurs the most then its most likely E and if F is the next then it is T