Cryptography 3

Classical Encryption Techniques:

As we mentioned earlier , the basic of all encryption techniques are based on 2 techniques

1- Substitution

2- Transposition

and we can also use a combination of both of them.

1- Substitution Encryption techniques :

Substitution is an encryption technique which elements in the plaintext are replaced or mapped with another elements.

There are many types of the substitution techniques such as (Monoalphabetic Cipher and Polyalphabetic Cipher)

A- Monoalphabetic Cipher :

we will drive an example of monoalphabetic cipher called (Caesar cipher)

Caesar Cipher :

Is the simplest and the oldest known encryption techniques which elements in the plaintext are shifted with fixed number for example 3 places

Example :

Plaintext : WELCOME TO CRYPTOGRAPHY

Ciphertext : ZHOFRPH WR FUBSWRJUDSKB

The ciphertext is produced by adding 3 position for every letter.

As we can see here the encryption algorithm for each plaintext P, and shifted by 3 places to produces a ciphertext C.

C= E(3,P) = (P+3)mod26

so, generally The encryption algorithm for Caesar cipher is

C= E(K,P) = (P+K)mod26

The decryption algorithm for Caesar cipher is

P= D(K,C) = (C-K)mod26

note : K takes a value from 1 to 25.

Caesar cipher is too easy to break because it's only uses 25 position keys, so simply try to preform a brute force using the 25 possible keys, and the language would help us in breaking this cipher.

Nowadays in modern encryption we uses a very large keys such as 2048 bits or greater key long

that gives us 2^2048 key space, it's a very wide range of possible of keys.

Caesar cipher and many of substitution ciphers can be broken by using frequency of letters analysis.

Frequency of letters analysis:

It is a method to break a cipher encrypted by a substitution techniques.

it is based on the relative of letters can be determined and compared to a standard frequency distribution for a language (English).

As we can see the previous figure , E is the most letter uses in English words by 12.7% , then T by 9.056%

Or look at the next figure

Example :

LIVITCSWPIYVEWHEVSRIQMXLEYVEOIEWHRXEXIPFEMVEWHKVSTYLXZIXLIKIIXPIJVSZEYPERRGERIM

WQLMGLMXQERIWGPSRIHMXQEREKIETXMJTPRGEVEKEITREWHEXXLEXXMZITWAWSQWXSWEXTVEPMRXRSJ

GSTVRIEYVIEXCVMUIMWERGMIWXMJMGCSMWXSJOMIQXLIVIQIVIXQSVSTWHKPEGARCSXRWIEVSWIIBXV

IZMXFSJXLIKEGAEWHEPSWYSWIWIEVXLISXLIVXLIRGEPIRQIVIIBGIIHMWYPFLEVHEWHYPSRRFQMXLE

PPXLIECCIEVEWGISJKTVWMRLIHYSPHXLIQIMYLXSJXLIMWRIGXQEROIVFVIZEVAEKPIEWHXEAMWYEPP

XLMWYRMWXSGSWRMHIVEXMSWMGSTPHLEVHPFKPEZINTCMXIVJSVLMRSCMWMSWVIRCIGXMWYMX

It's a classic encryption technique , we try to apply the relative frequency analysis.

letter frequencies :

i : 58

e : 48

x : 41

w : 35

m : 34

v : 31

s : 30

r : 27

l : 22

p : 21

g : 16

h : 16

y : 13

t : 12

q : 12

c : 9

k : 9

j : 9

z : 6

f : 6

a : 5

o : 3

b : 2

u : 1

n : 1

d : 0

With this numbers and with some good guessing some words we can solve it.

let's try I=e and L=H ,let's guessing X=t and E=a and we get the following

heVeTCSWPeYVaWHaVSReQMthaYVaOeaWHRtatePFaMVaWHKVSTYhtZetheKeetPeJVSZaYPaRRGaReM

WQhMGhMtQaReWGPSReHMtQaRaKeaTtMJTPRGaVaKaeTRaWHatthattMZeTWAWSQWtSWatTVaPMRtRSJ

GSTVReaYVeatCVMUeMWaRGMeWtMJMGCSMWtSJOMeQtheVeQeVetQSVSTWHKPaGARCStRWeaVSWeeBtV

eZMtFSJtheKaGAaWHaPSWYSWeWeaVtheStheVtheRGaPeRQeVeeBGeeHMWYPFhaVHaWHYPSRRFQMtha

PPtheaCCeaVaWGeSJKTVWMRheHYSPHtheQeMYhtSJtheMWReGtQaROeVFVeZaVAaKPeaWHtaAMWYaPP

we can substitute V=r in "heVe" to be "here" and R=s in "Rtate" to be "state"

M=i , Z=m from "atthattMZe" to be "atthattime"

we apply this change and get

hereTCSWPeYraWHarSseQithaYraOeaWHstatePFairaWHKrSTYhtmetheKeetPeJrSmaYPassGasei

WQhiGhitQaseWGPSseHitQasaKeaTtiJTPsGaraKaeTsaWHatthattimeTWAWSQWtSWatTraPistsSJ

GSTrseaYreatCriUeiWasGieWtiJiGCSiWtSJOieQthereQeretQSrSTWHKPaGAsCStsWearSWeeBtr

emitFSJtheKaGAaWHaPSWYSWeWeartheStherthesGaPesQereeBGeeHiWYPFharHaWHYPSssFQitha

PPtheaCCearaWGeSJKTrWisheHYSPHtheQeiYhtSJtheiWseGtQasOerFremarAaKPeaWHtaAiWYaPP

thiWYsiWtSGSWsiHeratiSWiGSTPHharHPFKPameNTCiterJSrhisSCiWiSWresCeGtiWYit

We go to deduce the substitution until we get a right message

hereuponlegrandarosewithagraveandstatelyairandbroughtmethebeetlefromaglasscasei

nwhichitwasencloseditwasabeautifulscarabaeusandatthattimeunknowntonaturalistsof

courseagreatprizeinascientificpointofviewthereweretworoundblackspotsnearoneextr

emityofthebackandalongoneneartheotherthescaleswereexceedinglyhardandglossywitha

lltheappearanceofburnishedgoldtheweightoftheinsectwasveryremarkableandtakingall

thingsintoconsiderationicouldhardlyblamejupiterforhisopinionrespectingit

After adding spaces

Hereupon Legrand arose, with a grave and stately air, and brought me the beetle

from a glass case in which it was enclosed. It was a beautiful scarabaeus, and, at

that time, unknown to naturalists—of course a great prize in a scientific point

of view. There were two round black spots near one extremity of the back, and a

long one near the other. The scales were exceedingly hard and glossy, with all the

appearance of burnished gold. The weight of the insect was very remarkable, and,

taking all things into consideration, I could hardly blame Jupiter for his opinion

respecting it.

Note : Frequency of letters analysis works better as long as the cipher text is large.